Engage NY Eureka Math 5th Grade Module 3 End of Module Assessment Answer Key
Eureka Math Grade 5 Module 3 End of Module Assessment Task Answer Key
Question 1.
On Sunday, Sheldon bought 4\(\frac{1}{2}\) kg of plant food. He used 1\(\frac{2}{3}\) kg on his strawberry plants and used \(\frac{1}{4}\) kg for his tomato plants.
a. How many kilograms of plant food did Sheldon have left? Write one or more equations to show how you reached your answer.
b. Sheldon wants to feed his strawberry plants 2 more times and his tomato plants one more time.
He will use the same amounts of plant food as before. How much plant food will he need? Does he have enough left to do so? Explain your answer using words, pictures, or numbers.
Answer:
a.
Fraction of plant food bought by Sheldon = 4\(\frac{1}{2}\) kg = \(\frac{9}{2}\) kg
Fraction of plant food used on strawberry plant = 1\(\frac{2}{3}\) kg = \(\frac{5}{3}\) kg
Fraction of plant food used on tomato plants = \(\frac{1}{4}\) kg
Fraction of plant food left with Sheldon = \(\frac{9}{2}\) – \(\frac{5}{3}\) – \(\frac{1}{4}\)
= \(\frac{54}{12}\) – \(\frac{20}{12}\) – \(\frac{3}{12}\)
= \(\frac{31}{12}\) = 2\(\frac{7}{12}\) kg .
Therefore, Fraction of plant food left with Sheldon = \(\frac{31}{12}\) = 2\(\frac{7}{12}\) kg .
b.
Fraction of plant food to feed stawberry plant = 2 more times = 2 × \(\frac{5}{3}\) kg = \(\frac{10}{3}\) kg
Fraction of plant food to feed tomato plant = \(\frac{1}{4}\) kg
Total Plant food to feed plants = \(\frac{10}{3}\) kg + \(\frac{1}{4}\) kg = \(\frac{40}{12}\) + \(\frac{3}{12}\) = \(\frac{43}{12}\) = 3\(\frac{7}{12}\)
3\(\frac{7}{12}\) is greater than 2\(\frac{7}{12}\)
Therefore the plant is not enough .
The plant required = \(\frac{43}{12}\) – \(\frac{31}{12}\) = \(\frac{12}{12}\) = 1 kg .
Question 2.
Sheldon harvests the strawberries and tomatoes in his garden.
a. He picks 1\(\frac{2}{5}\) kg less strawberries in the morning than in the afternoon. If Sheldon picks 2\(\frac{1}{4}\) kg in the morning, how many kilograms of strawberries does he pick in the afternoon? Explain your answer using words, pictures, or equations.
b. Sheldon also picks tomatoes from his garden. He picked 5\(\frac{3}{10}\) kg, but 1.5 kg were rotten and had to be thrown away. How many kilograms of tomatoes were not rotten? Write an equation that shows how you reached your answer.
c. After throwing away the rotten tomatoes, did Sheldon get more kilograms of strawberries or tomatoes? How many more kilograms? Explain your answer using an equation.
Answer:
a .
Fraction of strawberries picked in the morning = 2\(\frac{1}{4}\) kg = \(\frac{9}{4}\) kg
Fraction of strawberries picked in the afternoon = 1\(\frac{2}{5}\) kg less strawberries in the morning than in the afternoon = \(\frac{9}{4}\) + 1\(\frac{2}{5}\) = \(\frac{45}{20}\) + \(\frac{28}{20}\) = \(\frac{73}{20}\) = 3 \(\frac{13}{20}\) kg .
b .
Quantity of Tomatoes picked = 5\(\frac{3}{10}\) = \(\frac{53}{10}\) = 5.3 kg
Quantity of Tomatoes rotten = 1.5 kg
Quantity of tomatoes not rotten = 5.3 – 1.5 = 3.8 kg
c.
Fraction of Strawberries Morning + Evening = \(\frac{73}{20}\) kg + \(\frac{9}{4}\) kg = \(\frac{73}{20}\) kg + \(\frac{45}{20}\) kg = \(\frac{59}{10}\) = 5 \(\frac{9}{10}\) kg
Fraction of Tomatoes = 3.8 kg = \(\frac{38}{10}\) =3\(\frac{8}{10}\) kg .
Sheldon got more strawberries than Tomatoes .
Quantity of more strawberries than Tomatoes = \(\frac{59}{10}\) – \(\frac{38}{10}\) kg = \(\frac{21}{10}\) = 2.1 kg