4.1 Equivalent fractions and ordering — Learn

Prerequisites: multiplication and place value.

Objectives: Name the numerator and denominator; make equivalent fractions; order fractions, decimals and negative numbers.

Equivalent fractions

Multiply or divide the numerator and denominator by the same non-zero number. This keeps the fraction value unchanged. To compare fractions, use a common denominator or convert to decimals. A numerator counts the parts chosen; a denominator counts the equal parts in the whole.

Worked examples

Example 1. Make $\frac{3}{4}$ have denominator $20$.

$4\times5=20$, so multiply the numerator by $5$ too.

$\frac{3}{4}=\frac{3\times5}{4\times5}=\frac{15}{20}$.

Example 2. Order $\frac{5}{6}$ and $\frac{7}{9}$.

The lowest common denominator is $18$.

$\frac{5}{6}=\frac{15}{18}$ and $\frac{7}{9}=\frac{14}{18}$.

Therefore $\frac{7}{9}<\frac{5}{6}$.

Watch out. Do not compare fractions by looking only at their denominators. A larger denominator can mean smaller parts, but the numerator matters too. Compare using a common denominator: $\frac{3}{5}=\frac{12}{20}$ and $\frac{7}{10}=\frac{14}{20}$, so $\frac{3}{5}<\frac{7}{10}$.

Investigate equivalent fractions

Predict: how many shaded parts would show the same amount as $\frac{2}{3}$ if a strip had $12$ equal parts?

Test: select the number of parts and compare the shaded length. Explain: why does multiplying both fraction parts by the same number preserve the value?

Progress check

The keyboard discount is $\frac{1}{4}$. Write it as a percentage. Since $\frac{1}{4}=\frac{25}{100}$, the discount is $25\%$.

You should now be able to

• name the numerator and denominator;
• make equivalent fractions;
• order fractions and decimals using a common representation;
• compare positive and negative fractions on a number line.

Covers: [N1, N10].