Generate simple equivalent fractions

Equivalent fractions name the same quantity even when the whole is partitioned into different numbers of equal parts; for example, $1/2=2/4=3/6$ and $2/3=4/6$ . The relationship is represented with fraction strips, area models, or number lines, showing that multiplying both numerator and denominator by the same small whole number preserves the value. Formal cross-multiplication and general algebraic treatment are not included.

Detailed Explanation: 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 $6$ .

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

3 \times 2=6

Multiply the numerator by the same number:

2 \times 2=4

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}

Learn by doing: Generate simple equivalent fractions

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Fraction Strips - Two Strips and Fraction to Equivalent Fraction

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