Tag: Eureka Math Grade 5 Module 3

Engage NY Eureka Math 5th Grade Module 3 Lesson 8 Answer Key

Eureka Math Grade 5 Module 3 Lesson 8 Problem Set Answer Key

Question 1.
Add or subtract.
a. 2 + 1\(\frac{1}{5}\) =
b. 2 – 1\(\frac{3}{8}\) =
c. 5\(\frac{2}{5}\) + 2\(\frac{3}{5}\)=
d. 4 – 2\(\frac{2}{7}\) =
e. 9\(\frac{3}{4}\) + 8 =
f. 17 – 15\(\frac{2}{3}\) =
g. 15 + 17 \(\frac{2}{3}\) =
h. 100 – 20\(\frac{7}{8}\) =
Answer:
a.
2 + 1\(\frac{1}{5}\) = 2 + \(\frac{6}{5}\)
lcm of 5 and 1 is 5
\(\frac{10}{5}\)  + \(\frac{6}{5}\)
\(\frac{16}{5}\)
3\(\frac{1}{5}\)

b.
2 – 1\(\frac{3}{8}\)
2 – \(\frac{11}{8}\)
lcm is 8
2 – \(\frac{11}{8}\)
\(\frac{16}{8}\) – \(\frac{11}{8}\)
\(\frac{5}{8}\)

c.
5\(\frac{2}{5}\) + 2\(\frac{3}{5}\)
\(\frac{27}{5}\) + \(\frac{13}{5}\)
\(\frac{40}{5}\) = 8

d.
4 – 2\(\frac{2}{7}\) = 4 – \(\frac{16}{7}\)
lcm of 1 and 7 is 7
\(\frac{28}{7}\) – \(\frac{16}{7}\) =\(\frac{12}{7}\)
e.
9\(\frac{3}{4}\) + 8 = \(\frac{39}{4}\) + 8
lcm of 1 and 4 is 4 .
\(\frac{39}{4}\) + \(\frac{32}{4}\)  = \(\frac{71}{4}\) =17 \(\frac{2}{4}\)
f.
17 – 15\(\frac{2}{3}\) = 17 – \(\frac{47}{3}\)
lcm is 3
\(\frac{51}{3}\) – \(\frac{47}{3}\) = \(\frac{4}{3}\)
g.
15 + 17 \(\frac{2}{3}\) = 15 + \(\frac{53}{3}\)
lcm is 3
\(\frac{45}{3}\) + \(\frac{53}{3}\) = \(\frac{98}{3}\) = 32\(\frac{1}{3}\)
h.
100 – 20\(\frac{7}{8}\) = 100 – \(\frac{167}{8}\)
lcm is 8
\(\frac{800}{8}\) – \(\frac{167}{8}\) = \(\frac{733}{8}\) = 91\(\frac{5}{8}\)

Question 2.
Calvin had 30 minutes in time-out. For the first 23\(\frac{1}{3}\) minutes, Calvin counted spots on the ceiling. For the rest of the time, he made faces at his stuffed tiger. How long did Calvin spend making faces at his tiger?
Answer:
Number of Minutes of Time-out =30 minutes .
Fraction of Minutes did calvin counted spots on ceiling = 23\(\frac{1}{3}\) minutes
Fraction of Minutes did calvin did faces at his stuffed tiger = x
30 minutes = 23\(\frac{1}{3}\) + x
lcm is 3
30 minutes = \(\frac{70}{3}\) + x
\(\frac{90}{3}\) = \(\frac{70}{3}\) + x
x = \(\frac{90}{3}\) – \(\frac{70}{3}\)
x = \(\frac{20}{3}\)
Therefore, Fraction of Minutes did calvin did faces at his stuffed tiger = x = \(\frac{20}{3}\) .

Question 3.
Linda planned to spend 9 hours practicing piano this week. By Tuesday, she had spent 2\(\frac{1}{2}\) hours practicing. How much longer does she need to practice to reach her goal?
Answer:
Number of Hours required to practice = 9 hours .
Fraction of hours practiced till Tuesday = 2\(\frac{1}{2}\) hours.
Fraction of hours needed to practice to reach goal = x
9 hours = 2\(\frac{1}{2}\)  + x
lcm is 2
9 = \(\frac{5}{2}\) + x
\(\frac{18}{2}\) = \(\frac{5}{2}\) + x
x = \(\frac{18}{2}\) – \(\frac{5}{2}\)
x = \(\frac{13}{2}\) .
Therefore Fraction of hours needed to practice to reach goal =x = \(\frac{13}{2}\) .

Question 4.
Gary says that 3-1\(\frac{1}{3}\) will be more than 2, since 3 – 1 is 2. Draw a picture to prove that Gary is wrong.
Answer:
Gray is wrong
Explanation :
3-1\(\frac{1}{3}\) = 3 – \(\frac{4}{3}\)
lcm is 3
\(\frac{9}{3}\) – \(\frac{4}{3}\)  = \(\frac{5}{3}\)

Eureka Math Grade 5 Module 3 Lesson 8 Exit Ticket Answer Key

Add or subtract.
a. 5 + 1\(\frac{7}{8}\) =
b. 3 – 1\(\frac{3}{4}\) =
c. 7\(\frac{3}{8}\) + 4=
d. 4 – 2\(\frac{3}{7}\) =
Answer:
a.
5 + 1\(\frac{7}{8}\) = 5 + \(\frac{15}{8}\)
lcm of 1 and 8 is 8
\(\frac{40}{8}\) + \(\frac{15}{8}\)  = \(\frac{55}{8}\) = 6\(\frac{7}{8}\) .
b.
3 – 1\(\frac{3}{4}\) = 3 – \(\frac{7}{4}\)
lcm is 4
\(\frac{12}{4}\) – \(\frac{7}{4}\) = \(\frac{5}{4}\) =1\(\frac{1}{4}\)
c.
7\(\frac{3}{8}\) + 4= \(\frac{59}{8}\) + 4
lcm of 1 and 8 is 8
\(\frac{59}{8}\) +\(\frac{32}{8}\) = \(\frac{91}{8}\) =11\(\frac{3}{8}\) .
d.
4 – 2\(\frac{3}{7}\) = 4 – \(\frac{17}{7}\)
lcm of 1 and 7 is 7
\(\frac{28}{7}\) – \(\frac{17}{7}\) = \(\frac{11}{7}\) =1\(\frac{4}{7}\) .

Eureka Math Grade 5 Module 3 Lesson 8 Homework Answer Key

Question 1.
Add or subtract.
a. 3 + 1\(\frac{1}{4}\) =
b. 2 – 1\(\frac{5}{8}\) =
c. 5\(\frac{2}{5}\) + 2 \(\frac{3}{5}\) =
d. 4 – 2\(\frac{5}{7}\) =
e. 8\(\frac{4}{5}\) + 7 =
f. 18 – 15\(\frac{3}{4}\) =
g. 16 + 18\(\frac{5}{6}\) =
h. 100 -50\(\frac{3}{8}\) =
Answer:
a.
3 + 1\(\frac{1}{4}\) = 3 + \(\frac{5}{4}\)
lcm of 1 and 4 is 4
\(\frac{12}{4}\) + \(\frac{5}{4}\) = \(\frac{17}{4}\) = 4\(\frac{1}{4}\) .
b.
2 – 1\(\frac{5}{8}\) = 2 – \(\frac{13}{8}\)
lcm is 8
\(\frac{16}{8}\)  – \(\frac{13}{8}\) =\(\frac{3}{8}\) .
c.
5\(\frac{2}{5}\) + 2 \(\frac{3}{5}\) = \(\frac{27}{5}\) + \(\frac{13}{5}\) = \(\frac{40}{5}\) = 8.
d.
4 – 2\(\frac{5}{7}\) = 4 – \(\frac{19}{7}\)
lcm of 1 and 7 is 7 .
\(\frac{28}{7}\)  – \(\frac{19}{7}\) = \(\frac{9}{7}\) =1\(\frac{2}{7}\)
e.
8\(\frac{4}{5}\) + 7 = \(\frac{44}{5}\) + 7
lcm of  5 and 7 is  35.
\(\frac{308}{35}\) + \(\frac{245}{35}\) = \(\frac{553}{35}\) =15 \(\frac{28}{35}\)
f.
18 – 15\(\frac{3}{4}\) = 18 – \(\frac{63}{4}\)
lcm of 1 and 4 is 4.
18 – \(\frac{63}{4}\)  = \(\frac{72}{4}\) – \(\frac{63}{4}\)  = \(\frac{9}{4}\) =2\(\frac{1}{4}\)
g.
16 + 18\(\frac{5}{6}\) = 16 + \(\frac{113}{6}\)
lcm is 6
\(\frac{96}{6}\) + \(\frac{113}{6}\)  = \(\frac{209}{6}\) = 34\(\frac{5}{6}\)
h.
100 -50\(\frac{3}{8}\) = 100 –\(\frac{403}{8}\)
lcm of 1 and 8 is 8 .
\(\frac{800}{8}\) – \(\frac{403}{8}\) = \(\frac{397}{8}\) = 49\(\frac{5}{8}\) .

Question 2.
The total length of two ribbons is 13 meters. If one ribbon is 7\(\frac{5}{8}\) meters long, what is the length of the other ribbon?
Answer:
The total length of two ribbons = 13 meters.
Fraction of length of one ribbon = 7\(\frac{5}{8}\)
Fraction of length of other ribbon = x
13 = 7\(\frac{5}{8}\) + x
13 = \(\frac{61}{8}\) + x
lcm of 1 and 8 is 8
\(\frac{104}{8}\) = \(\frac{61}{8}\) + x
x = \(\frac{104}{8}\) – \(\frac{61}{8}\)
x = \(\frac{43}{8}\) = 5 \(\frac{3}{8}\)
Therefore, Fraction of length of other ribbon = x  = \(\frac{43}{8}\) = 5 \(\frac{3}{8}\) .

Question 3.
It took Sandy two hours to jog 13 miles. She ran 7\(\frac{1}{2}\) miles in the first hour. How far did she run during the second hour?
Answer:
Distance traveled by sandy in 2 hours = 13 miles.
Distance traveled in one hour = 7\(\frac{1}{2}\) miles
Distance traveled in second hour = x
13 miles = 7\(\frac{1}{2}\) + x miles.
13 = \(\frac{15}{2}\) + x
lcm of 1 and 2 is 2 .
\(\frac{26}{2}\) = \(\frac{15}{2}\) + x
x = \(\frac{26}{2}\) – \(\frac{15}{2}\)
x = \(\frac{11}{2}\) = 5\(\frac{1}{2}\) .
Therefore, Distance traveled in second hour = x = \(\frac{11}{2}\) = 5\(\frac{1}{2}\)

Question 4.
Andre says that 5\(\frac{3}{4}\) + 2\(\frac{1}{4}\) = 7\(\frac{1}{2}\) because 7\(\frac{4}{8}\) = 7 \(\frac{1}{2}\). Identify his mistake. Draw a picture to prove that he is wrong.
Answer:
5\(\frac{3}{4}\) + 2\(\frac{1}{4}\) = 7\(\frac{1}{2}\)
5\(\frac{3}{4}\) + 2\(\frac{1}{4}\) = \(\frac{23}{4}\) + \(\frac{9}{4}\) = \(\frac{32}{4}\) = 8
that means andre subtracted \(\frac{3}{4}\) and \(\frac{1}{4}\) instead of adding

Engage NY Eureka Math 5th Grade Module 3 Lesson 7 Answer Key

Eureka Math Grade 5 Module 3 Lesson 7 Sprint Answer Key

A
Circle the Equivalent Fraction

Question 1.
\(\frac{2}{4}\) = \(\frac{1}{2}\) \(\frac{1}{3}\)
Answer:
\(\frac{2}{4}\) = \(\frac{1}{2}\)
Explanation :
\(\frac{2}{4}\) when its numerator and denominator is divided by 2 we get \(\frac{1}{2}\)

Question 2.
\(\frac{2}{6}\) = \(\frac{1}{2}\) \(\frac{1}{3}\)
Answer:
\(\frac{2}{6}\) = \(\frac{1}{3}\)
Explanation :
\(\frac{2}{6}\) when its numerator and denominator is divided by 2 we get \(\frac{1}{3}\)

Question 3.
\(\frac{2}{8}\) = \(\frac{1}{2}\) \(\frac{1}{4}\)
Answer:
\(\frac{2}{8}\) = \(\frac{1}{4}\)
Explanation :
\(\frac{2}{8}\) when its numerator and denominator is divided by 2 we get \(\frac{1}{4}\)

Question 4.
\(\frac{5}{10}\) = \(\frac{1}{2}\) \(\frac{1}{4}\)
Answer:
\(\frac{5}{10}\) = \(\frac{1}{2}\)
Explanation :
\(\frac{5}{10}\) when its numerator and denominator is divided by 5 we get \(\frac{1}{2}[/latex

Question 5.
[latex]\frac{5}{15}\) = \(\frac{1}{2}\) \(\frac{1}{3}\)
Answer:
\(\frac{5}{15}\) = \(\frac{1}{3}\)
Explanation :
\(\frac{5}{15}\) when its numerator and denominator is divided by 5 we get \(\frac{1}{3}\)

Question 6.
\(\frac{5}{20}\) = \(\frac{1}{2}\) \(\frac{1}{4}\)
Answer:
\(\frac{5}{20}\) = \(\frac{1}{4}\)
Explanation :
\(\frac{5}{20}\) when its numerator and denominator is divided by 5 we get \(\frac{1}{4}\)

Question 7.
\(\frac{4}{8}\) = \(\frac{1}{2}\) \(\frac{1}{4}\)
Answer:
\(\frac{4}{8}\) = \(\frac{1}{2}\)
Explanation :
\(\frac{4}{8}\) when its numerator and denominator is divided by 4 we get \(\frac{1}{2}\)

