Lesson 4: Multiplying Fractions by Whole Numbers and Applications

Property

Any fraction can be decomposed, or broken down, into a product of a whole number and a unit fraction.

Property

To multiply a whole number $n$ by a fraction $\frac{a}{b}$, you can decompose the fraction, apply the associative property, and then multiply the whole number by the numerator.
This demonstrates the rule $n \times \frac{a}{b} = \frac{n \times a}{b}$.

Examples

Property

To multiply a whole number ($n$) by a fraction ($\frac{a}{b}$), multiply the whole number by the numerator ($a$) and keep the denominator ($b$) the same.

Examples

Property

To find the total amount in a real-world scenario involving repeated equal-sized fractional parts, multiply the whole number (number of groups) by the fraction (size of each part).

Examples

• A recipe calls for $\frac{3}{4}$ of a cup of flour. If you want to make 5 batches, you will need $5 \times \frac{3}{4} = \frac{15}{4}$ cups of flour.
• A person eats $\frac{3}{8}$ of a pizza. If there are 5 people and they each eat the same amount, they will eat a total of $5 \times \frac{3}{8} = \frac{15}{8}$ pizzas.
• An athlete runs $\frac{2}{3}$ of a mile each day. In 7 days, the athlete will run $7 \times \frac{2}{3} = \frac{14}{3}$ miles.

Explanation

This skill applies fraction multiplication to solve single-step word problems. You can identify these problems when a specific fractional quantity is repeated a certain number of times. To find the total, you multiply the whole number of repetitions by the fraction. This calculation helps determine the total amount needed or consumed in various practical situations.