Engage NY Eureka Math 5th Grade Module 3 Lesson 14 Answer Key

A
Make Larger Units

Question 1.
$$\frac{2}{4}$$ =
$$\frac{2}{4}$$ = $$\frac{2 × 2}{4 × 2}$$ = $$\frac{4}{8}$$
Explanation :
Multiply numerator and denominator by 2 to make the given fraction into a bigger fraction .

Question 2.
$$\frac{2}{6}$$ =
$$\frac{2}{6}$$ = $$\frac{2 × 2}{6 × 2}$$ = $$\frac{4}{12}$$
Explanation :
Multiply numerator and denominator by 2 or another number to make the given fraction into a larger fraction unit .

Question 3.
$$\frac{2}{8}$$ =
$$\frac{2}{8}$$ = $$\frac{2 × 2}{8 × 2}$$ = $$\frac{4}{16}$$
Explanation :
Multiply numerator and denominator by 2 or another number to make the given fraction into a larger fraction unit .

Question 4.
$$\frac{5}{10}$$ =
$$\frac{5}{10}$$ = $$\frac{5 × 2}{10 × 2}$$ = $$\frac{10}{20}$$
Explanation :
Multiply numerator and denominator by 2 or another number to make the given fraction into a larger fraction unit .

Question 5.
$$\frac{5}{15}$$ =
$$\frac{5}{15}$$ = $$\frac{5 × 2}{15 × 2}$$ = $$\frac{10}{30}$$
Explanation :
Multiply numerator and denominator by 2 or another number to make the given fraction into a larger fraction unit .

Question 6.
$$\frac{5}{20}$$ =
$$\frac{5}{20}$$ = $$\frac{5 × 2}{20 × 2}$$ = $$\frac{10}{40}$$
Explanation :
Multiply numerator and denominator by 2 or another number to make the given fraction into a larger fraction unit .

Question 7.
$$\frac{4}{8}$$ =
$$\frac{4}{8}$$ = $$\frac{4 × 2}{8 × 2}$$ = $$\frac{8}{16}$$
Explanation :
Multiply numerator and denominator by 2 or another number to make the given fraction into a larger fraction unit .

Question 8.
$$\frac{4}{12}$$ =
$$\frac{4}{12}$$ = $$\frac{4 × 2}{12 × 2}$$ = $$\frac{8}{24}$$
Explanation :
Multiply numerator and denominator by 2 or another number to make the given fraction into a larger fraction unit .

Question 9.
$$\frac{4}{16}$$ =
$$\frac{4}{16}$$ = $$\frac{4 × 2}{16 × 2}$$ = $$\frac{8}{32}$$
Explanation :
Multiply numerator and denominator by 2 or another number to make the given fraction into a larger fraction unit .

Question 10.
$$\frac{3}{6}$$ =
$$\frac{3}{6}$$ = $$\frac{3 × 2}{6 × 2}$$ = $$\frac{6}{12}$$
Explanation :
Multiply numerator and denominator by 2 or another number to make the given fraction into a larger fraction unit .

Question 11.
$$\frac{3}{9}$$ =
$$\frac{3}{9}$$ = $$\frac{3 × 2}{9 × 2}$$ = $$\frac{6}{18}$$
Explanation :
Multiply numerator and denominator by 2 or another number to make the given fraction into a larger fraction unit .

Question 12.
$$\frac{3}{12}$$ =
$$\frac{3}{12}$$ = $$\frac{3 × 2}{12 × 2}$$ = $$\frac{6}{24}$$
Explanation :
Multiply numerator and denominator by 2 or another number to make the given fraction into a larger fraction unit .

Question 13.
$$\frac{4}{6}$$ =
$$\frac{4}{6}$$ = $$\frac{4 × 2}{6 × 2}$$ = $$\frac{8}{12}$$
Explanation :
Multiply numerator and denominator by 2 or another number to make the given fraction into a larger fraction unit .

Question 14.
$$\frac{6}{12}$$ =
$$\frac{6}{12}$$ = $$\frac{6 × 2}{12 × 2}$$ = $$\frac{12}{24}$$
Explanation :
Multiply numerator and denominator by 2 or another number to make the given fraction into a larger fraction unit .

Question 15.
$$\frac{6}{18}$$ =
$$\frac{6}{8}$$ = $$\frac{6 × 2}{8 × 2}$$ = $$\frac{12}{16}$$
Explanation :
Multiply numerator and denominator by 2 or another number to make the given fraction into a larger fraction unit .

Question 16.
$$\frac{6}{30}$$ =
$$\frac{6}{30}$$ = $$\frac{6 × 2}{30 × 2}$$ = $$\frac{12}{60}$$
Explanation :
Multiply numerator and denominator by 2 or another number to make the given fraction into a larger fraction unit .

Question 17.
$$\frac{6}{9}$$ =
$$\frac{6}{9}$$ = $$\frac{6 × 2}{9 × 2}$$ = $$\frac{12}{18}$$
Explanation :
Multiply numerator and denominator by 2 or another number to make the given fraction into a larger fraction unit .

Question 18.
$$\frac{7}{14}$$ =
$$\frac{7}{14}$$ = $$\frac{7 × 2}{14 × 2}$$ = $$\frac{14}{28}$$
Explanation :
Multiply numerator and denominator by 2 or another number to make the given fraction into a larger fraction unit .

Question 19.
$$\frac{7}{21}$$ =
$$\frac{7}{21}$$ = $$\frac{7 × 2}{21 × 2}$$ = $$\frac{14}{42}$$
Explanation :
Multiply numerator and denominator by 2 or another number to make the given fraction into a larger fraction unit .

Question 20.
$$\frac{7}{42}$$ =
$$\frac{7}{42}$$ = $$\frac{7 × 2}{42 × 2}$$ = $$\frac{14}{84}$$
Explanation :
Multiply numerator and denominator by 2 or another number to make the given fraction into a larger fraction unit .

