5th Grade Math - Interpret Multiplication as Scaling: CCSS.Math.Content.5.NF.B.5

Which of the two quantities is larger?

Quantity A: $4\times9\times7$

Quantity B: $3\times8\times7$

Hint: You do not need to perform the multiplication to find the answer!

Quantity A

Quantity B

Quantity A and Quantity B are equal.

Explanation

Fill in the blank with the correct sign.

$\small 3$ __________ $\small \small 3\times\frac{3}{5}$

$\small >$

$\small <$

$\small =$

Explanation

$\small 3$ __________ $\small \small 3\times\frac{3}{5}$

When we multiply a fraction by a whole number, we first want to make the whole number into a fraction. We do that by putting the whole number over Then we multiply like normal.

$\small \frac{3}{1}\times\frac{3}{5}=\frac{9}{5}$

$\small \frac{9}{5}=1\frac{4}{5}$ Because can go into $\small 9$ only time, and $\small \small \frac{4}{5}$ is left over.

$\small 3$ __________ $\small 1\frac{4}{9}$

$\small 3>1\frac{4}{9}$

Fill in the blank with the correct sign.

$\small 8$ __________ $\small 8\times\frac{1}3{}$

$\small >$

$\small <$

$\small =$

Explanation

$\small 8$ __________ $\small 8\times\frac{1}3{}$

When we multiply a fraction by a whole number, we first want to make the whole number into a fraction. We do that by putting the whole number over $\small 1.$ Then we multiply like normal.

$\small \frac{8}{1}\times\frac{1}{3}=\frac{8}{3}$

$\small \frac{8}{3}=2\frac{2}3{}$ Because $\small 3$ can go into $\small 8$ only $\small 2$ times and $\small \frac{2}{3}$ is left over

$\small 8>2\frac{2}3{}$

Fill in the blank with the correct sign.

$\small 4\times\frac{1}{9}$ __________ $\small 4$

$\small <$

$\small >$

$\small =$

Explanation

$\small 4\times\frac{1}{9}$ __________ $\small 4$

When we multiply a fraction by a whole number, we first want to make the whole number into a fraction. We do that by putting the whole number over $\small 1.$ Then we multiply like normal.

$\small \frac{4}{1}\times\frac{1}{9}=\frac{4}{9}$

$\small \frac{4}{9}<4$

Fill in the blank with the correct sign.

$\small 9$ __________ $\small \small 9\times\frac{2}{3}$

$\small >$

Explanation

$\small 9$ __________ $\small \small 9\times\frac{2}{3}$

When we multiply a fraction by a whole number, we first want to make the whole number into a fraction. We do that by putting the whole number over $\small 1.$ Then we multiply like normal.

$\small \frac{9}{1}\times\frac{2}{3}=\frac{18}{3}$

$\small \frac{18}{3}=6$ Because can go into $\small 18$ and even times.

$\small 9>6$

Fill in the blank with the correct sign.

$\small 8$ __________ $\small 8\times\frac{1}{5}$

$\small >$

$\small <$

$\small =$

Explanation

$\small 8$ __________ $\small 8\times\frac{1}{5}$

When we multiply a fraction by a whole number, we first want to make the whole number into a fraction. We do that by putting the whole number over $\small 1.$ Then we multiply like normal.

$\small \frac{8}{1}\times\frac{1}{5}=\frac{8}{5}$

$\small \frac{8}{5}=1\frac{3}{5}$ Because $\small 5$ can go into $\small 8$ only $\small 1$ time and $\small \frac{3}{5}$ is left over.

$\small 8>1\frac{3}{5}$

Fill in the blank with the correct sign.

$\small 2\times\frac{1}{2}$ __________

$\small <$

$\small >$

$\small =$

Explanation

$\small 2\times\frac{1}{2}$ __________

When we multiply a fraction by a whole number, we first want to make the whole number into a fraction. We do that by putting the whole number over $\small 1.$ Then we multiply like normal.

$\small \frac{2}{1}\times\frac{1}{2}=\frac{2}{2}$

$\small \frac{2}{2}=1$ Because can go into an even $\small 1$ time.

$\small 1<2$

Fill in the blank with the correct sign.

$\small 12\times\frac{3}{4}$ ____________ $\small 12$

$\small >$

$\small =$

Explanation

$\small 12\times\frac{3}{4}$ ____________ $\small 12$

When we multiply a fraction by a whole number, we first want to make the whole number into a fraction. We do that by putting the whole number over $\small 1.$ Then we multiply like normal.

$\small \frac{12}{1}\times\frac{3}{4}=\frac{36}{4}$

$\small \frac{36}{4}=9$ Because can go into an even times

$\small 9<12$

Fill in the blank with the correct sign.

$\small 4\times\frac{2}{9}$ __________

$\small =$

Explanation

$\small 4\times\frac{2}{9}$ __________

When we multiply a fraction by a whole number, we first want to make the whole number into a fraction. We do that by putting the whole number over $\small 1.$ Then we multiply like normal.

$\small \frac{4}{1}\times\frac{2}{9}=\frac{8}{9}$

$\small \frac{8}{9}<4$

Fill in the blank with the correct sign.

$\small 7\times\frac{3}{4}$ __________ $\small 7$

$\small =$

Explanation

$\small 7\times\frac{3}{4}$ __________ $\small 7$

When we multiply a fraction by a whole number, we first want to make the whole number into a fraction. We do that by putting the whole number over Then we multiply like normal.