## Engage NY Eureka Math 5th Grade Module 6 Lesson 23 Answer Key

### Eureka Math Grade 5 Module 6 Lesson 23 Sprint Answer Key

A
Change Mixed Numbers into Improper Fractions

Question 1.
1$$\frac{1}{5}$$ =
Answer:
1$$\frac{1}{5}$$ = $$\frac{6}{5}$$

Question 2.
2$$\frac{1}{5}$$ =
Answer:
2$$\frac{1}{5}$$ = $$\frac{11}{5}$$

Question 3.
3$$\frac{1}{5}$$ =
Answer:
3$$\frac{1}{5}$$ = $$\frac{16}{5}$$

Question 4.
4$$\frac{1}{5}$$ =
Answer:
4 $$\frac{1}{5}$$ = $$\frac{21}{5}$$

Question 5.
1$$\frac{1}{4}$$ =
Answer:
1$$\frac{1}{4}$$ = $$\frac{5}{4}$$

Question 6.
1$$\frac{3}{4}$$ =
Answer:
1$$\frac{3}{4}$$ = $$\frac{7}{4}$$

Question 7.
1$$\frac{2}{5}$$ =
Answer:
1$$\frac{2}{5}$$ = $$\frac{7}{5}$$

Question 8.
1$$\frac{3}{5}$$ =
Answer:
1$$\frac{3}{5}$$ = $$\frac{8}{5}$$

Question 9.
1$$\frac{4}{5}$$ =
Answer:
1$$\frac{4}{5}$$ = $$\frac{9}{5}$$

Question 10.
2$$\frac{4}{5}$$ =
Answer:
2$$\frac{4}{5}$$ = $$\frac{14}{5}$$

Question 11.
3$$\frac{4}{5}$$ =
Answer:
3$$\frac{4}{5}$$ = $$\frac{19}{5}$$

Question 12.
2$$\frac{1}{4}$$ =
Answer:
2$$\frac{1}{4}$$  = $$\frac{9}{4}$$

Question 13.
2$$\frac{3}{4}$$ =
Answer:
2$$\frac{3}{4}$$ = $$\frac{11}{4}$$

Question 14.
3$$\frac{1}{4}$$ =
Answer:
3$$\frac{1}{4}$$ = $$\frac{13}{4}$$

Question 15.
3$$\frac{3}{4}$$ =
Answer:
3$$\frac{3}{4}$$ = $$\frac{15}{4}$$

Question 16.
4$$\frac{1}{3}$$ =
Answer:
4$$\frac{1}{3}$$ = $$\frac{1}3{3}$$

Question 17.
4$$\frac{2}{3}$$ =
Answer:
4$$\frac{2}{3}$$ = $$\frac{14}{3}$$

Question 18.
2$$\frac{3}{5}$$ =
Answer:
2$$\frac{3}{5}$$ = $$\frac{13}{5}$$

Question 19.
3$$\frac{3}{5}$$ =
Answer:
3$$\frac{3}{5}$$ = $$\frac{18}{5}$$

Question 20.
4$$\frac{3}{5}$$ =
Answer:
4$$\frac{3}{5}$$ = $$\frac{23}{5}$$

Question 21.
2$$\frac{1}{6}$$ =
Answer:
2$$\frac{1}{6}$$ = $$\frac{1}{6}$$

Question 22.
3$$\frac{1}{8}$$ =
Answer:
3$$\frac{1}{8}$$ = $$\frac{25}{8}$$

Question 23.
2$$\frac{7}{10}$$ =
Answer:
2$$\frac{7}{10}$$ = $$\frac{27}{10}$$

Question 24.
4$$\frac{9}{10}$$ =
Answer:
4$$\frac{9}{10}$$ =$$\frac{49}{10}$$

Question 25.
1$$\frac{1}{8}$$ =
Answer:
1$$\frac{1}{8}$$  = $$\frac{9}{8}$$

Question 26.
1$$\frac{5}{6}$$ =
Answer:
1$$\frac{5}{6}$$ = $$\frac{11}{6}$$

Question 27.
4$$\frac{5}{6}$$ =
Answer:
4$$\frac{5}{6}$$ = $$\frac{29}{6}$$

Question 28.
4$$\frac{5}{8}$$ =
Answer:
4$$\frac{5}{8}$$ = $$\frac{37}{8}$$

Question 29.
1$$\frac{5}{8}$$ =
Answer:
1$$\frac{5}{8}$$  = $$\frac{13}{8}$$

Question 30.
2$$\frac{3}{8}$$ =
Answer:
2$$\frac{3}{8}$$ = $$\frac{19}{8}$$

Question 31.
3$$\frac{3}{10}$$ =
Answer:
3$$\frac{3}{10}$$ = $$\frac{33}{10}$$

Question 32.
4$$\frac{7}{10}$$ =
Answer:
4$$\frac{7}{10}$$ = $$\frac{47}{10}$$

Question 33.
4$$\frac{4}{5}$$ =
Answer:
4$$\frac{4}{5}$$  = $$\frac{24}{5}$$

Question 34.
4$$\frac{1}{8}$$ =
Answer:
4$$\frac{1}{8}$$ = $$\frac{33}{8}$$

Question 35.
4$$\frac{3}{8}$$ =
Answer:
4$$\frac{3}{8}$$ = $$\frac{35}{8}$$

Question 36.
4$$\frac{7}{8}$$ =
Answer:
4$$\frac{7}{8}$$ = $$\frac{39}{8}$$

Question 37.
1$$\frac{5}{12}$$ =
Answer:
1$$\frac{5}{12}$$ = $$\frac{17}{12}$$

Question 38.
1$$\frac{7}{12}$$ =
Answer:
1$$\frac{7}{12}$$ = $$\frac{19}{12}$$

Question 39.
2$$\frac{1}{12}$$ =
Answer:
2$$\frac{1}{12}$$ = $$\frac{25}{12}$$

Question 40.
3$$\frac{1}{12}$$ =
Answer:
3$$\frac{1}{12}$$= $$\frac{37}{12}$$

Question 41.
2$$\frac{7}{12}$$ =
Answer:
2$$\frac{7}{12}$$ = $$\frac{31}{12}$$

Question 42.
3$$\frac{5}{12}$$ =
Answer:
3$$\frac{5}{12}$$ = $$\frac{41}{12}$$

Question 43.
3$$\frac{11}{12}$$ =
Answer:
3$$\frac{11}{12}$$ = $$\frac{47}{12}$$

Question 44.
4$$\frac{7}{12}$$ =
Answer:
4$$\frac{7}{12}$$ = $$\frac{55}{12}$$

B
Change Mixed Numbers into Improper Fractions

Question 1.
1$$\frac{1}{2}$$ =
Answer:
1$$\frac{1}{2}$$  = $$\frac{3}{2}$$

Question 2.
2$$\frac{1}{2}$$ =
Answer:
2$$\frac{1}{2}$$  = $$\frac{5}{2}$$

Question 3.
3$$\frac{1}{2}$$ =
Answer:
3$$\frac{1}{2}$$  = $$\frac{7}{2}$$

Question 4.
4$$\frac{1}{2}$$ =
Answer:
4$$\frac{1}{2}$$  = $$\frac{9}{2}$$

Question 5.
1$$\frac{1}{3}$$ =
Answer:
1$$\frac{1}{3}$$  = $$\frac{4}{3}$$

Question 6.
1$$\frac{2}{3}$$ =
Answer:
1$$\frac{2}{3}$$  = $$\frac{5}{3}$$

Question 7.
1$$\frac{3}{10}$$ =
Answer:
1$$\frac{3}{10}$$  = $$\frac{13}{10}$$

Question 8.
1$$\frac{7}{10}$$ =
Answer:
1$$\frac{7}{10}$$  = $$\frac{17}{10}$$

Question 9.
1$$\frac{9}{10}$$ =
Answer:
1$$\frac{9}{10}$$  = $$\frac{19}{10}$$

Question 10.
2$$\frac{9}{10}$$ =
Answer:
2$$\frac{9}{10}[/latex = [latex]\frac{29}{10}[/latex Question 11. 3[latex]\frac{9}{10}$$ =
Answer:
3$$\frac{9}{10}[/latex = [latex]\frac{39}{10}[/latex Question 12. 2[latex]\frac{1}{3}$$ =
Answer:
2$$\frac{1}{3}$$ = $$\frac{7}{3}$$

