Number and Operations—Fractions: Interpreting Multiplication as Scaling with Fractions (CCSS.5.NF.6)
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Common Core 5th Grade Math › Number and Operations—Fractions: Interpreting Multiplication as Scaling with Fractions (CCSS.5.NF.6)
A bag holds $1 \tfrac{1}{4}$ cups of trail mix when full. You fill it to $\tfrac{2}{3}$ of its capacity. How much trail mix is in the bag?
$\tfrac{5}{6}$
$1 \tfrac{11}{12}$
$2 \tfrac{1}{2}$
$\tfrac{1}{6}$
Explanation
Take $\tfrac{2}{3}$ of the full amount: $1 \tfrac{1}{4} = \tfrac{5}{4}$, so $\tfrac{5}{4} \times \tfrac{2}{3} = \tfrac{10}{12} = \tfrac{5}{6}$ cup.
A smoothie recipe uses $\tfrac{3}{4}$ cup of yogurt per batch. You make $2 \tfrac{1}{2}$ batches. How much yogurt do you use?
$3 \tfrac{1}{4}$
$1 \tfrac{7}{8}$
$3 \tfrac{3}{4}$
$\tfrac{3}{8}$
Explanation
Multiply the amount per batch by the number of batches: $\tfrac{3}{4} \times 2 \tfrac{1}{2} = \tfrac{3}{4} \times \tfrac{5}{2} = \tfrac{15}{8} = 1 \tfrac{7}{8}$. This finds the total yogurt for $2 \tfrac{1}{2}$ batches.
A ribbon is $3 \tfrac{1}{3}$ yards long. You use $\tfrac{3}{4}$ of the ribbon for a project. How much ribbon do you use?
$4 \tfrac{1}{12}$
$2 \tfrac{1}{4}$
$2 \tfrac{1}{2}$
$\tfrac{1}{4}$
Explanation
Find $\tfrac{3}{4}$ of the ribbon: $3 \tfrac{1}{3} = \tfrac{10}{3}$, so $\tfrac{10}{3} \times \tfrac{3}{4} = \tfrac{30}{12} = \tfrac{5}{2} = 2 \tfrac{1}{2}$ yards.
Each wall needs $\tfrac{2}{3}$ gallon of paint. You paint $3 \tfrac{1}{2}$ walls. How much paint is that?
$4 \tfrac{1}{6}$
$4 \tfrac{2}{3}$
$\tfrac{1}{3}$
$2 \tfrac{1}{3}$
Explanation
Multiply paint per wall by number of walls: $\tfrac{2}{3} \times 3 \tfrac{1}{2} = \tfrac{2}{3} \times \tfrac{7}{2} = \tfrac{14}{6} = \tfrac{7}{3} = 2 \tfrac{1}{3}$ gallons.