Number and Operations—Fractions: Finding Area of Rectangles with Fractional Side Lengths (CCSS.5.NF.5)

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Common Core 5th Grade Math › Number and Operations—Fractions: Finding Area of Rectangles with Fractional Side Lengths (CCSS.5.NF.5)

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Without calculating, which expression will give a product greater than 32?

$32 \times \frac{7}{6}$

CORRECT

$32 \times \frac{5}{6}$

$32 \times 1$

$32 \times \frac{9}{10}$

Explanation

Multiplying by a fraction greater than 1 makes a number larger, by 1 keeps it the same, and by a fraction less than 1 makes it smaller. Since $\frac{7}{6} > 1$, $32 \times \frac{7}{6}$ is greater than 32.

Which product is smaller than 50?

$50 \times \frac{5}{4}$

$50 \times 1$

$50 \times \frac{3}{4}$

CORRECT

$50 \times \frac{6}{5}$

Explanation

Multiplying by a fraction less than 1 makes a number smaller, by 1 keeps it the same, and by a fraction greater than 1 makes it larger. Since $\frac{3}{4} < 1$, $50 \times \frac{3}{4}$ is smaller than 50, while $\frac{5}{4}$ and $\frac{6}{5}$ are greater than 1 and would enlarge 50.

Which statement is true?

$9 \times \frac{4}{5}$ will be greater than 9.

$9 \times \frac{6}{5}$ will be smaller than 9.

$9 \times \frac{5}{5}$ will be smaller than 9.

$9 \times \frac{5}{5}$ will be equal to 9.

CORRECT

Explanation

$\frac{5}{5}=1$, so multiplying by it does not change the number. Fractions less than 1 (like $\frac{4}{5}$) shrink, and fractions greater than 1 (like $\frac{6}{5}$) enlarge.

A number is multiplied by $\frac{4}{5}$. The result is:

greater than the original number

less than the original number

CORRECT

equal to the original number

impossible to tell without multiplying