Question 8.
\(\frac{4}{12}\) = \(\frac{1}{2}\) \(\frac{1}{3}\)
Answer:
\(\frac{4}{12}\) = \(\frac{1}{3}\)
Explanation :
\(\frac{4}{12}\) when its numerator and denominator is divided by 4 we get \(\frac{1}{3}\)

Question 9.
\(\frac{4}{16}\) = \(\frac{1}{2}\) \(\frac{1}{4}\)
Answer:
\(\frac{4}{16}\) = \(\frac{1}{4}\)
Explanation :
\(\frac{4}{16}\) when its numerator and denominator is divided by 4 we get \(\frac{1}{4}\)

Question 10.
\(\frac{3}{6}\) = \(\frac{1}{2}\) \(\frac{1}{3}\)
Answer:
\(\frac{3}{6}\) = \(\frac{1}{2}\)
Explanation :
\(\frac{3}{6}\) when its numerator and denominator is divided by 3 we get \(\frac{1}{2}\)

Question 11.
\(\frac{3}{9}\) = \(\frac{1}{2}\) \(\frac{1}{3}\)
Answer:
\(\frac{3}{9}\) = \(\frac{1}{3}\)
Explanation :
\(\frac{3}{9}\) when its numerator and denominator is divided by 3 we get \(\frac{1}{3}\)

Question 12.
\(\frac{3}{12}\) = \(\frac{1}{2}\) \(\frac{1}{4}\)
Answer:
\(\frac{3}{12}\) = \(\frac{1}{4}\)
Explanation :
\(\frac{3}{12}\) when its numerator and denominator is divided by 3 we get \(\frac{1}{4}\)

Question 13.
\(\frac{4}{6}\) = \(\frac{2}{3}\) \(\frac{1}{3}\)
Answer:
\(\frac{4}{6}\) = \(\frac{2}{3}\)
Explanation :
\(\frac{4}{6}\) when its numerator and denominator is divided by 2 we get \(\frac{2}{3}\)

Question 14.
\(\frac{6}{12}\) = \(\frac{2}{3}\) \(\frac{1}{2}\)
Answer:
\(\frac{6}{12}\) = \(\frac{1}{2}\)
Explanation :
\(\frac{6}{12}\) when its numerator and denominator is divided by 6 we get \(\frac{1}{2}\)

Question 15.
\(\frac{6}{18}\) = \(\frac{2}{3}\) \(\frac{1}{3}\)
Answer:
\(\frac{6}{18}\) = \(\frac{1}{3}\)
Explanation :
\(\frac{6}{18}\) when its numerator and denominator is divided by 6 we get \(\frac{1}{3}\)

Question 16.
\(\frac{6}{30}\) = \(\frac{1}{5}\) \(\frac{1}{3}\)
Answer:
\(\frac{6}{30}\) = \(\frac{1}{5}\)
Explanation :
\(\frac{6}{30}\) when its numerator and denominator is divided by 6 we get \(\frac{1}{5}\)

Question 17.
\(\frac{6}{9}\) = \(\frac{2}{3}\) \(\frac{1}{3}\)
Answer:
\(\frac{6}{9}\) = \(\frac{2}{3}\)
Explanation :
\(\frac{6}{9}\) when its numerator and denominator is divided by 3 we get \(\frac{2}{3}\)

Question 18.
\(\frac{7}{14}\) = \(\frac{1}{2}\) \(\frac{1}{3}\)
Answer:
\(\frac{7}{14}\) = \(\frac{1}{2}\)
Explanation :
\(\frac{7}{14}\) when its numerator and denominator is divided by 7 we get \(\frac{1}{2}\)

Question 19.
\(\frac{7}{21}\) = \(\frac{1}{2}\) \(\frac{1}{3}\)
Answer:
\(\frac{7}{21}\) = \(\frac{1}{3}\)
Explanation :
\(\frac{7}{21}\) when its numerator and denominator is divided by 7 we get \(\frac{1}{3}\)

Question 20.
\(\frac{7}{42}\) = \(\frac{1}{6}\) \(\frac{1}{7}\)
Answer:
\(\frac{7}{42}\) = \(\frac{1}{6}\)
Explanation :
\(\frac{7}{42}\) when its numerator and denominator is divided by 7 we get \(\frac{1}{6}\)

Question 21.
\(\frac{8}{12}\) = \(\frac{2}{3}\) \(\frac{3}{4}\)
Answer:
\(\frac{8}{12}\) = \(\frac{2}{3}\)
Explanation :
\(\frac{8}{12}\) when its numerator and denominator is divided by 4 we get \(\frac{2}{3}\)

Question 22.
\(\frac{9}{18}\) = \(\frac{1}{2}\) \(\frac{1}{3}\)
Answer:
\(\frac{9}{18}\) = \(\frac{1}{2}\)
Explanation :
\(\frac{9}{18}\) when its numerator and denominator is divided by 9 we get \(\frac{1}{2}\)

Question 23.
\(\frac{9}{27}\) = \(\frac{2}{3}\) \(\frac{1}{3}\) \(\frac{1}{4}\)
Answer:
\(\frac{9}{27}\) = \(\frac{1}{3}\)
Explanation :
\(\frac{9}{27}\) when its numerator and denominator is divided by 9 we get \(\frac{1}{3}\)

Question 24.
\(\frac{9}{63}\) = \(\frac{1}{6}\) \(\frac{1}{7}\) \(\frac{1}{8}\)
Answer:
\(\frac{9}{63}\) = \(\frac{1}{7}\)
Explanation :
\(\frac{9}{63}\) when its numerator and denominator is divided by 9 we get \(\frac{1}{7}\)

Question 25.
\(\frac{8}{12}\) = \(\frac{2}{3}\) \(\frac{3}{4}\) \(\frac{4}{5}\)
Answer:
\(\frac{8}{12}\) = \(\frac{2}{3}\)
Explanation :
\(\frac{8}{12}\) when its numerator and denominator is divided by 4 we get \(\frac{2}{3}\)

Question 26.
\(\frac{8}{16}\) = \(\frac{1}{2}\) \(\frac{1}{3}\) \(\frac{1}{4}\)
Answer:
\(\frac{8}{16}\) = \(\frac{1}{2}\)
Explanation :
\(\frac{8}{16}\) when its numerator and denominator is divided by 8 we get \(\frac{1}{2}\)

Question 27.
\(\frac{8}{24}\) = \(\frac{1}{2}\) \(\frac{1}{3}\) \(\frac{1}{4}\)
Answer:
\(\frac{8}{24}\) = \(\frac{1}{3}\)
Explanation :
\(\frac{8}{24}\) when its numerator and denominator is divided by 8 we get \(\frac{1}{3}\)

Question 28.
\(\frac{8}{64}\) = \(\frac{1}{7}\) \(\frac{1}{8}\) \(\frac{1}{9}\)
Answer:
\(\frac{8}{64}\) = \(\frac{1}{8}\)
Explanation :
\(\frac{8}{64}\) when its numerator and denominator is divided by 8 we get \(\frac{1}{8}\)

Question 29.
\(\frac{12}{18}\) = \(\frac{3}{4}\) \(\frac{5}{6}\) \(\frac{2}{3}\)
Answer:
\(\frac{12}{18}\) = \(\frac{2}{3}\)
Explanation :
\(\frac{12}{18}\) when its numerator and denominator is divided by 6 we get \(\frac{2}{3}\)

Question 30.
\(\frac{12}{16}\) = \(\frac{3}{4}\) \(\frac{5}{6}\) \(\frac{2}{3}\)
Answer:
\(\frac{12}{16}\) = \(\frac{3}{4}\)
Explanation :
\(\frac{12}{16}\) when its numerator and denominator is divided by 4 we get \(\frac{3}{4}\)

Question 31.
\(\frac{9}{12}\) = \(\frac{3}{4}\) \(\frac{5}{6}\) \(\frac{2}{3}\)
Answer:
\(\frac{9}{12}\) = \(\frac{3}{4}\)
Explanation :
\(\frac{9}{12}\) when its numerator and denominator is divided by 3 we get \(\frac{3}{4}\)

Question 32.
\(\frac{6}{8}\) = \(\frac{3}{4}\) \(\frac{5}{6}\) \(\frac{2}{3}\)
Answer:
\(\frac{6}{8}\) = \(\frac{3}{4}\)
Explanation :
\(\frac{6}{8}\) when its numerator and denominator is divided by 2 we get \(\frac{3}{4}\)

Question 33.
\(\frac{10}{12}\) = \(\frac{3}{4}\) \(\frac{5}{6}\) \(\frac{2}{3}\)
Answer:
\(\frac{10}{12}\) = \(\frac{5}{6}\)
Explanation :
\(\frac{10}{12}\) when its numerator and denominator is divided by 2 we get \(\frac{5}{6}\)

Question 34.
\(\frac{15}{18}\) = \(\frac{3}{4}\) \(\frac{5}{6}\) \(\frac{2}{3}\)
Answer:
\(\frac{15}{18}\) = \(\frac{5}{6}\)
Explanation :
\(\frac{15}{18}\) when its numerator and denominator is divided by 3 we get \(\frac{5}{6}\)

Question 35.
\(\frac{8}{10}\) = \(\frac{3}{4}\) \(\frac{4}{5}\) \(\frac{2}{3}\)
Answer:
\(\frac{8}{10}\) = \(\frac{4}{5}\)
Explanation :
\(\frac{8}{10}\) when its numerator and denominator is divided by 2 we get \(\frac{4}{5}\)

Question 36.
\(\frac{16}{20}\) = \(\frac{3}{4}\) \(\frac{4}{5}\) \(\frac{2}{3}\)
Answer:
\(\frac{16}{20}\) = \(\frac{4}{5}\)
Explanation :
\(\frac{16}{20}\) when its numerator and denominator is divided by 4 we get \(\frac{4}{5}\)

Question 37.
\(\frac{12}{15}\) = \(\frac{3}{4}\) \(\frac{4}{5}\) \(\frac{2}{3}\)
Answer:
\(\frac{12}{15}\) = \(\frac{4}{5}\)
Explanation :
\(\frac{12}{15}\) when its numerator and denominator is divided by 3 we get \(\frac{4}{5}\)

Question 38.
\(\frac{18}{27}\) = \(\frac{3}{4}\) \(\frac{4}{5}\) \(\frac{2}{3}\)
Answer:
\(\frac{18}{27}\) = \(\frac{2}{3}\)
Explanation :
\(\frac{18}{27}\) when its numerator and denominator is divided by 9 we get \(\frac{2}{3}\)

Question 39.
\(\frac{27}{36}\) = \(\frac{3}{4}\) \(\frac{4}{5}\) \(\frac{2}{3}\)
Answer:
\(\frac{27}{36}\) = \(\frac{3}{4}\)
Explanation :
\(\frac{27}{36}\) when its numerator and denominator is divided by 9 we get \(\frac{3}{4}\)

Question 40.
\(\frac{32}{40}\) = \(\frac{3}{4}\) \(\frac{4}{5}\) \(\frac{2}{3}\)
Answer:
\(\frac{32}{40}\) = \(\frac{4}{5}\)
Explanation :
\(\frac{32}{40}\) when its numerator and denominator is divided by 8 we get \(\frac{4}{5}\)

Question 41.
\(\frac{45}{54}\) = \(\frac{3}{4}\) \(\frac{4}{5}\) \(\frac{5}{6}\)
Answer:
\(\frac{45}{54}\) = \(\frac{5}{6}\)
Explanation :
\(\frac{45}{54}\) when its numerator and denominator is divided by 9 we get \(\frac{5}{6}\)

Question 42.
\(\frac{24}{36}\) = \(\frac{3}{4}\) \(\frac{4}{5}\) \(\frac{2}{3}\)
Answer:
\(\frac{24}{36}\) = \(\frac{2}{3}\)
Explanation :
\(\frac{24}{36}\) when its numerator and denominator is divided by 12 we get \(\frac{2}{3}\)

Question 43.
\(\frac{60}{72}\) = \(\frac{3}{4}\) \(\frac{5}{6}\) \(\frac{2}{3}\)
Answer:
\(\frac{60}{72}\) = \(\frac{5}{6}\)
Explanation :
\(\frac{60}{72}\) when its numerator and denominator is divided by 12 we get \(\frac{5}{6}\)

Question 44.
\(\frac{48}{60}\) = \(\frac{3}{4}\) \(\frac{4}{5}\) \(\frac{5}{6}\)
Answer:
\(\frac{48}{60}\) = \(\frac{4}{5}\)
Explanation :
\(\frac{48}{60}\) when its numerator and denominator is divided by 12 we get \(\frac{4}{5}\)

B
Circle the Equivalent Fraction

Question 1.
\(\frac{5}{10}\) = \(\frac{1}{2}\) \(\frac{1}{3}\)
Answer:
\(\frac{5}{10}\) = \(\frac{1}{2}\)
Explanation :
\(\frac{5}{10}\) when its numerator and denominator is divided by 5 we get \(\frac{1}{2}\)

Question 2.
\(\frac{5}{15}\) = \(\frac{1}{2}\) \(\frac{1}{3}\)
Answer:
\(\frac{5}{15}\) = \(\frac{1}{3}\)
Explanation :
\(\frac{5}{15}\) when its numerator and denominator is divided by 5 we get \(\frac{1}{3}\)

Question 3.
\(\frac{5}{20}\) = \(\frac{1}{2}\) \(\frac{1}{4}\)
Answer:
\(\frac{5}{20}\) = \(\frac{1}{4}\)
Explanation :
\(\frac{5}{20}\) when its numerator and denominator is divided by 5 we get \(\frac{1}{4}\)

