Lesson 2: Multiplying a Fraction by a Whole Number

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

Due to the commutative property, multiplying a fraction by a whole number can be interpreted in two equivalent ways: finding a fraction of a set, or as repeated addition of the fraction.

Examples

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

When a number $a$ is multiplied by a fractional scaling factor $f$:

• If $f < 1$, the product is smaller than $a$. ($a \times f < a$)
• If $f = 1$, the product is equal to $a$. ($a \times f = a$)
• If $f > 1$, the product is larger than $a$. ($a \times f > a$)

Examples