Question 21.
$$\frac{8}{12}$$ =
$$\frac{8}{12}$$ = $$\frac{8 × 2}{12 × 2}$$ = $$\frac{16}{24}$$
Explanation :
Multiply numerator and denominator by 2 or another number to make the given fraction into a larger fraction unit .

Question 22.
$$\frac{9}{18}$$ =
$$\frac{9}{18}$$ = $$\frac{9 × 2}{18 × 2}$$ = $$\frac{18}{36}$$
Explanation :
Multiply numerator and denominator by 2 or another number to make the given fraction into a larger fraction unit .

Question 23.
$$\frac{9}{27}$$ =
$$\frac{9}{18}$$ = $$\frac{9 × 2}{27 × 2}$$ = $$\frac{18}{54}$$
Explanation :
Multiply numerator and denominator by 2 or another number to make the given fraction into a larger fraction unit .

Question 24.
$$\frac{2}{4}$$ =
$$\frac{2}{4}$$ = $$\frac{2 × 2}{4 × 2}$$ = $$\frac{4}{8}$$
Explanation :
Multiply numerator and denominator by 2 or another number to make the given fraction into a larger fraction unit .

Question 25.
$$\frac{8}{12}$$ =
$$\frac{8}{12}$$ = $$\frac{8 × 2}{12 × 2}$$ = $$\frac{16}{24}$$
Explanation :
Multiply numerator and denominator by 2 or another number to make the given fraction into a larger fraction unit .

Question 26.
$$\frac{8}{16}$$ =
$$\frac{8}{16}$$ = $$\frac{8 × 2}{16 × 2}$$ = $$\frac{16}{32}$$
Explanation :
Multiply numerator and denominator by 2 or another number to make the given fraction into a larger fraction unit .

Question 27.
$$\frac{8}{24}$$ =
$$\frac{8}{24}$$ = $$\frac{8 × 2}{24 × 2}$$ = $$\frac{16}{48}$$
Explanation :
Multiply numerator and denominator by 2 or another number to make the given fraction into a larger fraction unit .

Question 28.
$$\frac{8}{64}$$ =
$$\frac{8}{64}$$ = $$\frac{8 × 2}{64 × 2}$$ = $$\frac{16}{128}$$
Explanation :
Multiply numerator and denominator by 2 or another number to make the given fraction into a larger fraction unit .

Question 29.
$$\frac{12}{18}$$ =
$$\frac{12}{18}$$ = $$\frac{12 × 2}{18 × 2}$$ = $$\frac{24}{36}$$
Explanation :
Multiply numerator and denominator by 2 or another number to make the given fraction into a larger fraction unit .

Question 30.
$$\frac{12}{16}$$ =
$$\frac{12}{16}$$ = $$\frac{12 × 2}{16 × 2}$$ = $$\frac{24}{32}$$
Explanation :
Multiply numerator and denominator by 2 or another number to make the given fraction into a larger fraction unit .

Question 31.
$$\frac{9}{12}$$ =
$$\frac{9}{12}$$ = $$\frac{9 × 2}{12 × 2}$$ = $$\frac{18}{24}$$
Explanation :
Multiply numerator and denominator by 2 or another number to make the given fraction into a larger fraction unit .

Question 32.
$$\frac{6}{8}$$ =
$$\frac{6}{8}$$ = $$\frac{6 × 2}{8 × 2}$$ = $$\frac{12}{16}$$
Explanation :
Multiply numerator and denominator by 2 or another number to make the given fraction into a larger fraction unit .

Question 33.
$$\frac{10}{12}$$ =
$$\frac{10}{12}$$ = $$\frac{10 × 2}{12 × 2}$$ = $$\frac{20}{24}$$
Explanation :
Multiply numerator and denominator by 2 or another number to make the given fraction into a larger fraction unit .

Question 34.
$$\frac{15}{18}$$ =
$$\frac{15}{18}$$ = $$\frac{15 × 2}{18 × 2}$$ = $$\frac{30}{36}$$
Explanation :
Multiply numerator and denominator by 2 or another number to make the given fraction into a larger fraction unit .

Question 35.
$$\frac{8}{10}$$ =
$$\frac{8}{10}$$ = $$\frac{8 × 2}{10 × 2}$$ = $$\frac{16}{20}$$
Explanation :
Multiply numerator and denominator by 2 or another number to make the given fraction into a larger fraction unit .

Question 36.
$$\frac{16}{20}$$ =
$$\frac{16}{20}$$ = $$\frac{16 × 2}{20 × 2}$$ = $$\frac{32}{40}$$
Explanation :
Multiply numerator and denominator by 2 or another number to make the given fraction into a larger fraction unit .

Question 37.
$$\frac{12}{15}$$ =
$$\frac{12}{15}$$ = $$\frac{12 × 2}{15 × 2}$$ = $$\frac{24}{30}$$
Explanation :
Multiply numerator and denominator by 2 or another number to make the given fraction into a larger fraction unit .

Question 38.
$$\frac{18}{27}$$ =
$$\frac{18}{27}$$ = $$\frac{18 × 2}{27 × 2}$$ = $$\frac{36}{54}$$
Explanation :
Multiply numerator and denominator by 2 or another number to make the given fraction into a larger fraction unit .

Question 39.
$$\frac{27}{36}$$ =
$$\frac{27}{36}$$ = $$\frac{27 × 2}{36 × 2}$$ = $$\frac{54}{72}$$
Explanation :
Multiply numerator and denominator by 2 or another number to make the given fraction into a larger fraction unit .

Question 40.
$$\frac{32}{40}$$ =
$$\frac{32}{40}$$ = $$\frac{32 × 2}{40 × 2}$$ = $$\frac{64}{80}$$
Explanation :
Multiply numerator and denominator by 2 or another number to make the given fraction into a larger fraction unit .

Question 41.
$$\frac{45}{54}$$ =
$$\frac{45}{54}$$ = $$\frac{45 × 2}{54 × 2}$$ = $$\frac{90}{108}$$
Explanation :
Multiply numerator and denominator by 2 or another number to make the given fraction into a larger fraction unit .

