Lesson 1: Use the area model and multiplication to show the equivalence of two fractions.

Property

To find an equivalent fraction, multiply the numerator and the denominator by the same whole number, $n$, where $n > 1$.
This process corresponds to visually decomposing each part of an area model into $n$ smaller, equal parts.

Examples

Property

To verify that an equivalent fraction generated by multiplication is correct, you can draw an area model.
First, calculate the new fraction: $\frac{a}{b} = \frac{a \times n}{b \times n}$.
Then, draw an area model of the original fraction, $\frac{a}{b}$, and decompose it by drawing $n-1$ horizontal lines.
The resulting model will visually represent the new, equivalent fraction.

Examples