Skill: Generate simple equivalent fractions

Equivalent fractions name the same amount, even when the whole is divided into different-sized pieces.

To make an equivalent fraction, multiply the numerator and denominator by the same small whole number.

Example: Find a fraction equivalent to $\frac{2}{3}$ with a denominator of $6$.

1. Ask: “What number changes $3$ into $6$?”

$$3 \times 2=6$$

2. Multiply the numerator by the same number:

$$2 \times 2=4$$

3. Write the new fraction:

$$\frac{2}{3}=\frac{4}{6}$$

A fraction strip helps show why this is true. Imagine a strip divided into $3$ equal parts, with $2$ parts shaded. If each third is split into $2$ smaller equal parts, the strip has $6$ parts altogether, and $4$ are shaded. The same amount is shaded:

$$\frac{2}{3}=\frac{4}{6}$$