Question 42.
$$\frac{24}{36}$$ =
$$\frac{24}{36}$$ = $$\frac{24 × 2}{36 × 2}$$ = $$\frac{48}{72}$$
Explanation :
Multiply numerator and denominator by 2 or another number to make the given fraction into a larger fraction unit .

Question 43.
$$\frac{60}{72}$$ =
$$\frac{60}{72}$$ = $$\frac{60 × 2}{72 × 2}$$ = $$\frac{120}{144}$$
Explanation :
Multiply numerator and denominator by 2 or another number to make the given fraction into a larger fraction unit .

Question 44.
$$\frac{48}{60}$$ =
$$\frac{48}{60}$$ = $$\frac{48 × 2}{60 × 2}$$ = $$\frac{96}{120}$$
Explanation :
Multiply numerator and denominator by 2 or another number to make the given fraction into a larger fraction unit .

B
Make Larger Units

Question 1.
$$\frac{5}{10}$$ =
$$\frac{5}{10}$$ = $$\frac{5 × 2}{10 × 2}$$ = $$\frac{10}{20}$$
Explanation :
Multiply numerator and denominator by 2 or another number to make the given fraction into a larger fraction unit .

Question 2.
$$\frac{5}{15}$$ =
$$\frac{5}{15}$$ = $$\frac{5 × 2}{15 × 2}$$ = $$\frac{10}{30}$$
Explanation :
Multiply numerator and denominator by 2 or another number to make the given fraction into a larger fraction unit .

Question 3.
$$\frac{5}{20}$$ =
$$\frac{5}{20}$$ = $$\frac{5 × 2}{20 × 2}$$ = $$\frac{10}{40}$$
Explanation :
Multiply numerator and denominator by 2 or another number to make the given fraction into a larger fraction unit .

Question 4.
$$\frac{2}{4}$$ =
$$\frac{2}{4}$$ = $$\frac{2 × 2}{4 × 2}$$ = $$\frac{4}{8}$$
Explanation :
Multiply numerator and denominator by 2 or another number to make the given fraction into a larger fraction unit .

Question 5.
$$\frac{2}{6}$$ =
$$\frac{2}{6}$$ = $$\frac{2 × 2}{6 × 2}$$ = $$\frac{4}{12}$$
Explanation :
Multiply numerator and denominator by 2 or another number to make the given fraction into a larger fraction unit .

Question 6.
$$\frac{2}{8}$$ =
$$\frac{2}{8}$$ = $$\frac{2 × 2}{8 × 2}$$ = $$\frac{4}{16}$$
Explanation :
Multiply numerator and denominator by 2 or another number to make the given fraction into a larger fraction unit .

Question 7.
$$\frac{3}{6}$$ =
$$\frac{3}{6}$$ = $$\frac{3 × 2}{6 × 2}$$ = $$\frac{5}{12}$$
Explanation :
Multiply numerator and denominator by 2 or another number to make the given fraction into a larger fraction unit .

Question 8.
$$\frac{3}{9}$$ =
$$\frac{2}{4}$$ = $$\frac{2 × 2}{4 × 2}$$ = $$\frac{4}{8}$$
Explanation :
Multiply numerator and denominator by 2 or another number to make the given fraction into a larger fraction unit .

Question 9.
$$\frac{3}{12}$$ =
$$\frac{3}{12}$$ = $$\frac{3 × 2}{12 × 2}$$ = $$\frac{6}{24}$$
Explanation :
Multiply numerator and denominator by 2 or another number to make the given fraction into a larger fraction unit .

Question 10.
$$\frac{4}{8}$$ =
$$\frac{4}{8}$$ = $$\frac{4 × 2}{8 × 2}$$ = $$\frac{8}{16}$$
Explanation :
Multiply numerator and denominator by 2 or another number to make the given fraction into a larger fraction unit .

Question 11.
$$\frac{4}{12}$$ =
$$\frac{4}{12}$$ = $$\frac{4 × 2}{12 × 2}$$ = $$\frac{8}{24}$$
Explanation :
Multiply numerator and denominator by 2 or another number to make the given fraction into a larger fraction unit .

Question 12.
$$\frac{4}{16}$$ =
$$\frac{4}{16}$$ = $$\frac{4 × 2}{16 × 2}$$ = $$\frac{8}{32}$$
Explanation :
Multiply numerator and denominator by 2 or another number to make the given fraction into a larger fraction unit .

Question 13.
$$\frac{4}{6}$$ =
$$\frac{4}{6}$$ = $$\frac{4 × 2}{6 × 2}$$ = $$\frac{8}{12}$$
Explanation :
Multiply numerator and denominator by 2 or another number to make the given fraction into a larger fraction unit .

Question 14.
$$\frac{7}{14}$$ =
$$\frac{7}{14}$$ = $$\frac{7 × 2}{14 × 2}$$ = $$\frac{14}{28}$$
Explanation :
Multiply numerator and denominator by 2 or another number to make the given fraction into a larger fraction unit .

Question 15.
$$\frac{7}{21}$$ =
$$\frac{7}{21}$$ = $$\frac{7 × 2}{21 × 2}$$ = $$\frac{14}{42}$$
Explanation :
Multiply numerator and denominator by 2 or another number to make the given fraction into a larger fraction unit .

Question 16.
$$\frac{7}{35}$$ =
$$\frac{7}{35}$$ = $$\frac{7 × 2}{35 × 2}$$ = $$\frac{14}{70}$$
Explanation :
Multiply numerator and denominator by 2 or another number to make the given fraction into a larger fraction unit .

Question 17.
$$\frac{6}{9}$$ =
$$\frac{6}{9}$$ = $$\frac{6 × 2}{9 × 2}$$ = $$\frac{12}{18}$$
Explanation :
Multiply numerator and denominator by 2 or another number to make the given fraction into a larger fraction unit .