Question 4.
\(\frac{2}{4}\) = \(\frac{1}{2}\) \(\frac{1}{3}\)
Answer:
\(\frac{2}{4}\) = \(\frac{1}{2}\)
Explanation :
\(\frac{2}{4}\) when its numerator and denominator is divided by 2 we get \(\frac{1}{2}\)

Question 5.
\(\frac{2}{6}\) = \(\frac{1}{2}\) \(\frac{1}{3}\)
Answer:
\(\frac{2}{6}\) = \(\frac{1}{3}\)
Explanation :
\(\frac{2}{6}\) when its numerator and denominator is divided by 2 we get \(\frac{1}{3}\)

Question 6.
\(\frac{2}{8}\) = \(\frac{1}{2}\) \(\frac{1}{4}\)
Answer:
\(\frac{2}{8}\) = \(\frac{1}{4}\)
Explanation :
\(\frac{2}{8}\) when its numerator and denominator is divided by 2 we get \(\frac{1}{4}\)

Question 7.
\(\frac{3}{6}\) = \(\frac{1}{2}\) \(\frac{1}{3}\)
Answer:
\(\frac{3}{6}\) = \(\frac{1}{2}\)
Explanation :
\(\frac{3}{6}\) when its numerator and denominator is divided by 3 we get \(\frac{1}{2}\)

Question 8.
\(\frac{3}{9}\) = \(\frac{1}{2}\) \(\frac{1}{3}\)
Answer:
\(\frac{3}{9}\) = \(\frac{1}{3}\)
Explanation :
\(\frac{3}{9}\) when its numerator and denominator is divided by 3 we get \(\frac{1}{3}\)

Question 9.
\(\frac{3}{12}\) = \(\frac{1}{4}\) \(\frac{1}{3}\)
Answer:
\(\frac{3}{12}\) = \(\frac{1}{4}\)
Explanation :
\(\frac{3}{12}\) when its numerator and denominator is divided by 3 we get \(\frac{1}{4}\)

Question 10.
\(\frac{4}{8}\) = \(\frac{1}{2}\) \(\frac{1}{3}\)
Answer:
\(\frac{4}{8}\) = \(\frac{1}{2}\)
Explanation :
\(\frac{4}{8}\) when its numerator and denominator is divided by 4 we get \(\frac{1}{2}\)

Question 11.
\(\frac{4}{12}\) = \(\frac{1}{2}\) \(\frac{1}{3}\)
Answer:
\(\frac{4}{12}\) = \(\frac{1}{3}\)
Explanation :
\(\frac{4}{12}\) when its numerator and denominator is divided by 4 we get \(\frac{1}{3}\)

Question 12.
\(\frac{4}{16}\) = \(\frac{1}{4}\) \(\frac{1}{3}\)
Answer:
\(\frac{4}{16}\) = \(\frac{1}{4}\)
Explanation :
\(\frac{4}{16}\) when its numerator and denominator is divided by 4 we get \(\frac{1}{4}\)

Question 13.
\(\frac{4}{6}\) = \(\frac{2}{3}\) \(\frac{1}{2}\)
Answer:
\(\frac{4}{6}\) = \(\frac{2}{3}\)
Explanation :
\(\frac{4}{6}\) when its numerator and denominator is divided by 2 we get \(\frac{2}{3}\)

Question 14.
\(\frac{7}{14}\) = \(\frac{2}{3}\) \(\frac{1}{2}\)
Answer:
\(\frac{7}{14}\) = \(\frac{1}{2}\)
Explanation :
\(\frac{7}{14}\) when its numerator and denominator is divided by 7 we get \(\frac{1}{2}\)

Question 15.
\(\frac{7}{21}\) = \(\frac{1}{5}\) \(\frac{1}{3}\)
Answer:
\(\frac{7}{21}\) = \(\frac{1}{3}\)
Explanation :
\(\frac{7}{21}\) when its numerator and denominator is divided by 7 we get \(\frac{1}{3}\)

Question 16.
\(\frac{7}{35}\) = \(\frac{1}{5}\) \(\frac{1}{3}\)
Answer:
\(\frac{7}{35}\) = \(\frac{1}{5}\)
Explanation :
\(\frac{7}{35}\) when its numerator and denominator is divided by 7 we get \(\frac{1}{5}\)

Question 17.
\(\frac{6}{9}\) = \(\frac{2}{3}\) \(\frac{1}{3}\)
Answer:
\(\frac{6}{9}\) = \(\frac{2}{3}\)
Explanation :
\(\frac{6}{9}\) when its numerator and denominator is divided by 3 we get \(\frac{2}{3}\)

Question 18.
\(\frac{6}{12}\) = \(\frac{1}{2}\) \(\frac{1}{3}\)
Answer:
\(\frac{6}{12}\) = \(\frac{1}{2}\)
Explanation :
\(\frac{6}{12}\) when its numerator and denominator is divided by 6 we get \(\frac{1}{2}\)

Question 19.
\(\frac{6}{18}\) = \(\frac{1}{6}\) \(\frac{1}{3}\)
Answer:
\(\frac{6}{18}\) = \(\frac{1}{3}\)
Explanation :
\(\frac{6}{18}\) when its numerator and denominator is divided by 6 we get \(\frac{1}{3}\)

Question 20.
\(\frac{6}{36}\) = \(\frac{1}{6}\) \(\frac{1}{3}\)
Answer:
\(\frac{6}{36}\) = \(\frac{1}{6}\)
Explanation :
\(\frac{6}{36}\) when its numerator and denominator is divided by 6 we get \(\frac{1}{6}\)

Question 21.
\(\frac{8}{12}\) = \(\frac{2}{3}\) \(\frac{3}{4}\)
Answer:
\(\frac{8}{12}\) = \(\frac{2}{3}\)
Explanation :
\(\frac{8}{12}\) when its numerator and denominator is divided by 4 we get \(\frac{2}{3}\)

Question 22.
\(\frac{8}{16}\) = \(\frac{1}{2}\) \(\frac{1}{3}\)
Answer:
\(\frac{8}{16}\) = \(\frac{1}{2}\)
Explanation :
\(\frac{8}{16}\) when its numerator and denominator is divided by 8 we get \(\frac{1}{2}\)

Question 23.
\(\frac{8}{24}\) = \(\frac{2}{3}\) \(\frac{1}{3}\) \(\frac{1}{4}\)
Answer:
\(\frac{8}{24}\) = \(\frac{1}{3}\)
Explanation :
\(\frac{8}{24}\) when its numerator and denominator is divided by 8 we get \(\frac{1}{3}\)

Question 24.
\(\frac{8}{56}\) = \(\frac{1}{6}\) \(\frac{1}{7}\) \(\frac{1}{8}\)
Answer:
\(\frac{8}{24}\) = \(\frac{1}{3}\)
Explanation :
\(\frac{8}{56}\) when its numerator and denominator is divided by 8 we get \(\frac{1}{7}\)

Question 25.
\(\frac{8}{12}\) = \(\frac{2}{3}\) \(\frac{3}{4}\) \(\frac{4}{5}\)
Answer:
\(\frac{8}{12}\) = \(\frac{2}{3}\)
Explanation :
\(\frac{8}{12}\) when its numerator and denominator is divided by 4 we get \(\frac{2}{3}\)

Question 26.
\(\frac{9}{18}\) = \(\frac{1}{2}\) \(\frac{1}{3}\) \(\frac{1}{4}\)
Answer:
\(\frac{9}{18}\) = \(\frac{1}{2}\)
Explanation :
\(\frac{9}{18}\) when its numerator and denominator is divided by 9 we get \(\frac{1}{2}\)

Question 27.
\(\frac{9}{27}\) = \(\frac{1}{2}\) \(\frac{1}{3}\) \(\frac{1}{4}\)
Answer:
\(\frac{9}{27}\) = \(\frac{1}{3}\)
Explanation :
\(\frac{9}{27}\) when its numerator and denominator is divided by 9 we get \(\frac{1}{3}\)

Question 28.
\(\frac{9}{72}\) = \(\frac{1}{7}\) \(\frac{1}{8}\) \(\frac{1}{9}\)
Answer:
\(\frac{9}{72}\) = \(\frac{1}{8}\)
Explanation :
\(\frac{9}{72}\) when its numerator and denominator is divided by 9 we get \(\frac{1}{8}\)

Question 29.
\(\frac{12}{18}\) = \(\frac{3}{4}\) \(\frac{5}{6}\) \(\frac{2}{3}\)
Answer:
\(\frac{12}{18}\) = \(\frac{2}{3}\)
Explanation :
\(\frac{12}{18}\) when its numerator and denominator is divided by 6 we get \(\frac{2}{3}\)

Question 30.
\(\frac{6}{8}\) = \(\frac{3}{4}\) \(\frac{5}{6}\) \(\frac{2}{3}\)
Answer:
\(\frac{6}{8}\) = \(\frac{3}{4}\)
Explanation :
\(\frac{6}{8}\) when its numerator and denominator is divided by 2 we get \(\frac{3}{4}\)

Question 31.
\(\frac{9}{12}\) = \(\frac{3}{4}\) \(\frac{5}{6}\) \(\frac{2}{3}\)
Answer:
\(\frac{9}{12}\) = \(\frac{3}{4}\)
Explanation :
\(\frac{9}{12}\) when its numerator and denominator is divided by 3 we get \(\frac{3}{4}\)

Question 32.
\(\frac{12}{16}\) = \(\frac{3}{4}\) \(\frac{5}{6}\) \(\frac{2}{3}\)
Answer:
\(\frac{12}{16}\) = \(\frac{3}{4}\)
Explanation :
\(\frac{12}{16}\) when its numerator and denominator is divided by 4 we get \(\frac{3}{4}\)

Question 33.
\(\frac{8}{10}\) = \(\frac{3}{4}\) \(\frac{4}{5}\) \(\frac{2}{3}\)
Answer:
\(\frac{8}{10}\) = \(\frac{4}{5}\)
Explanation :
\(\frac{8}{10}\) when its numerator and denominator is divided by 2 we get \(\frac{4}{5}\)

Question 34.
\(\frac{16}{20}\) = \(\frac{3}{4}\) \(\frac{4}{5}\) \(\frac{2}{3}\)
Answer:
\(\frac{16}{20}\) = \(\frac{4}{5}\)
Explanation :
\(\frac{16}{20}\) when its numerator and denominator is divided by 4 we get \(\frac{4}{5}\)

Question 35.
\(\frac{12}{15}\) = \(\frac{3}{4}\) \(\frac{4}{5}\) \(\frac{2}{3}\)
Answer:
\(\frac{12}{15}\) = \(\frac{4}{5}\)
Explanation :
\(\frac{12}{15}\) when its numerator and denominator is divided by 3 we get \(\frac{4}{5}\)

Question 36.
\(\frac{10}{12}\) = \(\frac{3}{4}\) \(\frac{4}{5}\) \(\frac{5}{6}\)
Answer:
\(\frac{10}{12}\) = \(\frac{5}{6}\)
Explanation :
\(\frac{10}{12}\) when its numerator and denominator is divided by 2 we get \(\frac{5}{6}\)

Question 37.
\(\frac{15}{18}\) = \(\frac{3}{4}\) \(\frac{5}{6}\) \(\frac{2}{3}\)
Answer:
\(\frac{15}{18}\) = \(\frac{5}{6}\)
Explanation :
\(\frac{15}{18}\) when its numerator and denominator is divided by 3 we get \(\frac{5}{6}\)

Question 38.
\(\frac{16}{24}\) = \(\frac{3}{4}\) \(\frac{4}{5}\) \(\frac{2}{3}\)
Answer:
\(\frac{16}{24}\) = \(\frac{2}{3}\)
Explanation :
\(\frac{16}{24}\) when its numerator and denominator is divided by 8 we get \(\frac{2}{3}\)

Question 39.
\(\frac{24}{32}\) = \(\frac{3}{4}\) \(\frac{4}{5}\) \(\frac{2}{3}\)
Answer:
\(\frac{24}{32}\) = \(\frac{3}{4}\)
Explanation :
\(\frac{24}{32}\) when its numerator and denominator is divided by 12 we get \(\frac{3}{4}\)

Question 40.
\(\frac{36}{45}\) = \(\frac{3}{4}\) \(\frac{4}{5}\) \(\frac{2}{3}\)
Answer:
\(\frac{36}{45}\) = \(\frac{4}{5}\)
Explanation :
\(\frac{36}{45}\) when its numerator and denominator is divided by 9 we get \(\frac{4}{5}\)

Question 41.
\(\frac{40}{48}\) = \(\frac{3}{4}\) \(\frac{4}{5}\) \(\frac{5}{6}\)
Answer:
\(\frac{40}{48}\) = \(\frac{5}{6}\)
Explanation :
\(\frac{40}{48}\) when its numerator and denominator is divided by 8 we get \(\frac{5}{}\)

Question 42.
\(\frac{24}{36}\) = \(\frac{3}{4}\) \(\frac{4}{5}\) \(\frac{2}{3}\)
Answer:
\(\frac{24}{36}\) = \(\frac{2}{3}\)
Explanation :
\(\frac{24}{36}\) when its numerator and denominator is divided by 12 we get \(\frac{2}{3}\)

Question 43.
\(\frac{48}{60}\) = \(\frac{3}{4}\) \(\frac{5}{6}\) \(\frac{4}{5}\)
Answer:
\(\frac{48}{60}\) = \(\frac{4}{5}\)
Explanation :
\(\frac{48}{60}\) when its numerator and denominator is divided by 12 we get \(\frac{4}{5}\)

Question 44.
\(\frac{60}{72}\) = \(\frac{3}{4}\) \(\frac{5}{6}\) \(\frac{2}{3}\)
Answer:
\(\frac{60}{72}\) = \(\frac{5}{6}\)
Explanation :
\(\frac{60}{72}\) when its numerator and denominator is divided by 12 we get \(\frac{5}{6}\)

Eureka Math Grade 5 Module 3 Lesson 7 Problem Set Answer Key

Solve the word problems using the RDW strategy. Show all of your work.
Question 1.
George weeded \(\frac{1}{5}\) of the garden, and Summer weeded some, too. When they were finished, \(\frac{2}{3}\) of the garden still needed to be weeded. What fraction of the garden did Summer weed?
Answer:
Total Garden = 1 whole .
Fraction of garden weeded by George = \(\frac{1}{5}\)
Fraction of garden needed to be weeded = \(\frac{2}{3}\)
Fraction of garden weeded by summer = x
1 = \(\frac{1}{5}\) + x + \(\frac{2}{3}\)
x = 1 – \(\frac{1}{5}\) – \(\frac{2}{3}\)
lcm of 5 and 3 is 15.
x = \(\frac{15}{15}\)  – \(\frac{3}{15}\) – \(\frac{10}{15}\)
x = \(\frac{15}{15}\)  – \(\frac{13}{15}\)
x = \(\frac{2}{15}\)
Therefore , Fraction of garden weeded by summer = x = \(\frac{2}{15}\)

Question 2.
Jing spent \(\frac{1}{3}\) of her money on a pack of pens, \(\frac{1}{2}\) of her money on a pack of markers, and \(\frac{1}{8}\) of her money on a pack of pencils. What fraction of her money is left?
Answer:
Total Money = 1
Money spent on pack of pens = \(\frac{1}{3}\)
Money spent on pack of markers = \(\frac{1}{2}\)
Money spent on pack of pencils = \(\frac{1}{8}\)
Fraction of Money left = x
1 = \(\frac{1}{3}\) + \(\frac{1}{2}\) + \(\frac{1}{8}\) + x
lcm of 3, 2 and 8 is 24
\(\frac{24}{24}\) = \(\frac{8}{24}\) + \(\frac{12}{24}\) + \(\frac{3}{24}\) + x
\(\frac{24}{24}\) = \(\frac{23}{24}\) + x
x = \(\frac{24}{24}\) – \(\frac{23}{24}\)
x = \(\frac{1}{24}\) .
Therefore, Fraction of Money left = \(\frac{1}{24}\)

Question 3.
Shelby bought a 2-ounce tube of blue paint. She used \(\frac{2}{3}\) ounce to paint the water, \(\frac{3}{5}\) ounce to paint the sky, and some to paint a flag. After that, she has \(\frac{2}{15}\) ounce left. How much paint did Shelby use to paint her flag?
Answer:
Quantity of Blue paint = 2 – ounce
Fraction of blue paint used for painting water = \(\frac{2}{3}\)
Fraction of blue paint used for painting sky = \(\frac{3}{5}\)
Fraction of blue paint used for painting flag = x
Fraction of blue paint left = \(\frac{2}{15}\)
2 = \(\frac{2}{3}\) + \(\frac{3}{5}\) + x + \(\frac{2}{15}\)
lcm of 3, 5 and 15 is 15 .
\(\frac{30}{15}\) = \(\frac{10}{15}\) + \(\frac{9}{15}\) + x + \(\frac{2}{15}\)
\(\frac{30}{15}\) = \(\frac{21}{15}\) + x
x = \(\frac{30}{15}\) – \(\frac{21}{15}\)
x = \(\frac{9}{15}\) = \(\frac{3}{5}\)
Therefore , Fraction of blue paint used for painting flag = x = \(\frac{9}{15}\) = \(\frac{3}{5}\) .ounce

Question 4.
Jim sold \(\frac{3}{4}\) gallon of lemonade. Dwight sold some lemonade, too. Together, they sold 1\(\frac{5}{12}\) gallons. Who sold more lemonade, Jim or Dwight? How much more?
Answer:
Fraction of lemonade sold by Jim = \(\frac{3}{4}\) gallon
Fraction of lemonade sold by Dwight = x gallon
Fraction of lemonade sold by Jim and Dwight = 1\(\frac{5}{12}\) gallon
1\(\frac{5}{12}\) = \(\frac{3}{4}\) + x
x = 1\(\frac{5}{12}\) – \(\frac{3}{4}\)
lcm of 12 and 4 is 12 .
x = \(\frac{17}{12}\) – \(\frac{9}{12}\)
x = \(\frac{8}{12}\) = \(\frac{2}{3}\)
Therefore, Fraction of lemonade sold by Dwight = x = \(\frac{8}{12}\) = \(\frac{2}{3}\) gallon .

Question 5.
Leonard spent \(\frac{1}{4}\) of his money on a sandwich. He spent 2 times as much on a gift for his brother as on some comic books. He had \(\frac{3}{8}\) of his money left. What fraction of his money did he spend on the comic books?
Answer:
Fraction of Money spent on sandwich = \(\frac{1}{4}\)
Fraction of money left with him = \(\frac{3}{8}\)
Total Money = 1
1 = \(\frac{1}{4}\) + \(\frac{3}{8}\) + x .
Lcm of 4 and 8 is 8.
\(\frac{8}{8}\) = \(\frac{2}{8}\) + \(\frac{3}{8}\) + x
\(\frac{8}{8}\) = \(\frac{5}{8}\) + x
x = \(\frac{8}{8}\) – \(\frac{5}{8}\)
x = \(\frac{3}{8}\)
Fraction of Money spent on his brother = \(\frac{2}{8}\) = \(\frac{1}{4}\)
Fraction of Money spent on Comic books = \(\frac{1}{8}\) .

Eureka Math Grade 5 Module 3 Lesson 7 Exit Ticket Answer Key

Solve the word problem using the RDW strategy. Show all of your work.
Mr. Pham mowed \(\frac{2}{7}\) of his lawn. His son mowed \(\frac{1}{4}\) of it. Who mowed the most? How much of the lawn still needs to be mowed?
Answer:
Fraction Of Lawn mowed by Mr.Pham = \(\frac{2}{7}\)
Fraction Of Lawn mowed by his Son = \(\frac{1}{4}\)
lcm of 7 and 4 is 28 .
\(\frac{2}{7}\) = \(\frac{8}{28}\)
\(\frac{1}{4}\) = \(\frac{7}{28}\)
\(\frac{8}{28}\) > \(\frac{7}{28}\)
Mr. Pham mowed most than his son .
Fraction of lawn still needed to mowed = x
1= \(\frac{8}{28}\) + \(\frac{7}{28}\)  + x
\(\frac{28}{28}\) = \(\frac{15}{28}\) + x
x = \(\frac{28}{28}\) – \(\frac{15}{28}\)
x = \(\frac{13}{28}\)
Therefore, Fraction of lawn still needed to mowed = x = \(\frac{13}{28}\) .

Eureka Math Grade 5 Module 3 Lesson 7 Homework Answer Key

Solve the word problems using the RDW strategy. Show all of your work.
Question 1.
Christine baked a pumpkin pie. She ate \(\frac{1}{6}\) of the pie. Her brother ate \(\frac{1}{6}\) of it and gave the leftovers to his friends. What fraction of the pie did he give to his friends?
Answer:
Total pie = 1 .
Fraction of pie ate by Christine = \(\frac{1}{6}\)
Fraction of pie ate by her Brother =\(\frac{1}{6}\)
Fraction of pie leftover to her friends = x
1 = \(\frac{1}{6}\) + \(\frac{1}{6}\) + x
lcm is 6
\(\frac{6}{6}\) = \(\frac{2}{6}\) + x
x = \(\frac{6}{6}\) – \(\frac{2}{6}\)
x = \(\frac{4}{6}\) = \(\frac{2}{3}\)
Therefore, Fraction of pie leftover to her friends = x = \(\frac{4}{6}\) = \(\frac{2}{3}\) .

Question 2.
Liang went to the bookstore. He spent \(\frac{1}{3}\) of his money on a pen and \(\frac{4}{7}\) of it on books. What fraction of his money did he have left?
Answer:
Total money = 1
Fraction of Money spent on Pen =\(\frac{1}{3}\)
Fraction of Money spent on Books =\(\frac{4}{7}\)
Fraction of Money left = x
1 = \(\frac{1}{3}\) + \(\frac{4}{7}\) + x
lcm of 3 and 7 is 21 .
\(\frac{21}{21}\) = \(\frac{7}{21}\) + \(\frac{12}{21}\) + x
\(\frac{21}{21}\) = \(\frac{19}{21}\) + x
x = \(\frac{3}{21}\) = \(\frac{1}{7}\) .
Therefore, Fraction of Money left = x = \(\frac{3}{21}\) = \(\frac{1}{7}\) .

Question 3.
Tiffany bought \(\frac{2}{5}\) kg of cherries. Linda bought \(\frac{1}{10}\) kg of cherries less than Tiffany. How many kilograms of cherries did they buy altogether?
Answer:
Fraction of Quantity of Cherries bought by Tiffany = \(\frac{2}{5}\) kg
Fraction of Quantity of Cherries bought by Linda = x kg
Fraction of Quantity of cherries Linda bought \(\frac{1}{10}\) kg of cherries less than Tiffany.
Fraction of Quantity of Cherries bought by Linda = x = \(\frac{2}{5}\) – \(\frac{1}{10}\)
lcm of 2 and 5 is 10 .
x = \(\frac{4}{10}\) – \(\frac{1}{10}\)
x = \(\frac{3}{10}\)
Fraction of Quantity of cherries bought by both = \(\frac{2}{5}\)  + \(\frac{3}{10}\)  =  \(\frac{4}{10}\) + \(\frac{3}{10}\)  = \(\frac{7}{10}\)
Therefore, Fraction of Quantity of cherries bought by both = \(\frac{7}{10}\)

Question 4.
Mr. Rivas bought a can of paint. He used \(\frac{3}{8}\) of it to paint a bookshelf. He used \(\frac{1}{4}\) of it to paint a wagon. He used some of it to paint a birdhouse and has \(\frac{1}{8}\) of the paint left. How much paint did he use for the birdhouse?
Answer:
Fraction of paint used to paint a bookshelf = \(\frac{3}{8}\)
Fraction of paint used to paint a wagon = \(\frac{1}{4}\)
Fraction of paint used to paint a birdhouse = x
Fraction of paint left = \(\frac{1}{8}\)
Total paint = 1 .
1 = \(\frac{3}{8}\) + \(\frac{1}{4}\) + x + \(\frac{1}{8}\)
lcm of 4 and 8 is 8 .
\(\frac{8}{8}\) = \(\frac{3}{8}\) +\(\frac{2}{8}\) + x + \(\frac{1}{8}\)
\(\frac{8}{8}\) = \(\frac{6}{8}\) + x
x = \(\frac{8}{8}\) – \(\frac{6}{8}\)
x = \(\frac{2}{8}\) = \(\frac{1}{4}\) .
Therefore, Fraction of paint used to paint a bird house = x = \(\frac{2}{8}\) = \(\frac{1}{4}\)

Question 5.
Ribbon A is \(\frac{1}{3}\) m long. It is \(\frac{2}{5}\) m shorter than Ribbon B. What’s the total length of the two ribbons?
Answer:
Fraction of length of Ribbon A = \(\frac{1}{3}\) m
Fraction of length of Ribbon A = Fraction of length of Ribbon B – \(\frac{2}{5}\) m
Fraction of length of Ribbon B = \(\frac{1}{3}\) + \(\frac{2}{5}\)
lcm of 3 and 5 is 15 .
Fraction of length of Ribbon B = \(\frac{1}{3}\) + \(\frac{2}{5}\) = \(\frac{5}{15}\) + \(\frac{6}{15}\) = \(\frac{11}{15}\)
Fraction of Total Length of two ribbons = \(\frac{1}{3}\) + \(\frac{11}{15}\) = \(\frac{5}{15}\) + \(\frac{11}{15}\) = \(\frac{16}{15}\) m .
Therefore, Fraction of Total Length of two ribbons =\(\frac{16}{15}\) m

Engage NY Eureka Math 5th Grade Module 3 Lesson 6 Answer Key

Eureka Math Grade 5 Module 3 Lesson 6 Problem Set Answer Key

Question 1.
For the following problems, draw a picture using the rectangular fraction model and write the answer. Simplify your answer, if possible.
a. 1\(\frac{1}{4}\) – \(\frac{1}{3}\) =
b. 1\(\frac{1}{5}\) – \(\frac{1}{3}\) =
c. 1\(\frac{3}{8}\) – \(\frac{1}{2}\) =
d. 1\(\frac{2}{5}\) – \(\frac{1}{2}\) =
e. 1\(\frac{2}{7}\) – \(\frac{1}{3}\) =
f. 1\(\frac{2}{3}\) – \(\frac{3}{5}\) =
Answer:
a.
1\(\frac{1}{4}\) – \(\frac{1}{3}\) = \(\frac{5}{4}\) – \(\frac{1}{3}\)
lcm of 4 and 3 is 12 .
\(\frac{15}{12}\) – \(\frac{4}{12}\) = \(\frac{11}{12}\).

Explanation :
The Rectangle is divided into 4 parts using vertical lines and 2 rectangles are drawn and shaded to represent the fraction 1\(\frac{1}{4}\) .
1\(\frac{1}{4}\) and  \(\frac{1}{3}\) have lcm 12 so, the rectangle is divided into 12 parts by drawing 2 horizontal lines . after making lcm equal then subtraction is done and subtraction is done by showing x-mark on the shaded parts.
The left over shaded parts represent the difference of the given fraction to its total parts .

b.
1\(\frac{1}{5}\) – \(\frac{1}{3}\) = \(\frac{6}{5}\) – \(\frac{1}{3}\)
lcm of 5 and 3 is 15 .
\(\frac{18}{15}\) – \(\frac{5}{15}\) = \(\frac{13}{15}\)

Explanation :
The Rectangle is divided into 5 parts using vertical lines and 2 rectangles are drawn and shaded to represent the fraction 1\(\frac{1}{5}\) .
1\(\frac{1}{5}\) and  \(\frac{1}{3}\) have lcm 15 so, the rectangle is divided into 15 parts by drawing 2 horizontal lines . after making lcm equal then subtraction is done and subtraction is done by showing x-mark on the shaded parts.
The left over shaded parts represent the difference of the given fraction to its total parts .

c.
1\(\frac{3}{8}\) – \(\frac{1}{2}\) = \(\frac{11}{8}\) – \(\frac{1}{2}\)
lcm of 8 and 2 is 8 .
\(\frac{11}{8}\) – \(\frac{4}{8}\) =\(\frac{7}{8}\) .

Explanation :
The Rectangle is divided into 8 parts using vertical lines and 2 rectangles are drawn and shaded to represent the fraction 1\(\frac{3}{8}\) .
1\(\frac{3}{8}\) and  \(\frac{1}{2}\) have lcm 8 so, the rectangle is divided into 8 parts . after making lcm equal then subtraction is done and subtraction is done by showing x-mark on the shaded parts.
The left over shaded parts represent the difference of the given fraction to its total parts .

d.
1\(\frac{2}{5}\) – \(\frac{1}{2}\) = \(\frac{7}{5}\) – \(\frac{1}{2}\)
lcm of 5 and 2 is 10.
\(\frac{14}{10}\) – \(\frac{5}{10}\) = \(\frac{9}{10}\)

Explanation :
The Rectangle is divided into 5 parts using vertical lines and 2 rectangles are drawn and shaded to represent the fraction 1\(\frac{2}{5}\) .
1\(\frac{2}{5}\) and  \(\frac{1}{2}\) have lcm 10 so, the rectangle is divided into 10 parts by drawing 1 horizontal lines . after making lcm equal then subtraction is done and subtraction is done by showing x-mark on the shaded parts.
The left over shaded parts represent the difference of the given fraction to its total parts .

e.
1\(\frac{2}{7}\) – \(\frac{1}{3}\) = \(\frac{9}{7}\) – \(\frac{1}{3}\)
lcm of 7 and 3 is 21 .
\(\frac{27}{21}\) – \(\frac{7}{21}\) = \(\frac{20}{21}\) .

Explanation :
The Rectangle is divided into 7 parts using vertical lines and 2 rectangles are drawn and shaded to represent the fraction 1\(\frac{2}{7}\) .
1\(\frac{2}{7}\) and  \(\frac{1}{3}\) have lcm 21 so, the rectangle is divided into 21 parts by drawing 2 horizontal lines . after making lcm equal then subtraction is done and subtraction is done by showing x-mark on the shaded parts.
The left over shaded parts represent the difference of the given fraction to its total parts .

f.
1\(\frac{2}{3}\) – \(\frac{3}{5}\) = \(\frac{5}{3}\) – \(\frac{3}{5}\)
lcm of 3 and 5 is 15 .
\(\frac{25}{15}\) – \(\frac{9}{15}\) = \(\frac{16}{15}\)

Explanation :
The Rectangle is divided into 5 parts using vertical lines and 2 rectangles are drawn and shaded to represent the fraction 1\(\frac{2}{3}\) .
1\(\frac{2}{3}\) and  \(\frac{3}{5}\) have lcm 15 so, the rectangle is divided into 15 parts by drawing 4 horizontal lines . after making lcm equal then subtraction is done and subtraction is done by showing x-mark on the shaded parts.
The left over shaded parts represent the difference of the given fraction to its total parts .

Question 2.
Jean-Luc jogged around the lake in 1\(\frac{1}{4}\) hour. William jogged the same distance in \(\frac{5}{6}\) hour. How much longer did Jean-Luc take than William in hours?
Answer:
Time taken to jog for Jean-Luc = 1\(\frac{1}{4}\) hour .
Time taken to jog for William = \(\frac{5}{6}\) hour .
Time taken by Jean-Luc than William = 1\(\frac{1}{4}\) – \(\frac{5}{6}\)  = \(\frac{5}{4}\) – \(\frac{5}{6}\)  = \(\frac{30}{24}\)  – \(\frac{20}{24}\) = \(\frac{10}{24}\) = \(\frac{5}{12}\) hour .

Question 3.
Is it true that 1\(\frac{2}{5}\) – \(\frac{3}{4}\) = \(\frac{1}{4}\) + \(\frac{2}{5}\)? Prove your answer.
Answer:
Yes , 1\(\frac{2}{5}\) – \(\frac{3}{4}\) = \(\frac{1}{4}\) + \(\frac{2}{5}\)
Explanation :
1\(\frac{2}{5}\) – \(\frac{3}{4}\) = \(\frac{7}{5}\) – \(\frac{3}{4}\) = \(\frac{28}{20}\) – \(\frac{15}{20}\) = \(\frac{13}{20}\) .
\(\frac{1}{4}\) + \(\frac{2}{5}\) = \(\frac{5}{20}\) + \(\frac{8}{20}\) = \(\frac{13}{20}\)
Therefore, 1\(\frac{2}{5}\) – \(\frac{3}{4}\) = \(\frac{1}{4}\) + \(\frac{2}{5}\) = \(\frac{13}{20}\)  .

Eureka Math Grade 5 Module 3 Lesson 6 Exit Ticket Answer Key

For the following problems, draw a picture using the rectangular fraction model and write the answer. Simplify your answer, if possible.
a. 1\(\frac{1}{5}\) – \(\frac{1}{2}\) =
b. 1\(\frac{1}{3}\) – \(\frac{5}{6}\) =
Answer:
a.
1\(\frac{1}{5}\) – \(\frac{1}{2}\) = \(\frac{6}{5}\) – \(\frac{1}{2}\)
lcm of 5 and 2 is 10 .
\(\frac{12}{10}\) – \(\frac{5}{10}\) = \(\frac{7}{10}\)

Explanation :
The Rectangle is divided into 5 parts using vertical lines and 2 rectangles are drawn and shaded to represent the fraction 1\(\frac{2}{5}\) .
1\(\frac{2}{5}\) and  \(\frac{1}{2}\) have lcm 10 so, the rectangle is divided into 10 parts by drawing 1 horizontal line . after making lcm equal then subtraction is done and subtraction is done by showing x-mark on the shaded parts.
The left over shaded parts represent the difference of the given fraction to its total parts .

b.
1\(\frac{1}{3}\) – \(\frac{5}{6}\) = \(\frac{4}{3}\) – \(\frac{5}{6}\)
lcm of 3 and 6 is  6 .
\(\frac{8}{6}\) – \(\frac{5}{6}\) = \(\frac{3}{6}\) = \(\frac{1}{2}\)

Explanation :
The Rectangle is divided into 3 parts using vertical lines and 2 rectangles are drawn and shaded to represent the fraction 1\(\frac{1}{3}\) .
1\(\frac{1}{3}\) and  \(\frac{5}{6}\) have lcm 6 so, the rectangle is divided into 6 parts by drawing 2 horizontal lines . after making lcm equal then subtraction is done and subtraction is done by showing x-mark on the shaded parts.
The left over shaded parts represent the difference of the given fraction to its total parts .

Eureka Math Grade 5 Module 3 Lesson 6 Homework Answer Key

Question 1.
For the following problems, draw a picture using the rectangular fraction model and write the answer. Simplify your answer, if possible.
a. 1 – \(\frac{5}{6}\) =
b. \(\frac{3}{2}\) – \(\frac{5}{6}\) =
c. \(\frac{4}{3}\) – \(\frac{5}{7}\) =
d. 1\(\frac{1}{8}\) – \(\frac{3}{5}\) =
e. 1\(\frac{2}{5}\) – \(\frac{3}{4}\) =
f. 1\(\frac{5}{6}\) – \(\frac{7}{8}\) =
g. \(\frac{9}{7}\) – \(\frac{3}{4}\) =
h. 1\(\frac{3}{12}\) – \(\frac{2}{3}\) =
Answer:
a.
1 – \(\frac{5}{6}\)
lcm of 1 and 6 is 6 .
\(\frac{6}{6}\) – \(\frac{5}{6}\) = \(\frac{1}{6}\) .

Explanation :
The Rectangle is divided into 6 parts using vertical lines and shaded to represent the fraction \(\frac{6}{6}\) .
1 and  \(\frac{5}{6}\) have lcm 6 . after making lcm equal then subtraction is done and subtraction is done by showing x-mark on the shaded parts.
The left over shaded parts without x marks represent the difference of the given fraction to its total parts .

b.
\(\frac{3}{2}\) – \(\frac{5}{6}\)
lcm of 2 and 6 is  6 .
\(\frac{9}{6}\) – \(\frac{5}{6}\) = \(\frac{4}{6}\) = \(\frac{2}{3}\)

Explanation :
The Rectangle is divided into 2 parts using vertical lines and 2 rectangles are drawn and shaded to represent the fraction 1\(\frac{1}{2}\) .
1\(\frac{1}{2}\) and  \(\frac{5}{6}\) have lcm 6 so, the rectangle is divided into 6 parts by drawing 2 horizontal lines . after making lcm equal then subtraction is done and subtraction is done by showing x-mark on the shaded parts.
The left over shaded parts without x marks represent the difference of the given fraction to its total parts .
c.
\(\frac{4}{3}\) – \(\frac{5}{7}\)
lcm of 3 and 7 is 21 .
\(\frac{28}{21}\) – \(\frac{15}{21}\) = \(\frac{13}{21}\)

Explanation :
The Rectangle is divided into 3 parts using vertical lines and 2 rectangles are drawn and shaded to represent the fraction 1\(\frac{1}{3}\) .
1\(\frac{1}{3}\) and  \(\frac{5}{7}\) have lcm 21 so, the rectangle is divided into 21 parts by drawing 6 horizontal lines . after making lcm equal then subtraction is done and subtraction is done by showing x-mark on the shaded parts.
The left over shaded parts without x marks represent the difference of the given fraction to its total parts .

d.
1\(\frac{1}{8}\) – \(\frac{3}{5}\) = \(\frac{9}{8}\) – \(\frac{3}{5}\)
lcm of 8 and 5 is 40
\(\frac{45}{40}\) – \(\frac{24}{40}\) = \(\frac{21}{40}\)

Explanation :
The Rectangle is divided into 8 parts using vertical lines and 2 rectangles are drawn and shaded to represent the fraction 1\(\frac{1}{8}\) .
1\(\frac{1}{8}\) and  \(\frac{3}{5}\) have lcm 40 so, the rectangle is divided into 40 parts by drawing 4 horizontal lines . after making lcm equal then subtraction is done and subtraction is done by showing x-mark on the shaded parts.
The left over shaded parts without x marks represent the difference of the given fraction to its total parts .

e.
1\(\frac{2}{5}\) – \(\frac{3}{4}\) = \(\frac{7}{5}\) – \(\frac{3}{4}\)
lcm of 5 and 4 is 20 .
\(\frac{28}{20}\) – \(\frac{15}{20}\) = \(\frac{13}{20}\) .

Explanation :
The Rectangle is divided into 5 parts using vertical lines and 2 rectangles are drawn and shaded to represent the fraction 1\(\frac{2}{5}\) .
1\(\frac{2}{5}\) and  \(\frac{3}{4}\) have lcm 20 so, the rectangle is divided into 20 parts by drawing 3 horizontal lines . after making lcm equal then subtraction is done and subtraction is done by showing x-mark on the shaded parts.
The left over shaded parts without x marks represent the difference of the given fraction to its total parts .

f.
1\(\frac{5}{6}\) – \(\frac{7}{8}\) = \(\frac{11}{6}\) – \(\frac{7}{8}\)
lcm of 6 and 8 is 24 .
\(\frac{44}{24}\) – \(\frac{21}{24}\) = \(\frac{23}{24}\) .

Explanation :
The Rectangle is divided into 6 parts using vertical lines and 2 rectangles are drawn and shaded to represent the fraction 1\(\frac{5}{6}\) .
1\(\frac{5}{6}\) and  \(\frac{7}{8}\) have lcm 24 so, the rectangle is divided into 24 parts by drawing 3 horizontal lines . after making lcm equal then subtraction is done and subtraction is done by showing x-mark on the shaded parts.
The left over shaded parts without x marks represent the difference of the given fraction to its total parts .

g.
\(\frac{9}{7}\) – \(\frac{3}{4}\)
lcm of 7 and 4 is 28 .
\(\frac{36}{28}\) – \(\frac{21}{28}\) = \(\frac{15}{28}\)

Explanation :
The Rectangle is divided into 7 parts using vertical lines and 2 rectangles are drawn and shaded to represent the fraction 1\(\frac{2}{7}\) .
1\(\frac{2}{7}\) and  \(\frac{3}{4}\) have lcm 28 so, the rectangle is divided into 28 parts by drawing 3 horizontal lines . after making lcm equal then subtraction is done and subtraction is done by showing x-mark on the shaded parts.
The left over shaded parts without x marks represent the difference of the given fractions to its total parts .

h.
1\(\frac{3}{12}\) – \(\frac{2}{3}\) = \(\frac{15}{12}\) – \(\frac{2}{3}\)
lcm of 12 and 3 is 12 .
\(\frac{15}{12}\) – \(\frac{8}{12}\) = \(\frac{7}{12}\)

Explanation :
The Rectangle is divided into 12 parts using vertical lines and 2 rectangles are drawn and shaded to represent the fraction 1\(\frac{3}{12}\) .
1\(\frac{3}{12}\) and  \(\frac{2}{3}\) have lcm 12 . After making lcm equal then subtraction is done and subtraction is done by showing x-mark on the shaded parts.
The left over shaded parts without x marks represent the difference of the given fractions to its total parts .

Question 2.
Sam had 1\(\frac{1}{2}\) m of rope. He cut off \(\frac{5}{8}\) m and used it for a project. How much rope does Sam have left?
Answer:
Length of Rope with Sam = 1\(\frac{1}{2}\) m
Length of rope used for project = \(\frac{5}{8}\) m
Length of Rope left = 1\(\frac{1}{2}\) – \(\frac{5}{8}\) = \(\frac{3}{2}\) – \(\frac{5}{8}\) =
\(\frac{12}{8}\) – \(\frac{5}{8}\) = \(\frac{7}{8}\) .
Therefore, Length of rope left with sam = \(\frac{7}{8}\) m .

Question 3.
Jackson had 1\(\frac{3}{8}\) kg of fertilizer. He used some to fertilize a flower bed, and he only had \(\frac{2}{3}\) kg left. How much fertilizer was used in the flower bed?
Answer:
Quantity of fertilizers with Jackson = 1\(\frac{3}{8}\) kg
Quantity of fertilizers left = \(\frac{2}{3}\) kg .
Quantity of Fertilizers used for flower bed  = 1\(\frac{3}{8}\) kg  – \(\frac{2}{3}\) kg = \(\frac{11}{8}\) – \(\frac{2}{3}\) = \(\frac{33}{24}\) – \(\frac{16}{24}\) = \(\frac{17}{24}\) .
Therefore, Quantity of Fertilizers used for flower bed  =\(\frac{17}{24}\)

Engage NY Eureka Math 5th Grade Module 3 Lesson 5 Answer Key

Eureka Math Grade 5 Module 3 Lesson 5 Sprint Answer Key

A
Subtracting Fractions from a Whole Number

Question 1.
4 – \(\frac{1}{2}\) =
Answer:
4 – \(\frac{1}{2}\) = 3\(\frac{1}{2}\)
Explanation :
4 – \(\frac{1}{2}\) = \(\frac{8}{2}\) – \(\frac{1}{2}\) = \(\frac{7}{2}\) = 3\(\frac{1}{2}\)

Question 2.
3 – \(\frac{1}{2}\) =
Answer:
3 – \(\frac{1}{2}\) = 2\(\frac{1}{2}\)
Explanation :
3 – \(\frac{1}{2}\) = \(\frac{6}{2}\) – \(\frac{1}{2}\) = \(\frac{5}{2}\) = 2\(\frac{1}{2}\)

Question 3.
2 – \(\frac{1}{2}\) =
Answer:
2 – \(\frac{1}{2}\) = 1\(\frac{1}{2}\)
Explanation :
2 – \(\frac{1}{2}\) = \(\frac{4}{2}\) – \(\frac{1}{2}\) = \(\frac{3}{2}\) = 1\(\frac{1}{2}\)

Question 4.
1 – \(\frac{1}{2}\) =
Answer:
1 – \(\frac{1}{2}\) = \(\frac{1}{2}\)
Explanation :
1 – \(\frac{1}{2}\) = \(\frac{2}{2}\) – \(\frac{1}{2}\) = \(\frac{1}{2}\)

Question 5.
1 – \(\frac{1}{3}\) =
Answer:
1 – \(\frac{1}{3}\) = \(\frac{2}{3}\)
Explanation :
1 – \(\frac{1}{3}\) = \(\frac{3}{3}\) – \(\frac{1}{3}\) = \(\frac{2}{3}\)

Question 6.
2 – \(\frac{1}{3}\) =
Answer:
2 – \(\frac{1}{3}\) = 1\(\frac{2}{3}\)
Explanation :
2 – \(\frac{1}{3}\) = \(\frac{6}{3}\) – \(\frac{1}{3}\) = \(\frac{5}{3}\) = 1\(\frac{2}{3}\)

Question 7.
4 – \(\frac{1}{3}\) =
Answer:
4 – \(\frac{1}{3}\) = 3\(\frac{2}{3}\)
Explanation :
4 – \(\frac{1}{3}\) = \(\frac{12}{3}\) – \(\frac{1}{3}\) = \(\frac{11}{3}\) = 3\(\frac{2}{3}\)

Question 8.
4 – \(\frac{2}{3}\) =
Answer:
4 – \(\frac{2}{3}\) = 3\(\frac{1}{3}\)
Explanation :
4 – \(\frac{2}{3}\) = \(\frac{12}{3}\) – \(\frac{2}{3}\) = \(\frac{10}{3}\) = 3\(\frac{1}{3}\)

Question 9.
2 – \(\frac{2}{3}\) =
Answer:
2 – \(\frac{1}{3}\) = 1\(\frac{2}{3}\)
Explanation :
2 – \(\frac{1}{3}\) = \(\frac{6}{3}\) – \(\frac{1}{3}\) = \(\frac{5}{3}\) = 1\(\frac{2}{3}\)

Question 10.
2 – \(\frac{1}{4}\) =
Answer:
2 – \(\frac{1}{4}\) = 1\(\frac{3}{4}\)
Explanation :
2 – \(\frac{1}{4}\) = \(\frac{8}{4}\) – \(\frac{1}{4}\) = \(\frac{7}{4}\) = 1\(\frac{3}{4}\)

Question 11.
2 – \(\frac{3}{4}\) =
Answer:
2 – \(\frac{3}{4}\) = 1\(\frac{1}{4}\)
Explanation :
2 – \(\frac{3}{4}\) = \(\frac{8}{4}\) – \(\frac{3}{4}\) = \(\frac{5}{4}\) = 1\(\frac{1}{4}\)

Question 12.
3 – \(\frac{3}{4}\) =
Answer:
3 – \(\frac{3}{4}\) = 2\(\frac{1}{4}\)
Explanation :
3 – \(\frac{3}{4}\) = \(\frac{12}{4}\) – \(\frac{3}{4}\) = \(\frac{9}{4}\) = 2\(\frac{1}{4}\)

Question 13.
3 – \(\frac{1}{4}\) =
Answer:
3 – \(\frac{1}{4}\) = 2\(\frac{3}{4}\)
Explanation :
3 – \(\frac{1}{4}\) = \(\frac{12}{4}\) – \(\frac{1}{4}\) = \(\frac{11}{4}\) = 2\(\frac{3}{4}\)

Question 14.
4 – \(\frac{3}{4}\) =
Answer:
4 – \(\frac{3}{4}\) = 3\(\frac{1}{4}\)
Explanation :
4 – \(\frac{3}{4}\) = \(\frac{16}{4}\) – \(\frac{3}{4}\) = \(\frac{13}{4}\) = 3\(\frac{1}{4}\)

Question 15.
2 – \(\frac{1}{10}\) =
Answer:
2 – \(\frac{1}{10}\) = 1\(\frac{9}{10}\)
Explanation :
2 – \(\frac{1}{10}\) = \(\frac{20}{10}\) – \(\frac{1}{10}\) = \(\frac{19}{10}\) = 1\(\frac{9}{10}\)

Question 16.
3 – \(\frac{9}{10}\) =
Answer:
3 – \(\frac{9}{10}\) = 2\(\frac{1}{10}\)
Explanation :
3 – \(\frac{9}{10}\) = \(\frac{30}{10}\) – \(\frac{9}{10}\) = \(\frac{21}{10}\) = 2\(\frac{1}{10}\)

Question 17.
2 – \(\frac{7}{10}\) =
Answer:
Answer:
2 – \(\frac{7}{10}\) = 1\(\frac{3}{10}\)
Explanation :
2 – \(\frac{7}{10}\) = \(\frac{20}{10}\) – \(\frac{7}{10}\) = \(\frac{13}{10}\) = 1\(\frac{3}{10}\)

Question 18.
4 – \(\frac{3}{10}\) =
Answer:
4 – \(\frac{1}{10}\) = 3\(\frac{9}{10}\)
Explanation :
4 – \(\frac{1}{10}\) = \(\frac{40}{10}\) – \(\frac{1}{10}\) = \(\frac{39}{10}\) = 3\(\frac{9}{10}\)

Question 19.
3 – \(\frac{1}{5}\) =
Answer:
3 – \(\frac{1}{5}\) = 2\(\frac{4}{5}\)
Explanation :
3 – \(\frac{1}{5}\) = \(\frac{15}{5}\) – \(\frac{1}{5}\) = \(\frac{14}{5}\) = 2\(\frac{4}{5}\)

Question 20.
3 – \(\frac{2}{5}\) =
Answer:
3 – \(\frac{2}{5}\) = 2\(\frac{3}{5}\)
Explanation :
3 – \(\frac{2}{5}\) = \(\frac{15}{5}\) – \(\frac{2}{5}\) = \(\frac{13}{5}\) = 2\(\frac{3}{5}\)

Question 21.
3 – \(\frac{4}{5}\) =
Answer:
3 – \(\frac{4}{5}\) = 2\(\frac{1}{5}\)
Explanation :
3 – \(\frac{4}{5}\) = \(\frac{15}{5}\) – \(\frac{4}{5}\) = \(\frac{11}{5}\) = 2\(\frac{1}{5}\)

Question 22.
3 – \(\frac{3}{5}\) =
Answer:
3 – \(\frac{3}{5}\) = 2\(\frac{2}{5}\)
Explanation :
3 – \(\frac{3}{5}\) = \(\frac{15}{5}\) – \(\frac{3}{5}\) = \(\frac{12}{5}\) = 2\(\frac{2}{5}\)

Question 23.
3 – \(\frac{1}{8}\) =
Answer:
3 – \(\frac{1}{8}\) = 2\(\frac{7}{8}\)
Explanation :
3 – \(\frac{1}{8}\) = \(\frac{24}{8}\) – \(\frac{1}{8}\) = \(\frac{23}{8}\) = 2\(\frac{7}{8}\)

Question 24.
3 – \(\frac{3}{8}\) =
Answer:
3 – \(\frac{3}{8}\) = 2\(\frac{5}{8}\)
Explanation :
3 – \(\frac{3}{8}\) = \(\frac{24}{8}\) – \(\frac{3}{8}\) = \(\frac{21}{8}\) = 2\(\frac{5}{8}\)

Question 25.
3 – \(\frac{5}{8}\) =
Answer:
3 – \(\frac{5}{8}\) = 2\(\frac{3}{8}\)
Explanation :
3 – \(\frac{5}{8}\) = \(\frac{24}{8}\) – \(\frac{5}{8}\) = \(\frac{19}{8}\) = 2\(\frac{3}{8}\)

Question 26.
3 – \(\frac{7}{8}\) =
Answer:
3 – \(\frac{7}{8}\) = 2\(\frac{1}{8}\)
Explanation :
3 – \(\frac{7}{8}\) = \(\frac{24}{8}\) – \(\frac{7}{8}\) = \(\frac{17}{8}\) = 2\(\frac{1}{8}\)

Question 27.
2 – \(\frac{7}{8}\) =
Answer:
2 – \(\frac{7}{8}\) = 1\(\frac{1}{8}\)
Explanation :
2 – \(\frac{7}{8}\) = \(\frac{16}{8}\) – \(\frac{7}{8}\) = \(\frac{9}{8}\) = 1\(\frac{1}{8}\)

Question 28.
4 – \(\frac{1}{7}\) =
Answer:
4 – \(\frac{1}{7}\) = 3\(\frac{6}{7}\)
Explanation :
4 – \(\frac{1}{7}\) = \(\frac{28}{7}\) – \(\frac{1}{7}\) = \(\frac{27}{7}\) = 3\(\frac{6}{7}\)

Question 29.
3 – \(\frac{6}{7}\) =
Answer:
3 – \(\frac{6}{7}\) = 2\(\frac{1}{7}\)
Explanation :
3 – \(\frac{6}{7}\) = \(\frac{21}{7}\) – \(\frac{6}{7}\) = \(\frac{15}{7}\) = 2\(\frac{1}{7}\)

Question 30.
2 – \(\frac{3}{7}\) =
Answer:
2 – \(\frac{3}{7}\) =
Answer:
2 – \(\frac{3}{7}\) = 1\(\frac{4}{7}\)
Explanation :
2 – \(\frac{3}{7}\) = \(\frac{14}{7}\) – \(\frac{3}{7}\) = \(\frac{11}{7}\) = 1\(\frac{4}{7}\)

Question 31.
4 – \(\frac{4}{7}\) =
Answer:
4 – \(\frac{4}{7}\) =
Answer:
4 – \(\frac{4}{7}\) = 3\(\frac{3}{7}\)
Explanation :
4 – \(\frac{4}{7}\) = \(\frac{28}{7}\) – \(\frac{4}{7}\) = \(\frac{24}{7}\) = 3\(\frac{3}{7}\)

Question 32.
3 – \(\frac{5}{7}\) =
Answer:
3 – \(\frac{5}{7}\) = 2\(\frac{2}{7}\)
Explanation :
3 – \(\frac{5}{7}\) = \(\frac{21}{7}\) – \(\frac{5}{7}\) = \(\frac{16}{7}\) = 2\(\frac{2}{7}\)

Question 33.
4 – \(\frac{3}{4}\) =
Answer:
4 – \(\frac{3}{4}\) = 3\(\frac{1}{4}\)
Explanation :
4 – \(\frac{3}{4}\) = \(\frac{16}{4}\) – \(\frac{3}{4}\) = \(\frac{13}{4}\) = 3\(\frac{1}{4}\)

Question 34.
2 – \(\frac{5}{8}\) =
Answer:
2 – \(\frac{5}{8}\) = 1\(\frac{3}{8}\)
Explanation :
2 – \(\frac{5}{8}\) = \(\frac{16}{8}\) – \(\frac{5}{8}\) = \(\frac{11}{8}\) = 1\(\frac{3}{8}\)

Question 35.
3 – \(\frac{3}{10}\) =
Answer:
3 – \(\frac{3}{10}\) = 2\(\frac{7}{10}\)
Explanation :
3 – \(\frac{3}{10}\) = \(\frac{30}{10}\) – \(\frac{3}{10}\) = \(\frac{27}{10}\) = 2\(\frac{7}{10}\)

Question 36.
4 – \(\frac{2}{5}\) =
Answer:
4 – \(\frac{2}{5}\) = 3\(\frac{3}{5}\)
Explanation :
4 – \(\frac{2}{5}\) = \(\frac{20}{5}\) – \(\frac{2}{5}\) = \(\frac{18}{5}\) = 3\(\frac{3}{5}\)

Question 37.
4 – \(\frac{3}{7}\) =
Answer:
4 – \(\frac{3}{7}\) =
Answer:
4 – \(\frac{3}{7}\) = 3\(\frac{4}{7}\)
Explanation :
4 – \(\frac{3}{7}\) = \(\frac{28}{7}\) – \(\frac{3}{7}\) = \(\frac{25}{7}\) = 3\(\frac{4}{7}\)

Question 38.
3 – \(\frac{7}{10}\) =
Answer:
3 – \(\frac{7}{10}\) = 2\(\frac{3}{10}\)
Explanation :
3 – \(\frac{7}{10}\) = \(\frac{30}{10}\) – \(\frac{7}{10}\) = \(\frac{23}{10}\) = 2\(\frac{3}{10}\)

Question 39.
3 – \(\frac{5}{10}\) =
Answer:
3 – \(\frac{5}{10}\) = 2\(\frac{5}{10}\)
Explanation :
3 – \(\frac{5}{10}\) = \(\frac{30}{10}\) – \(\frac{5}{10}\) = \(\frac{25}{10}\) = 2\(\frac{5}{10}\)

Question 40.
4 – \(\frac{2}{8}\) =
Answer:
4 – \(\frac{2}{8}\) = 3\(\frac{6}{8}\)
Explanation :
4 – \(\frac{2}{8}\) = \(\frac{32}{8}\) – \(\frac{2}{8}\) = \(\frac{30}{8}\) = 3\(\frac{6}{8}\)

Question 41.
2 – \(\frac{9}{12}\) =
Answer:
2 – \(\frac{9}{12}\) = 2 – \(\frac{3}{4}\) = 1\(\frac{1}{4}\)
Explanation :
2 – \(\frac{3}{4}\) = \(\frac{8}{4}\) – \(\frac{3}{4}\) = \(\frac{5}{4}\) = 1\(\frac{1}{4}\)

Question 42.
4 – \(\frac{2}{12}\) = 3\(\frac{5}{6}\)
Answer:
4 – \(\frac{2}{12}\) = 4 – \(\frac{1}{6}\) = 3\(\frac{5}{6}\)
Explanation :
4 – \(\frac{1}{6}\) = \(\frac{24}{6}\) – \(\frac{1}{6}\) = \(\frac{23}{6}\) = 3\(\frac{5}{6}\)

Question 43.
3 – \(\frac{2}{6}\) =
Answer:
3 – \(\frac{2}{6}\) = 3 – \(\frac{1}{3}\) = 2\(\frac{2}{3}\)
Explanation :
3 – \(\frac{1}{3}\) = \(\frac{9}{3}\) – \(\frac{1}{3}\) = \(\frac{8}{3}\) = 2\(\frac{2}{3}\)

Question 44.
2 – \(\frac{8}{12}\) =
Answer:
2 – \(\frac{8}{12}\) = 2 – \(\frac{2}{3}\) = 1\(\frac{1}{3}\)
Explanation :
2 – \(\frac{2}{3}\) = \(\frac{6}{3}\) – \(\frac{2}{3}\) = \(\frac{4}{3}\) = 2\(\frac{1}{3}\)

B
Subtracting Fractions from a Whole Number

Question 1.
1 – \(\frac{1}{2}\) =
Answer:
1 – \(\frac{1}{2}\) = \(\frac{1}{2}\)
Explanation :
1 – \(\frac{1}{2}\) = \(\frac{2}{2}\) – \(\frac{1}{2}\) = \(\frac{1}{2}\)

Question 2.
2 – \(\frac{1}{2}\) =
Answer:
2 – \(\frac{1}{2}\) = 1\(\frac{1}{2}\)
Explanation :
2 – \(\frac{1}{2}\) = \(\frac{4}{2}\) – \(\frac{1}{2}\) = \(\frac{3}{2}\) = 1\(\frac{1}{2}\)

Question 3.
3 – \(\frac{1}{2}\) =
Answer:
3 – \(\frac{1}{2}\) = 2\(\frac{1}{2}\)
Explanation :
3 – \(\frac{1}{2}\) = \(\frac{6}{2}\) – \(\frac{1}{2}\) = \(\frac{5}{2}\) = 2\(\frac{1}{2}\)

Question 4.
4 – \(\frac{1}{2}\) =
Answer:
4 – \(\frac{1}{2}\) = 3\(\frac{1}{2}\)
Explanation :
4 – \(\frac{1}{2}\) = \(\frac{8}{2}\) – \(\frac{1}{2}\) = \(\frac{7}{2}\) = 3\(\frac{1}{2}\)

Question 5.
1 – \(\frac{1}{4}\) =
Answer:
1 – \(\frac{1}{4}\) = \(\frac{3}{4}\)
Explanation :
1 – \(\frac{1}{4}\) = \(\frac{4}{4}\) – \(\frac{1}{4}\) = \(\frac{3}{4}\)

Question 6.
2 – \(\frac{1}{4}\) =
Answer:
2 – \(\frac{1}{4}\) = 1\(\frac{3}{4}\)
Explanation :
2 – \(\frac{1}{4}\) = \(\frac{8}{4}\) – \(\frac{1}{4}\) = \(\frac{7}{4}\) = 1\(\frac{3}{4}\)

Question 7.
4 – \(\frac{1}{4}\) =
Answer:
4 – \(\frac{1}{4}\) = 3\(\frac{3}{4}\)
Explanation :
4 – \(\frac{1}{4}\) = \(\frac{16}{4}\) – \(\frac{1}{4}\) = \(\frac{15}{4}\) = 3\(\frac{3}{4}\)

Question 8.
4 – \(\frac{3}{4}\) =
Answer:
4 – \(\frac{3}{4}\) = 3\(\frac{1}{4}\)
Explanation :
4 – \(\frac{3}{4}\) = \(\frac{16}{4}\) – \(\frac{3}{4}\) = \(\frac{13}{4}\) = 3\(\frac{1}{4}\)

Question 9.
2 – \(\frac{3}{4}\) =
Answer:
2 – \(\frac{3}{4}\) = 1\(\frac{1}{4}\)
Explanation :
2 – \(\frac{3}{4}\) = \(\frac{8}{4}\) – \(\frac{3}{4}\) = \(\frac{5}{4}\) = 1\(\frac{1}{4}\)

Question 10.
2 – \(\frac{1}{3}\) =
Answer:
2 – \(\frac{1}{3}\) = 1\(\frac{2}{3}\)
Explanation :
2 – \(\frac{1}{3}\) = \(\frac{6}{3}\) – \(\frac{1}{3}\) = \(\frac{5}{3}\) = 1\(\frac{2}{3}\)

Question 11.
2 – \(\frac{2}{3}\) =
Answer:
2 – \(\frac{2}{3}\) = 1\(\frac{1}{3}\)
Explanation :
2 – \(\frac{2}{3}\) = \(\frac{6}{3}\) – \(\frac{2}{3}\) = \(\frac{4}{3}\) = 1\(\frac{1}{3}\)

Question 12.
3 – \(\frac{2}{3}\) =
Answer:
3 – \(\frac{2}{3}\) = 2\(\frac{1}{3}\)
Explanation :
3 – \(\frac{2}{3}\) = \(\frac{9}{3}\) – \(\frac{2}{3}\) = \(\frac{7}{3}\) = 2\(\frac{1}{3}\)

Question 13.
3 – \(\frac{1}{3}\) =
Answer:
3 – \(\frac{1}{3}\) = 2\(\frac{2}{3}\)
Explanation :
3 – \(\frac{1}{3}\) = \(\frac{9}{3}\) – \(\frac{1}{3}\) = \(\frac{8}{3}\) = 2\(\frac{2}{3}\)

Question 14.
4 – \(\frac{2}{3}\) =
Answer:
4 – \(\frac{2}{3}\) = 3\(\frac{1}{3}\)
Explanation :
4 – \(\frac{2}{3}\) = \(\frac{12}{3}\) – \(\frac{2}{3}\) = \(\frac{10}{3}\) = 3\(\frac{1}{3}\)

Question 15.
3 – \(\frac{1}{10}\) =
Answer:
3 – \(\frac{1}{10}\) = 2\(\frac{9}{10}\)
Explanation :
3 – \(\frac{1}{10}\) = \(\frac{30}{10}\) – \(\frac{9}{10}\) = \(\frac{21}{10}\) = 2\(\frac{1}{10}\)

Question 16.
2 – \(\frac{9}{10}\) =
Answer:
2 – \(\frac{9}{10}\) = 1\(\frac{1}{10}\)
Explanation :
2 – \(\frac{9}{10}\) = \(\frac{20}{10}\) – \(\frac{9}{10}\) = \(\frac{11}{10}\) = 1\(\frac{1}{10}\)

Question 17.
4 – \(\frac{7}{10}\) =
Answer:
4 – \(\frac{7}{10}\) = 3\(\frac{3}{10}\)
Explanation :
4 – \(\frac{7}{10}\) = \(\frac{40}{10}\) – \(\frac{7}{10}\) = \(\frac{33}{10}\) = 3\(\frac{3}{10}\)

Question 18.
3 – \(\frac{3}{10}\) =
Answer:
3 – \(\frac{3}{10}\) = 2\(\frac{7}{10}\)
Explanation :
3 – \(\frac{3}{10}\) = \(\frac{30}{10}\) – \(\frac{3}{10}\) = \(\frac{27}{10}\) = 2\(\frac{7}{10}\)

Question 19.
2 – \(\frac{1}{5}\) =
Answer:
2 – \(\frac{1}{5}\) = 1\(\frac{4}{5}\)
Explanation :
2 – \(\frac{1}{5}\) = \(\frac{10}{5}\) – \(\frac{1}{5}\) = \(\frac{9}{5}\) = 1\(\frac{4}{5}\)

Question 20.
2 – \(\frac{2}{5}\) =
Answer:
2 – \(\frac{2}{5}\) = 1\(\frac{3}{5}\)
Explanation :
2 – \(\frac{2}{5}\) = \(\frac{10}{5}\) – \(\frac{2}{5}\) = \(\frac{8}{5}\) = 1\(\frac{3}{5}\)

Question 21.
2 – \(\frac{4}{5}\) =
Answer:
2 – \(\frac{4}{5}\) = 1\(\frac{1}{5}\)
Explanation :
2 – \(\frac{1}{5}\) = \(\frac{10}{5}\) – \(\frac{4}{5}\) = \(\frac{6}{5}\) = 1\(\frac{1}{5}\)

Question 22.
3 – \(\frac{3}{5}\) =
Answer:
3 – \(\frac{3}{5}\) = 2\(\frac{2}{5}\)
Explanation :
3 – \(\frac{3}{5}\) = \(\frac{15}{5}\) – \(\frac{3}{5}\) = \(\frac{12}{5}\) = 2\(\frac{2}{5}\)

Question 23.
2 – \(\frac{1}{8}\) =
Answer:
2 – \(\frac{1}{8}\) = 1\(\frac{7}{8}\)
Explanation :
2 – \(\frac{1}{8}\) = \(\frac{16}{8}\) – \(\frac{1}{8}\) = \(\frac{15}{8}\) = 1\(\frac{7}{8}\)

Question 24.
2 – \(\frac{3}{8}\) =
Answer:
2 – \(\frac{3}{8}\) = 1\(\frac{5}{8}\)
Explanation :
2 – \(\frac{3}{8}\) = \(\frac{16}{8}\) – \(\frac{3}{8}\) = \(\frac{13}{8}\) = 1\(\frac{4}{8}\)

Question 25.
2 – \(\frac{5}{8}\) =
Answer:
2 – \(\frac{5}{8}\) = 1\(\frac{3}{8}\)
Explanation :
2 – \(\frac{5}{8}\) = \(\frac{16}{8}\) – \(\frac{5}{8}\) = \(\frac{11}{8}\) = 1\(\frac{3}{8}\)

Question 26.
2 – \(\frac{7}{8}\) =
Answer:
2 – \(\frac{7}{8}\) = 1\(\frac{1}{8}\)
Explanation :
2 – \(\frac{7}{8}\) = \(\frac{16}{8}\) – \(\frac{7}{8}\) = \(\frac{9}{8}\) = 1\(\frac{1}{8}\)

Question 27.
4 – \(\frac{7}{8}\) =
Answer:
4 – \(\frac{7}{8}\) = 3\(\frac{1}{8}\)
Explanation :
4 – \(\frac{7}{8}\) = \(\frac{32}{8}\) – \(\frac{3}{8}\) = \(\frac{13}{8}\) = 1\(\frac{4}{8}\)

Question 28.
3 – \(\frac{1}{7}\) =
Answer:
3 – \(\frac{1}{7}\) = 2\(\frac{6}{7}\)
Explanation :
3 – \(\frac{1}{7}\) = \(\frac{21}{7}\) – \(\frac{1}{7}\) = \(\frac{20}{7}\) = 2\(\frac{6}{7}\)

Question 29.
2 – \(\frac{6}{7}\) =
Answer:
2 – \(\frac{6}{7}\) = 1\(\frac{1}{7}\)
Explanation :
2 – \(\frac{6}{7}\) = \(\frac{14}{7}\) – \(\frac{6}{7}\) = \(\frac{8}{7}\) = 1\(\frac{1}{7}\)

Question 30.
4 – \(\frac{3}{7}\) =
Answer:
4 – \(\frac{3}{7}\) = 3\(\frac{4}{7}\)
Explanation :
4 – \(\frac{3}{7}\) = \(\frac{28}{7}\) – \(\frac{3}{7}\) = \(\frac{25}{7}\) = 3\(\frac{4}{7}\)

Question 31.
3 – \(\frac{4}{7}\) =
Answer:
3 – \(\frac{4}{7}\) = 2\(\frac{3}{7}\)
Explanation :
3 – \(\frac{4}{7}\) = \(\frac{21}{7}\) – \(\frac{4}{7}\) = \(\frac{17}{7}\) = 2\(\frac{3}{7}\)

Question 32.
2 – \(\frac{5}{7}\) =
Answer:
2 – \(\frac{5}{7}\) = 1\(\frac{2}{7}\)
Explanation :
2 – \(\frac{5}{7}\) = \(\frac{14}{7}\) – \(\frac{5}{7}\) = \(\frac{9}{7}\) = 1\(\frac{2}{7}\)

Question 33.
3 – \(\frac{3}{4}\) =
Answer:
3 – \(\frac{3}{4}\) = 2\(\frac{1}{4}\)
Explanation :
3 – \(\frac{3}{4}\) = \(\frac{12}{4}\) – \(\frac{3}{4}\) = \(\frac{9}{4}\) = 2\(\frac{1}{4}\)

Question 34.
4 – \(\frac{5}{8}\) =
Answer:
4 – \(\frac{5}{8}\) = 3\(\frac{3}{8}\)
Explanation :
4 – \(\frac{5}{8}\) = \(\frac{32}{8}\) – \(\frac{5}{8}\) = \(\frac{27}{8}\) = 3\(\frac{3}{8}\)

Question 35.
2 – \(\frac{3}{10}\) =
Answer:
2 – \(\frac{3}{10}\) = 1\(\frac{7}{10}\)
Explanation :
2 – \(\frac{3}{10}\) = \(\frac{20}{10}\) – \(\frac{3}{10}\) = \(\frac{17}{10}\) = 1\(\frac{7}{10}\)

Question 36.
3 – \(\frac{2}{5}\) =
Answer:
3 – \(\frac{2}{5}\) = 2\(\frac{3}{5}\)
Explanation :
3 – \(\frac{2}{5}\) = \(\frac{15}{5}\) – \(\frac{2}{5}\) = \(\frac{13}{5}\) = 2\(\frac{3}{5}\)

Question 37.
3 – \(\frac{3}{7}\) =
Answer:
3 – \(\frac{3}{7}\) = 2\(\frac{4}{7}\)
Explanation :
3 – \(\frac{3}{7}\) = \(\frac{21}{7}\) – \(\frac{3}{7}\) = \(\frac{18}{7}\) = 2\(\frac{4}{7}\)

Question 38.
2 – \(\frac{7}{10}\) =
Answer:
2 – \(\frac{7}{10}\) = 1\(\frac{3}{10}\)
Explanation :
2 – \(\frac{7}{10}\) = \(\frac{20}{10}\) – \(\frac{7}{10}\) = \(\frac{13}{10}\) = 1\(\frac{3}{10}\)

Question 39.
2 – \(\frac{5}{10}\) =
Answer:
2 – \(\frac{5}{10}\) = 1\(\frac{1}{2}\)
Explanation :
2 – \(\frac{5}{10}\) = \(\frac{20}{10}\) – \(\frac{5}{10}\) = \(\frac{15}{10}\) = \(\frac{3}{2}\) = 1\(\frac{1}{2}\)

Question 40.
3 – \(\frac{6}{8}\) =
Answer:
3 – \(\frac{6}{8}\) = 2\(\frac{1}{4}\)
Explanation :
3 – \(\frac{6}{8}\) = \(\frac{24}{8}\) – \(\frac{6}{8}\) = \(\frac{18}{8}\) = 2\(\frac{1}{4}\)

Question 41.
4 – \(\frac{3}{12}\) =
Answer:
4 – \(\frac{3}{12}\) = 4 – \(\frac{1}{4}\) = 3\(\frac{3}{4}\)
Explanation :
4 – \(\frac{1}{4}\) = \(\frac{16}{4}\) – \(\frac{1}{4}\) = \(\frac{15}{4}\) = 3\(\frac{3}{4}\)

Question 42.
3 – \(\frac{10}{12}\) =
Answer:
3 – \(\frac{10}{12}\) = 3 – \(\frac{5}{6}\) = 2\(\frac{1}{6}\)
Explanation :
3 – \(\frac{5}{6}\) = \(\frac{18}{6}\) – \(\frac{5}{6}\) = \(\frac{13}{6}\) = 2\(\frac{1}{6}\)

Question 43.
2 – \(\frac{4}{6}\) =
Answer:
2 – \(\frac{4}{6}\) = 2 – \(\frac{2}{3}\) = 1\(\frac{1}{3}\)
Explanation :
2 – \(\frac{2}{3}\) = \(\frac{6}{3}\) – \(\frac{2}{3}\) = \(\frac{4}{3}\) = 1\(\frac{1}{3}\)

Question 44.
4 – \(\frac{4}{12}\) =
Answer:
4 – \(\frac{4}{12}\) = 4 – \(\frac{1}{3}\) = 3\(\frac{2}{3}\)
Explanation :
4 – \(\frac{1}{3}\) = \(\frac{12}{3}\) – \(\frac{1}{3}\) = \(\frac{11}{3}\) = 3\(\frac{2}{3}\)

Eureka Math Grade 5 Module 3 Lesson 5 Problem Set Answer Key

Question 1.
For the following problems, draw a picture using the rectangular fraction model and write the answer. Simplify your answer, if possible.
a. \(\frac{1}{3}\) – \(\frac{1}{4}\) =
b. \(\frac{2}{3}\) – \(\frac{1}{2}\) =
c. \(\frac{5}{6}\) – \(\frac{1}{4}\) =
d. \(\frac{2}{3}\) – \(\frac{1}{7}\) =
e. \(\frac{3}{4}\) – \(\frac{3}{8}\) =
f. \(\frac{3}{4}\) – \(\frac{2}{7}\) =
Answer:
a.
\(\frac{1}{3}\) – \(\frac{1}{4}\)
L.c.m of 3 and 4 is 12
\(\frac{4}{12}\) – \(\frac{3}{12}\) = \(\frac{1}{12}\)

b.
\(\frac{2}{3}\) – \(\frac{1}{2}\)
lcm of 3 and 2 is 6
\(\frac{4}{6}\) – \(\frac{3}{6}\) = \(\frac{1}{6}\)

c.
\(\frac{5}{6}\) – \(\frac{1}{4}\)
lcm of 6 and 4 is 12
\(\frac{10}{12}\) – \(\frac{3}{12}\) = \(\frac{7}{12}\)

d.
\(\frac{2}{3}\) – \(\frac{1}{7}\)
lcm of 3 and 7 is 21 .
\(\frac{14}{21}\) – \(\frac{3}{21}\)  = \(\frac{11}{21}\)

e.
\(\frac{3}{4}\) – \(\frac{3}{8}\)
lcm of 4 and 8 is 8
\(\frac{6}{8}\) – \(\frac{3}{8}\) = \(\frac{3}{8}\)

f.
\(\frac{3}{4}\) – \(\frac{2}{7}\)
lcm of 4 and 7 is 28
\(\frac{21}{28}\) – \(\frac{8}{28}\) = \(\frac{13}{28}\)

Question 2.
Mr. Penman had \(\frac{2}{3}\) liter of salt water. He used \(\frac{1}{5}\) of a liter for an experiment. How much salt water does Mr. Penman have left?
Answer:
Quantity of salt water = \(\frac{2}{3}\)
Quantity of salt water used = \(\frac{1}{5}\)
Quantity of salt water left = \(\frac{2}{3}\) – \(\frac{1}{5}\) = \(\frac{10}{15}\) – \(\frac{3}{15}\)
= \(\frac{7}{15}\) .

Question 3.
Sandra says that \(\frac{4}{7}\) – \(\frac{1}{3}\) = \(\frac{3}{4}\) because all you have to do is subtract the numerators and subtract the denominators. Convince Sandra that she is wrong. You may draw a rectangular fraction model to support your thinking.
Answer:
No, \(\frac{4}{7}\) – \(\frac{1}{3}\) = \(\frac{5}{21}\) not \(\frac{3}{4}\)

Explanation :
\(\frac{4}{7}\) – \(\frac{1}{3}\) = \(\frac{12}{21}\) – \(\frac{7}{21}\) =  \(\frac{5}{21}\)
no, first find the l.c.m of the denominators that is lcm of 7 and 3 is 21 . then multiply the denominators to make 21 and and also multiply same number with the numerator . then after making denominators equal subtract the numerators .

Eureka Math Grade 5 Module 3 Lesson 5 Exit Ticket Answer Key

For the following problems, draw a picture using the rectangular fraction model and write the answer. Simplify your answer, if possible.
a. \(\frac{1}{2}\) – \(\frac{1}{7}\) =
b. \(\frac{3}{5}\) – \(\frac{1}{2}\) =
Answer:
a.
\(\frac{1}{2}\) – \(\frac{1}{7}\)
lcm of 2 and 7 is 14
\(\frac{7}{14}\) – \(\frac{2}{14}\) = \(\frac{5}{14}\)

b.
\(\frac{3}{5}\) – \(\frac{1}{2}\)
lcm of 5 and 2 is 10 .
\(\frac{6}{10}\) – \(\frac{5}{10}\) = \(\frac{1}{10}\)

Eureka Math Grade 5 Module 3 Lesson 5 Homework Answer Key

Question 1.
The picture below shows \(\frac{3}{4}\) of the rectangle shaded. Use the picture to show how to create an equivalent fraction for \(\frac{3}{4}\), and then subtract \(\frac{1}{3}\).
\(\frac{3}{4}\) – \(\frac{1}{3}\) =

Answer:

Explanation :
\(\frac{3}{4}\) – \(\frac{1}{3}\)
l.c.m of 4 and 3 is 12
\(\frac{9}{12}\) – \(\frac{4}{12}\) = \(\frac{5}{12}\)

Question 2.
Find the difference. Use a rectangular fraction model to find common denominators. Simplify your answer, if possible.
a. \(\frac{5}{6}\) – \(\frac{1}{3}\) =
b. \(\frac{2}{3}\) – \(\frac{1}{2}\) =
c. \(\frac{5}{6}\) – \(\frac{1}{4}\) =
d. \(\frac{4}{5}\) – \(\frac{1}{2}\) =
e. \(\frac{2}{3}\) – \(\frac{2}{5}\) =
f. \(\frac{5}{7}\) – \(\frac{2}{3}\) =
Answer:
a.

\(\frac{5}{6}\) – \(\frac{1}{3}\)
Lcm of 6 and 3 is 6 .
\(\frac{5}{6}\) – \(\frac{2}{6}\) = \(\frac{3}{6}\) = \(\frac{1}{2}\)

b.
\(\frac{2}{3}\) – \(\frac{1}{2}\)
lcm of 3 and 2 is 6
\(\frac{4}{6}\) – \(\frac{3}{6}\) = \(\frac{2}{6}\) = \(\frac{1}{3}\)

c.
\(\frac{5}{6}\) – \(\frac{1}{4}\)
lcm of 6 and 4
\(\frac{10}{12}\) – \(\frac{3}{12}\) = \(\frac{7}{12}\)

d.
\(\frac{4}{5}\) – \(\frac{1}{2}\)
lcm of 5 and 2 is 10
\(\frac{8}{10}\) – \(\frac{5}{10}\) = \(\frac{3}{10}\)

e.
\(\frac{2}{3}\) – \(\frac{2}{5}\)
lcm of 3 and 5 is 15
\(\frac{10}{15}\) – \(\frac{6}{15}\)= \(\frac{4}{15}\)

f.
\(\frac{5}{7}\) – \(\frac{2}{3}\)
lcm of 7 and 3 is 21.
\(\frac{15}{21}\) – \(\frac{14}{21}\) = \(\frac{1}{21}\)

Question 3.
Robin used \(\frac{1}{4}\) of a pound of butter to make a cake. Before she started, she had \(\frac{7}{8}\) of a pound of butter. How much butter did Robin have when she was done baking? Give your answer as a fraction of a pound.
Answer:
Quantity of butter used to make cake = \(\frac{1}{4}\)  pound
Quantity of butter with Robin before baking cake = \(\frac{7}{8}\)  pound .
Total Quantity of butter with Robin after baking = \(\frac{7}{8}\)  – \(\frac{1}{4}\) pound  = \(\frac{7}{8}\)  – \(\frac{2}{8}\) = \(\frac{5}{8}\) pound
Therefore, Robin have \(\frac{5}{8}\) pound  when she was done baking .

Question 4.
Katrina needs \(\frac{3}{5}\) kilogram of flour for a recipe. Her mother has \(\frac{3}{7}\) kilogram of flour in her pantry. Is this enough flour for the recipe? If not, how much more will she need?
Answer:
Quantity of Flour Required for Recipe = \(\frac{3}{5}\)
Quantity of Flour with her mother = \(\frac{3}{7}\)
Quantity of Flour Enough or not = \(\frac{3}{7}\) – \(\frac{3}{5}\)  = \(\frac{15}{35}\) – \(\frac{21}{35}\) = – \(\frac{6}{35}\) that means negative indicate doenot enough.
She needs more \(\frac{6}{35}\) Quantity of Flour for the Recipe .