5Th Grade: Complex Questions for Test Prep on the Pivotal Standards

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5th Grade: Complex Questions for Test Prep on the Pivotal Standards

5.NF.6 Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem.

5.NF.7 Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.

a. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for 1/3 ÷ 4 and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 1/3 ÷ 4 = 1/12 because 1/12 x 4 = 1/3.

b. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ 1/5, and use a visual fraction model to show the quotient. Use the relationships between multiplication and division to explain that 4 ÷ 1/5 = 20 because 20 x 1/5 = 4.

c. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins?

1) On a farm, of each acre is planted with blue spruce trees. If there are 16 acres of trees on the farm, how many acres are planted with blue spruce trees?

A. 4 acres

B. 4 acres

C. 12 acres

D. 12 acres

2) Jacqueline had 12 ounces of honey Victoria had 3 times as much honey. How many ounces of honey did Victoria have?

A. 3 ounces

B. 9 ounces

C. 42 ounces

D. 84 ounces

3) Traci mixed nuts and raisins together in bags to make a trail mix. She had a total of 6 cups of nuts and 8 cups of raisins. She placed cup of nuts in each bag, and cup of raisins in each bag. Traci wanted each bag to have a mixture of nuts and raisins. After Traci uses all the nuts she has, how many more bags need nuts added?

A. 14

B. 18

C. 32

D. 40

4) Three gallons of paint are divided into pans holding gallon each. How many pans can be filled with paint?

C. 4

D. 12

5) A landscaper bought 6 tons of mulch. So far, he has used of it. How many tons of mulch has the landscaper used?

A. ton

B. 1 tons

C. 1 tons

D. 6 tons

Worked Example

A. 14

B. 18

C. 32

D. 40

How did these tools (the diagram, the expressions, equations) show the mathematics in this problem?

Set 17 5.NF.6&7 – multiplication fraction