Question 18.
$$\frac{6}{12}$$ =
$$\frac{6}{12}$$ = $$\frac{6 × 2}{12 × 2}$$ = $$\frac{12}{24}$$
Explanation :
Multiply numerator and denominator by 2 or another number to make the given fraction into a larger fraction unit .

Question 19.
$$\frac{6}{18}$$ =
$$\frac{6}{18}$$ = $$\frac{6 × 2}{18 × 2}$$ = $$\frac{12}{36}$$
Explanation :
Multiply numerator and denominator by 2 or another number to make the given fraction into a larger fraction unit .

Question 20.
$$\frac{6}{36}$$ =
$$\frac{6}{36}$$ = $$\frac{6 × 2}{36 × 2}$$ = $$\frac{12}{72}$$
Explanation :
Multiply numerator and denominator by 2 or another number to make the given fraction into a larger fraction unit .

Question 21.
$$\frac{8}{12}$$ =
$$\frac{8}{12}$$ = $$\frac{8 × 2}{12 × 2}$$ = $$\frac{16}{24}$$
Explanation :
Multiply numerator and denominator by 2 or another number to make the given fraction into a larger fraction unit .

Question 22.
$$\frac{8}{16}$$ =
$$\frac{8}{16}$$ = $$\frac{8 × 2}{16 × 2}$$ = $$\frac{16}{32}$$
Explanation :
Multiply numerator and denominator by 2 or another number to make the given fraction into a larger fraction unit .

Question 23.
$$\frac{8}{24}$$ =
$$\frac{8}{24}$$ = $$\frac{8 × 2}{24 × 2}$$ = $$\frac{16}{48}$$
Explanation :
Multiply numerator and denominator by 2 or another number to make the given fraction into a larger fraction unit .

Question 24.
$$\frac{8}{56}$$ =
$$\frac{8}{56}$$ = $$\frac{8 × 2}{56 × 2}$$ = $$\frac{16}{112}$$
Explanation :
Multiply numerator and denominator by 2 or another number to make the given fraction into a larger fraction unit .

Question 25.
$$\frac{8}{12}$$ =
$$\frac{8}{12}$$ = $$\frac{8 × 2}{12 × 2}$$ = $$\frac{16}{24}$$
Explanation :
Multiply numerator and denominator by 2 or another number to make the given fraction into a larger fraction unit .

Question 26.
$$\frac{9}{18}$$ =
$$\frac{8}{12}$$ = $$\frac{8 × 2}{12 × 2}$$ = $$\frac{16}{24}$$
Explanation :
Multiply numerator and denominator by 2 or another number to make the given fraction into a larger fraction unit .

Question 27.
$$\frac{9}{27}$$ =
$$\frac{9}{27}$$ = $$\frac{9 × 2}{27 × 2}$$ = $$\frac{18}{54}$$
Explanation :
Multiply numerator and denominator by 2 or another number to make the given fraction into a larger fraction unit .

Question 28.
$$\frac{9}{72}$$ =
$$\frac{9}{72}$$ = $$\frac{9 × 2}{72 × 2}$$ = $$\frac{18}{144}$$
Explanation :
Multiply numerator and denominator by 2 or another number to make the given fraction into a larger fraction unit .

Question 29.
$$\frac{12}{18}$$ =
$$\frac{12}{18}$$ = $$\frac{12 × 2}{18 × 2}$$ = $$\frac{24}{36}$$
Explanation :
Multiply numerator and denominator by 2 or another number to make the given fraction into a larger fraction unit .

Question 30.
$$\frac{12}{16}$$ =
$$\frac{12}{16}$$ = $$\frac{12 × 2}{16 × 2}$$ = $$\frac{24}{32}$$
Explanation :
Multiply numerator and denominator by 2 or another number to make the given fraction into a larger fraction unit .

Question 31.
$$\frac{9}{12}$$ =
$$\frac{9}{12}$$ = $$\frac{9 × 2}{12 × 2}$$ = $$\frac{18}{24}$$
Explanation :
Multiply numerator and denominator by 2 or another number to make the given fraction into a larger fraction unit .

Question 32.
$$\frac{12}{16}$$ =
$$\frac{12}{16}$$ = $$\frac{12 × 2}{16 × 2}$$ = $$\frac{24}{32}$$
Explanation :
Multiply numerator and denominator by 2 or another number to make the given fraction into a larger fraction unit .

Question 33.
$$\frac{8}{10}$$ =
$$\frac{8}{10}$$ = $$\frac{8 × 2}{10 × 2}$$ = $$\frac{16}{20}$$
Explanation :
Multiply numerator and denominator by 2 or another number to make the given fraction into a larger fraction unit .

Question 34.
$$\frac{16}{20}$$ =
$$\frac{16}{20}$$ = $$\frac{16 × 2}{20 × 2}$$ = $$\frac{32}{40}$$
Explanation :
Multiply numerator and denominator by 2 or another number to make the given fraction into a larger fraction unit .

Question 35.
$$\frac{12}{15}$$ =
$$\frac{12}{15}$$ = $$\frac{12 × 2}{15 × 2}$$ = $$\frac{24}{30}$$
Explanation :
Multiply numerator and denominator by 2 or another number to make the given fraction into a larger fraction unit .

Question 36.
$$\frac{10}{12}$$ =
$$\frac{10}{12}$$ = $$\frac{10 × 2}{12 × 2}$$ = $$\frac{20}{24}$$
Explanation :
Multiply numerator and denominator by 2 or another number to make the given fraction into a larger fraction unit .

Question 37.
$$\frac{15}{18}$$ =
$$\frac{15}{18}$$ = $$\frac{15 × 2}{18 × 2}$$ = $$\frac{30}{36}$$
Explanation :
Multiply numerator and denominator by 2 or another number to make the given fraction into a larger fraction unit .