Question 13.
2$$\frac{2}{3}$$ =
Answer:
2$$\frac{2}{3}$$ =$$\frac{8}{3}$$

Question 14.
3$$\frac{1}{3}$$ =
Answer:
3$$\frac{1}{3}$$ = $$\frac{10}{3}$$

Question 15.
3$$\frac{2}{3}$$ =
Answer:
3$$\frac{2}{3}$$ = $$\frac{11}{3}$$

Question 16.
4$$\frac{1}{4}$$ =
Answer:
4$$\frac{1}{4}$$  = $$\frac{17}{4}$$

Question 17.
4$$\frac{3}{4}$$ =
Answer:
4$$\frac{3}{4}$$ = $$\frac{19}{4}$$

Question 18.
2$$\frac{2}{5}$$ =
Answer:
2$$\frac{2}{5}$$ = $$\frac{12}{5}$$

Question 19.
3$$\frac{2}{5}$$ =
Answer:
3$$\frac{2}{5}$$ = $$\frac{17}{5}$$

Question 20.
4$$\frac{2}{5}$$ =
Answer:
4$$\frac{2}{5}$$ = $$\frac{22}{5}$$

Question 21.
3$$\frac{1}{6}$$ =
Answer:
3$$\frac{1}{6}$$ = $$\frac{19}{6}$$

Question 22.
2$$\frac{1}{8}$$ =
Answer:
2$$\frac{1}{8}$$ = $$\frac{17}{6}$$

Question 23.
2$$\frac{3}{10}$$ =
Answer:
2$$\frac{3}{10}$$ = $$\frac{23}{10}$$

Question 24.
3$$\frac{1}{10}$$ =
Answer:
3$$\frac{1}{10}$$ = $$\frac{31}{10}$$

Question 25.
1$$\frac{1}{6}$$ =
Answer:
1$$\frac{1}{6}$$ = $$\frac{7}{6}$$

Question 26.
1$$\frac{3}{8}$$ =
Answer:
1$$\frac{3}{8}$$ = $$\frac{11}{8}$$

Question 27.
3$$\frac{5}{6}$$ =
Answer:
3$$\frac{5}{6}$$  = $$\frac{23}{6}$$

Question 28.
3$$\frac{5}{8}$$ =
Answer:
3$$\frac{5}{8}$$  = $$\frac{29}{8}$$

Question 29.
2$$\frac{5}{8}$$ =
Answer:
2$$\frac{5}{8}$$ = $$\frac{21}{8}$$

Question 30.
1$$\frac{7}{8}$$ =
Answer:
1$$\frac{7}{8}$$  = $$\frac{15}{8}$$

Question 31.
4$$\frac{3}{10}$$ =
Answer:
4$$\frac{3}{10}$$ = $$\frac{43}{10}$$

Question 32.
3$$\frac{7}{10}$$ =
Answer:
3$$\frac{7}{10}$$ =$$\frac{37}{10}$$

Question 33.
2$$\frac{5}{6}$$ =
Answer:
2$$\frac{5}{6}$$  =$$\frac{17}{6}$$

Question 34.
2$$\frac{7}{8}$$ =
Answer:
2$$\frac{7}{8}$$  = $$\frac{23}{8}$$

Question 35.
3$$\frac{7}{8}$$ =
Answer:
3$$\frac{7}{8}$$  =$$\frac{31}{8}$$

Question 36.
4$$\frac{1}{6}$$ =
Answer:
4$$\frac{1}{6}$$ = $$\frac{25}{6}$$

Question 37.
1$$\frac{1}{12}$$ =
Answer:
1$$\frac{1}{12}$$  =$$\frac{13}{12}$$

Question 38.
1$$\frac{11}{12}$$ =
Answer:
1$$\frac{11}{12}$$  = $$\frac{23}{12}$$

Question 39.
4$$\frac{1}{12}$$ =
Answer:
4$$\frac{1}{12}$$  = $$\frac{49}{12}$$

Question 40.
2$$\frac{5}{12}$$ =
Answer:
2$$\frac{5}{12}$$  = $$\frac{29}{12}$$

Question 41.
2$$\frac{11}{12}$$ =
Answer:
2$$\frac{11}{12}$$  = $$\frac{35}{12}$$

Question 42.
3$$\frac{7}{12}$$ =
Answer:
3$$\frac{7}{12}$$ = $$\frac{43}{12}$$

Question 43.
4$$\frac{5}{12}$$ =
Answer:
4$$\frac{5}{12}$$ = $$\frac{53}{12}$$

Question 44.
4$$\frac{11}{12}$$ =
Answer:
4$$\frac{11}{12}$$  = $$\frac{59}{12}$$

### Eureka Math Grade 5 Module 6 Lesson 23 Homework Answer Key

Question 1.
In the diagram, the length of Figure S is $$\frac{1}{2}$$ the length of Figure T. If S has an area of 368 cm2, find the perimeter of the figure.

Answer:
Length of Figure T = x
length of Figure S = $$\frac{1}{2}$$ the length of Figure T = $$\frac{x}{2}$$ .
Breadth = 16 cm
Area of Figure S = 368 cm2,
Area = Length × Breadth = $$\frac{x}{2}$$ × 16 = 368
$$\frac{x}{2}$$ = 23
x = 24 cms.
Length of figure S = $$\frac{x}{2}$$ = 23 cms .
Length of figure T = x = 46 cms .
Total Length of Figure S and T = 23 + 46 = 69 cms
Perimeter of given Figure = S +T = 2 ( l + b) = 2 ( 69 + 16 ) = 2 ( 85 ) = 170 cms .

The following problems are puzzles for your enjoyment. They are intended to encourage working together and family problem-solving fun and are not a required element of this homework assignment.
Question 2.
Take 12 matchsticks arranged in a grid as shown below, and remove 2 matchsticks so 2 squares remain. How can you do this? Draw the new arrangement.

Answer:

If we remove any one vertical match sticks or one horizontal match sticks in the middle then 2 squares will be remained and is shown in below figure .

Question 3.
Moving only 3 matchsticks makes the fish turn around and swim the opposite way. Which matchsticks did you move? Draw the new shape.

Answer: