5th Grade Math - Solve Real World Problems Involving Multiplication of Fractions and Mixed Numbers: CCSS.Math.Content.5.NF.B.6

A recipe calls for $\frac{1}{6}$ of a cup of flour. If you only want to make half of the recipe, how much flour do you need?

$\frac{1}{12}\ cup$

$\frac{2}{6}\ cup$

$\frac{1}{2}\ cup$

$\frac{1}{10}\ cup$

$\frac{1}{9}\ cup$

Explanation

When you cut something in half, you can either divide by or multiply by $\frac{1}{2}$ . Remember, when you divide fractions, you actually multiply by the reciprocal. The reciprocal of is $\frac{1}{2}$ .

$\frac{1}{6}\times\frac{1}{2}=\frac{1}{12}$

Molly is trying out for the track team this year. On Monday she ran laps. On Tuesday she runs $1\tfrac{2}{5}$ times as many laps as she did on Monday. How many laps does she run on Tuesday?

$18\frac{1}{5}\ laps$

$26\frac{1}{3}\ laps$

$26\frac{1}{5}\ laps$

$19\ laps$

$25\ laps$

Explanation

First, you need to change the mixed number into an improper fraction. To do this, you multiply the denominator by the whole number, then add the numerator. That number becomes the numerator of your improper fraction. The denominator stays the same.

$1\frac{2}{5}=\frac{7}{5}$

Then put your whole number over to make it a fraction, and multiply like normal.

$\frac{13}{1}\times\frac{7}{5}=\frac{91}{5}$

Finally, reduce to find your final answer.

$\frac{91}{5}=18\frac{1}{5}$

A recipe calls for $\frac{2}{5}$ of a cup of flour. If you triple the recipe, how much flour do you need?

$1\frac{1}{5}\ cups$

$2\frac{1}{5}\ cups$

$3\frac{1}{5}\ cups$

$1\frac{2}{5}\ cups$

$1\frac{3}{5}\ cups$

Explanation

When you multiply a fraction by a whole number, you first want to make the whole number into a fraction. You do that by putting the whole number over $\small 1.$ Then multiply the numerator by the numerator and denominator by the denominator.

$\frac{2}{5}\times\frac{3}{1}=\frac{6}{5}$

Reduce to find your final answer.

$\frac{6}{5}=1\frac{1}{5}$

A recipe calls for $\frac{4}{5}$ of a cup of flour. If you only want to make half of the recipe, how much flour do you need?

$\frac{2}{5}\ cup$

$\frac{1}{5}\ cup$

$\frac{3}{5}\ cup$

$\frac{3}{10}\ cup$

$\frac{1}{10}\ cup$

Explanation

$\frac{4}{5}\times\frac{1}{2}=\frac{4}{10}$

Reduce to find your final answer

$\frac{4}{10}\div\frac{2}{2}=\frac{2}{5}$

Dave collected $\small \frac{5}{7}$ of a bag of leaves. Wes collected $\small 4$ times as many bags as Dave. How many bags did Wes collect?

$\small 2\frac{6}{7}$

$\small 3\frac{6}{7}$

$\small \frac{5}{28}$

Explanation

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.

$\small \frac{4}{1}\times \frac{5}{7}=\frac{20}{7}$

$\small \frac{20}{7}=2\frac{6}{7}$ Because $\small 7$ can go into only times and $\small \frac{6}{7}$ is left over.

Wes collected $\small 2\frac{6}{7}$ bags of leaves.

Liz collected $\small \frac{3}{4}$ of a bag of leaves. Tammy collected $\small 12$ times as many bags as Liz. How many bags did Tammy collect?

$\small 9$

$\small 8$

$\small 7$

$\small \frac{3}{48}$

$\small \frac{48}{3}$

Explanation

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 $\small 4$ can go into $\small 36$ an even $\small 9$ times.

Tammy collected $\small 9$ bags of leaves.

Claire is trying out for the track team this year. On Monday she ran laps. On Tuesday she runs $1\tfrac{2}{3}$ times as many laps as she did on Monday. How many laps does she run on

$20\ laps$

$24\ laps$

$35\ laps$

$36\frac{2}{3}\ laps$

$12\frac{2}{3}\ laps$

Explanation

$1\frac{2}{3}=\frac{5}{3}$

Then put your whole number over to make it a fraction, and multiply like normal.

$\frac{12}{1}\times\frac{5}{3}=\frac{60}{3}$

Finally, reduce to find your final answer.

$\frac{60}{3}=20$

Mary is trying out for the track team this year. On Monday she ran laps. On Tuesday she runs $1\tfrac{1}{2}$ times as many laps as she did on Monday. How many laps does she run on Tuesday?