Question 38.
$$\frac{16}{24}$$ =
$$\frac{16}{24}$$ = $$\frac{16 × 2}{24 × 2}$$ = $$\frac{32}{48}$$
Explanation :
Multiply numerator and denominator by 2 or another number to make the given fraction into a larger fraction unit .

Question 39.
$$\frac{24}{32}$$ =
$$\frac{24}{32}$$ = $$\frac{24 × 2}{32 × 2}$$ = $$\frac{48}{64}$$
Explanation :
Multiply numerator and denominator by 2 or another number to make the given fraction into a larger fraction unit .

Question 40.
$$\frac{36}{45}$$ =
$$\frac{36}{45}$$ = $$\frac{36 × 2}{45 × 2}$$ = $$\frac{72}{90}$$
Explanation :
Multiply numerator and denominator by 2 or another number to make the given fraction into a larger fraction unit .

Question 41.
$$\frac{40}{48}$$ =
$$\frac{40}{48}$$ = $$\frac{40 × 2}{48 × 2}$$ = $$\frac{80}{96}$$
Explanation :
Multiply numerator and denominator by 2 or another number to make the given fraction into a larger fraction unit .

Question 42.
$$\frac{24}{36}$$ =
$$\frac{24}{36}$$ = $$\frac{24 × 2}{36 × 2}$$ = $$\frac{48}{72}$$
Explanation :
Multiply numerator and denominator by 2 or another number to make the given fraction into a larger fraction unit .

Question 43.
$$\frac{48}{60}$$ =
$$\frac{48}{60}$$ = $$\frac{48 × 2}{60 × 2}$$ = $$\frac{96}{120}$$
Explanation :
Multiply numerator and denominator by 2 or another number to make the given fraction into a larger fraction unit .

Question 44.
$$\frac{60}{72}$$ =
$$\frac{60}{72}$$ = $$\frac{60 × 2}{72 × 2}$$ = $$\frac{120}{144}$$
Explanation :
Multiply numerator and denominator by 2 or another number to make the given fraction into a larger fraction unit .

Eureka Math Grade 5 Module 3 Lesson 14 Problem Set Answer Key

Question 1.
Rearrange the terms so that you can add or subtract mentally. Then, solve.
a. $$\frac{1}{4}$$ + 2$$\frac{2}{3}$$ + $$\frac{7}{4}$$ + $$\frac{1}{3}$$
b. 2$$\frac{3}{5}$$ – $$\frac{3}{4}$$ + $$\frac{2}{5}$$
c. 4$$\frac{3}{7}$$ – $$\frac{3}{4}$$ – 2$$\frac{1}{4}$$ – $$\frac{3}{7}$$
d. $$\frac{5}{6}$$ + $$\frac{1}{3}$$ – $$\frac{4}{3}$$ + $$\frac{1}{6}$$
a. $$\frac{1}{4}$$ + 2$$\frac{2}{3}$$ + $$\frac{7}{4}$$ + $$\frac{1}{3}$$ = 5
b. 2$$\frac{3}{5}$$ – $$\frac{3}{4}$$ + $$\frac{2}{5}$$ = 2 $$\frac{1}{4}$$
c. 4$$\frac{3}{7}$$ – $$\frac{3}{4}$$ – 2$$\frac{1}{4}$$ – $$\frac{3}{7}$$ = 1
d. $$\frac{5}{6}$$ + $$\frac{1}{3}$$ – $$\frac{4}{3}$$ + $$\frac{1}{6}$$ = 0
Explanation :
a. $$\frac{1}{4}$$ + 2$$\frac{2}{3}$$ + $$\frac{7}{4}$$ + $$\frac{1}{3}$$
= $$\frac{1}{4}$$ + $$\frac{7}{4}$$  + $$\frac{8}{3}$$ + $$\frac{1}{3}$$
= $$\frac{8}{4}$$ + $$\frac{9}{3}$$ = 2 + 3 = 5

b. 2$$\frac{3}{5}$$ – $$\frac{3}{4}$$ + $$\frac{2}{5}$$
= $$\frac{13}{5}$$ – $$\frac{3}{4}$$ + $$\frac{2}{5}$$
= $$\frac{13}{5}$$ + $$\frac{2}{5}$$ – $$\frac{3}{4}$$
= $$\frac{15}{5}$$ – $$\frac{3}{4}$$ = 3 – $$\frac{3}{4}$$ = 2 $$\frac{1}{4}$$

c. 4$$\frac{3}{7}$$ – $$\frac{3}{4}$$ – 2$$\frac{1}{4}$$ – $$\frac{3}{7}$$
= $$\frac{31}{7}$$ – $$\frac{3}{7}$$ – $$\frac{3}{4}$$ – $$\frac{9}{4}$$
= $$\frac{28}{7}$$ – $$\frac{12}{4}$$ = 4 – 3 = 1

d. $$\frac{5}{6}$$ + $$\frac{1}{3}$$ – $$\frac{4}{3}$$ + $$\frac{1}{6}$$
=  $$\frac{5}{6}$$ + $$\frac{1}{6}$$ + $$\frac{1}{3}$$ – $$\frac{4}{3}$$
= $$\frac{6}{6}$$ – $$\frac{3}{3}$$ = 1 – 1 = 0

Question 2.
Fill in the blank to make the statement true.
a. 11$$\frac{2}{5}$$ – 3$$\frac{2}{3}$$ – $$\frac{11}{3}$$ = ________
b. 11$$\frac{7}{8}$$ + 3$$\frac{1}{5}$$ – ____________ = 15
c.$$\frac{5}{12}$$ -________+ $$\frac{5}{4}$$ = $$\frac{2}{3}$$
d. ________- 30 – 7$$\frac{1}{4}$$ = 21$$\frac{2}{3}$$
e. $$\frac{24}{5}$$ + ________ + $$\frac{8}{7}$$ = 9
f. 11.1 + 3 $$\frac{1}{10}$$ – ________= $$\frac{99}{10}$$
a. 11$$\frac{2}{5}$$ – 3$$\frac{2}{3}$$ – $$\frac{11}{3}$$ =4$$\frac{1}{15}$$
b. 11$$\frac{7}{8}$$ + 3$$\frac{1}{5}$$ – $$\frac{3}{40}$$ = 15
c.$$\frac{5}{12}$$ -1+ $$\frac{5}{4}$$ = $$\frac{2}{3}$$
d. 58$$\frac{11}{12}$$ . – 30 – 7$$\frac{1}{4}$$ = 21$$\frac{2}{3}$$
e. $$\frac{24}{5}$$ + 21$$\frac{2}{5}$$ + $$\frac{8}{7}$$ = 9
f. 11.1 + 3 $$\frac{1}{10}$$ – 8 = $$\frac{99}{10}$$
Explanation :
a. 11$$\frac{2}{5}$$ – 3$$\frac{2}{3}$$ – $$\frac{11}{3}$$
= $$\frac{57}{5}$$ – $$\frac{11}{3}$$ – $$\frac{11}{3}$$
= $$\frac{57}{5}$$ – $$\frac{22}{3}$$
lcm of 5 and 3 is 15 .
= $$\frac{171}{15}$$ – $$\frac{110}{15}$$
= $$\frac{61}{15}$$ = 4$$\frac{1}{15}$$

b. 11$$\frac{7}{8}$$ + 3$$\frac{1}{5}$$ – x = 15
= $$\frac{95}{8}$$ + $$\frac{16}{5}$$ – x = 15
x = $$\frac{95}{8}$$ + $$\frac{16}{5}$$ – 15
lcm is 40 .
x = $$\frac{475}{40}$$ + $$\frac{128}{40}$$ – $$\frac{600}{40}$$
x = $$\frac{3}{40}$$

c. $$\frac{5}{12}$$ – y + $$\frac{5}{4}$$ = $$\frac{2}{3}$$
= $$\frac{5}{12}$$ – y + $$\frac{5}{4}$$ = $$\frac{2}{3}$$
lcm of 12 , 4 and 3 is 12 .
y = $$\frac{5}{12}$$  + $$\frac{15}{12}$$ – $$\frac{8}{12}$$
y = $$\frac{12}{12}$$ = 1
y = 1.

d. x – 30 – 7$$\frac{1}{4}$$ = 21$$\frac{2}{3}$$ = x – 30 – $$\frac{29}{4}$$ = $$\frac{65}{3}$$
lcm of 4 and 3 is 12.
x = $$\frac{260}{12}$$ + $$\frac{360}{12}$$ + $$\frac{87}{12}$$
x = $$\frac{707}{12}$$ = 58$$\frac{11}{12}$$ .

e. $$\frac{24}{5}$$ + y + $$\frac{8}{7}$$ = 9
y = 9 – $$\frac{24}{5}$$  – $$\frac{8}{7}$$
lcm of 5 and 7 is 35 .
y = $$\frac{315}{35}$$  – $$\frac{168}{35}$$  – $$\frac{40}{35}$$
y =  $$\frac{107}{5}$$ = 21$$\frac{2}{5}$$

f. 11.1 + 3 $$\frac{1}{10}$$ – x = $$\frac{99}{10}$$
11.1 + $$\frac{31}{10}$$ –  $$\frac{99}{10}$$ = x
11.1  – $$\frac{31}{10}$$ = x
11.1  – 3.1 = x
8.0 = x

Question 3.
DeAngelo needs 100 lb of garden soil to landscape a building. In the company’s storage area, he finds 2 cases holding 24$$\frac{3}{4}$$ lb of garden soil each, and a third case holding 19$$\frac{3}{8}$$ lb. How much gardening soil does DeAngelo still need in order to do the job?
Fraction of soil needed to landscape a building = 100lb .
Fraction of 2 cases holding soil = 2 × 24$$\frac{3}{4}$$ =  $$\frac{99}{2}$$ lb
Fraction of third case holding soil = 19$$\frac{3}{8}$$ = $$\frac155}{8}$$ lb
Fraction of cases holding capacity = $$\frac{99}{2}$$ lb + $$\frac{155}{8}$$ lb  = $$\frac{396}{8}$$ + $$\frac{155}{8}$$ = $$\frac{551}{8}$$ = 68 $$\frac{7}{8}$$ .
Fraction of gardening soil still need to do = 100 – 68 $$\frac{7}{8}$$ = $$\frac{800}{8}$$ – $$\frac{551}{8}$$ = $$\frac{249}{8}$$ = 31$$\frac{1}{8}$$ .
Therefore Fraction of gardening soil still need to do = 31$$\frac{1}{8}$$ .

Question 4.
Volunteers helped clean up 8.2 kg of trash in one neighborhood and 11$$\frac{1}{2}$$ kg in another. They sent 1$$\frac{1}{4}$$ kg to be recycled and threw the rest away. How many kilograms of trash did they throw away?
Fraction of trash cleaned up in one neighborhood = 8.2 kg
Fraction of trash cleaned up in another neighborhood = 11$$\frac{1}{2}$$ = $$\frac{23}{2}$$ kg
Fraction of capacity of recycled = 1$$\frac{1}{4}$$ = $$\frac{5}{4}$$ = 1.25 kg
Total trash cleaned up = 8.2 + $$\frac{23}{2}$$ = $$\frac{16.4}{2}$$ + $$\frac{23}{2}$$ = $$\frac{39.4}{2}$$ = 19.7 kg .
Fraction of trash threw = 19.7 – 1.25kg = 18.45 kg
Therefore fraction of trash threw = 18.45 kg .

Eureka Math Grade 5 Module 3 Lesson 14 Exit Ticket Answer Key

Fill in the blank to make the statement true.
Question 1.
1$$\frac{3}{4}$$ + $$\frac{1}{6}$$ + __________ = 7$$\frac{1}{2}$$
1$$\frac{3}{4}$$ + $$\frac{1}{6}$$ + $$\frac{67}{12}$$  = 7$$\frac{1}{2}$$
Explanation :
1$$\frac{3}{4}$$ + $$\frac{1}{6}$$ + x = 7$$\frac{1}{2}$$
x = $$\frac{15}{2}$$ – $$\frac{7}{4}$$ – $$\frac{1}{6}$$
lcm of 2 , 4 and 6 is 12 .
x = $$\frac{90}{12}$$ – $$\frac{21}{12}$$ – $$\frac{2}{12}$$
x = $$\frac{67}{12}$$

Question 2.
8$$\frac{4}{5}$$ – $$\frac{2}{3}$$ – _____________ = 3$$\frac{1}{10}$$
8$$\frac{4}{5}$$ – $$\frac{2}{3}$$ – _____________ = 3$$\frac{1}{10}$$
Explanation :
8$$\frac{4}{5}$$ – $$\frac{2}{3}$$ – y = 3$$\frac{1}{10}$$
y = $$\frac{44}{5}$$ – $$\frac{2}{3}$$ – $$\frac{31}{10}$$
lcm of 5 , 3 and 10 is 30.
y = $$\frac{264}{30}$$ – $$\frac{20}{30}$$ – $$\frac{186}{30}$$
y = $$\frac{58}{30}$$ = 1$$\frac{28}{30}$$ .

Question 1.
Rearrange the terms so that you can add or subtract mentally. Then, solve.
a. 1$$\frac{3}{4}$$ + $$\frac{1}{2}$$ + $$\frac{1}{4}$$ +$$\frac{1}{2}$$
b. 3$$\frac{1}{6}$$ – $$\frac{3}{4}$$ + $$\frac{5}{6}$$
c. 5$$\frac{5}{8}$$ – 2$$\frac{6}{7}$$ – $$\frac{2}{7}$$ – $$\frac{5}{8}$$
d. $$\frac{7}{9}$$ + $$\frac{1}{2}$$ – $$\frac{3}{2}$$ + $$\frac{2}{9}$$
a. 1$$\frac{3}{4}$$ + $$\frac{1}{2}$$ + $$\frac{1}{4}$$ +$$\frac{1}{2}$$ = 3
b. 3$$\frac{1}{6}$$ – $$\frac{3}{4}$$ + $$\frac{5}{6}$$ = 3$$\frac{1}{4}$$
c. 5$$\frac{5}{8}$$ – 2$$\frac{6}{7}$$ – $$\frac{2}{7}$$ – $$\frac{5}{8}$$ =1$$\frac{6}{7}$$
d. $$\frac{7}{9}$$ + $$\frac{1}{2}$$ – $$\frac{3}{2}$$ + $$\frac{2}{9}$$ = 0
Explanation :
a. 1$$\frac{3}{4}$$ + $$\frac{1}{2}$$ + $$\frac{1}{4}$$ +$$\frac{1}{2}$$
= $$\frac{7}{4}$$ + $$\frac{1}{2}$$ + $$\frac{1}{4}$$ +$$\frac{1}{2}$$
= $$\frac{7}{4}$$+ $$\frac{1}{4}$$ +$$\frac{1}{2}$$ + $$\frac{1}{2}$$
= $$\frac{8}{4}$$ + $$\frac{2}{2}$$
= 2 + 1
=3

b. 3$$\frac{1}{6}$$ – $$\frac{3}{4}$$ + $$\frac{5}{6}$$
= $$\frac{19}{6}$$+ $$\frac{5}{6}$$ – $$\frac{3}{4}$$
= $$\frac{24}{6}$$ – $$\frac{3}{4}$$
lcm of 6 and 4 is 24 .
= $$\frac{96}{24}$$ – $$\frac{18}{24}$$
= $$\frac{78}{24}$$
= $$\frac{13}{4}$$
= 3$$\frac{1}{4}$$

c. 5$$\frac{5}{8}$$ – 2$$\frac{6}{7}$$ – $$\frac{2}{7}$$ – $$\frac{5}{8}$$
= $$\frac{45}{8}$$ – $$\frac{5}{8}$$ – $$\frac{20}{7}$$ – $$\frac{2}{7}$$
= $$\frac{40}{8}$$ – $$\frac{22}{7}$$
= $$\frac{280}{56}$$ – $$\frac{176}{56}$$
= $$\frac{104}{56}$$
= $$\frac{13}{7}$$
=1$$\frac{6}{7}$$

d. $$\frac{7}{9}$$ + $$\frac{1}{2}$$ – $$\frac{3}{2}$$ + $$\frac{2}{9}$$
= $$\frac{7}{9}$$ + $$\frac{2}{9}$$ + $$\frac{1}{2}$$ – $$\frac{3}{2}$$
= $$\frac{9}{9}$$ – $$\frac{2}{2}$$
= 1- 1
= 0

Question 2.
Fill in the blank to make the statement true.
a. 7$$\frac{3}{4}$$ – 1$$\frac{2}{7}$$ – $$\frac{3}{2}$$ = ________
b. 9$$\frac{5}{6}$$ + 1$$\frac{1}{4}$$ + ________ = 14
c. $$\frac{7}{10}$$ – _______ + $$\frac{3}{2}$$ = $$\frac{6}{5}$$
d. ________ – 20 – 3$$\frac{1}{4}$$ = 14$$\frac{5}{8}$$
e. $$\frac{17}{3}$$ + ________ + $$\frac{5}{2}$$ = 10$$\frac{4}{5}$$
f. 23.1 + 1$$\frac{7}{10}$$ – ________= $$\frac{66}{10}$$
a. 7$$\frac{3}{4}$$ – 1$$\frac{2}{7}$$ – $$\frac{3}{2}$$ = = 4$$\frac{27}{28}$$
b. 9$$\frac{5}{6}$$ + 1$$\frac{1}{4}$$ + 2$$\frac{11}{12}$$ = 14
c. $$\frac{7}{10}$$ – 1 + $$\frac{3}{2}$$ = $$\frac{6}{5}$$
d. 34$$\frac{5}{8}$$  – 20 – 3$$\frac{1}{4}$$ = 14$$\frac{5}{8}$$
e. $$\frac{17}{3}$$ + 2 $$\frac{19}{30}$$ + $$\frac{5}{2}$$ = 10$$\frac{4}{5}$$
f. 23.1 + 1$$\frac{7}{10}$$ – 18.2 = $$\frac{66}{10}$$

Explanation :
a. 7$$\frac{3}{4}$$ – 1$$\frac{2}{7}$$ – $$\frac{3}{2}$$
= $$\frac{31}{4}$$ – $$\frac{9}{7}$$ – $$\frac{3}{2}$$
lcm of 4 , 7 and 2 is 28
= $$\frac{217}{28}$$ – $$\frac{36}{28}$$ – $$\frac{42}{28}$$
= $$\frac{139}{28}$$
= 4$$\frac{27}{28}$$
b. 9$$\frac{5}{6}$$ + 1$$\frac{1}{4}$$ + x = 14
x = 14 – $$\frac{59}{6}$$ – $$\frac{5}{4}$$
x = $$\frac{168}{12}$$ – $$\frac{118}{12}$$ – $$\frac{15}{12}$$
x = $$\frac{35}{12}$$
x = 2$$\frac{11}{12}$$

c. $$\frac{7}{10}$$ – y + $$\frac{3}{2}$$ = $$\frac{6}{5}$$
y = $$\frac{7}{10}$$ + $$\frac{3}{2}$$ – $$\frac{6}{5}$$
lcm of 10, 2 and 5 is 10 .
y = $$\frac{7}{10}$$ + $$\frac{15}{10}$$ – $$\frac{12}{10}$$
y = $$\frac{10}{10}$$
y = 1.

d. x – 20 – 3$$\frac{1}{4}$$ = 14$$\frac{5}{8}$$
x = 14$$\frac{5}{8}$$ + 20 + 3$$\frac{1}{4}$$
x = $$\frac{117}{8}$$ + 20 + $$\frac{13}{4}$$
lcm is 8
x = $$\frac{117}{8}$$ + $$\frac{26}{8}$$ + $$\frac{160}{8}$$
x = $$\frac{277}{8}$$
x = 34$$\frac{5}{8}$$

e. $$\frac{17}{3}$$ + y + $$\frac{5}{2}$$ = 10$$\frac{4}{5}$$
y = $$\frac{54}{5}$$ – $$\frac{17}{3}$$ – $$\frac{5}{2}$$
lcm of 5 , 3 and 2 is 30 .
y = $$\frac{324}{30}$$ – $$\frac{170}{30}$$ – $$\frac{75}{30}$$
y = $$\frac{79}{30}$$
y = 2 $$\frac{19}{30}$$ .

f. 23.1 + 1$$\frac{7}{10}$$ – y = $$\frac{66}{10}$$
y = 23.1 + $$\frac{17}{10}$$ – $$\frac{66}{10}$$
y = 23.1 – $$\frac{49}{10}$$
y = 23.1 – 4.9
y = 18.2

Question 3.
Laura bought 8$$\frac{3}{10}$$ yd of ribbon. She used 1$$\frac{2}{5}$$ yd to tie a package and 2$$\frac{1}{3}$$ yd to make a bow. Joe later gave her 4$$\frac{3}{5}$$ yd. How much ribbon does she now have?
Fraction of Ribbon brought by Laura = 8$$\frac{3}{10}$$ yd = $$\frac{83}{10}$$
Fraction of Ribbon used to tie a package = 1$$\frac{2}{5}$$ yd
Fraction of Ribbon used to make a bow = 2$$\frac{1}{3}$$ yd
Fraction of ribbon used by Laura = 1$$\frac{2}{5}$$ yd + 2$$\frac{1}{3}$$ yd = $$\frac{7}{5}$$ + $$\frac{7}{3}$$ = $$\frac{21}{15}$$ + $$\frac{35}{15}$$ = $$\frac{56}{15}$$
Fraction of ribbon left with laura = $$\frac{83}{10}$$ – $$\frac{56}{15}$$ = $$\frac{249}{10}$$ + $$\frac{112}{15}$$ = $$\frac{137}{15}$$= 9$$\frac{2}{15}$$ .
Fraction of ribbon joe gave to laura = 4$$\frac{3}{5}$$ = $$\frac{23}{5}$$ yd.
Fraction of ribbon with laura now = $$\frac{137}{15}$$ + $$\frac{23}{5}$$ =$$\frac{137}{15}$$ + $$\frac{69}{15}$$ = $$\frac{206}{15}$$ = 13$$\frac{11}{15}$$ .
Therefore Fraction of ribbon with laura now = 13$$\frac{11}{15}$$ .

Question 4.
Mia bought 10$$\frac{1}{9}$$ lb of flour. She used 2$$\frac{3}{4}$$ lb of flour to bake banana cakes and some to bake chocolate cakes. After baking all the cakes, she had 3$$\frac{5}{6}$$ lb of flour left. How much flour did she use to bake the chocolate cakes?
Fraction of Flour with Mia = 10$$\frac{1}{9}$$ = $$\frac{91}{9}$$ lb
Fraction of Flour used to bake bake banana cakes = 2$$\frac{3}{4}$$ = $$\frac{11}{4}$$ lb
Fraction of flour left = 3$$\frac{5}{6}$$ = $$\frac{23}{6}$$ lb
Fraction of flour used for chocolate cake = $$\frac{91}{9}$$ – $$\frac{11}{4}$$ – $$\frac{23}{6}$$ =
$$\frac{364}{36}$$ – $$\frac{99}{36}$$ – $$\frac{138}{36}$$ = $$\frac{127}{36}$$ = 3$$\frac{17}{36}$$.
Therefore, Fraction of flour used for chocolate cake = 3$$\frac{17}{36}$$.