#### Tier: #Foundation #Higher
Equivalent fractions represent the same value but are written with different numerators and denominators. You create them by multiplying or dividing both the numerator and denominator by the same number.
$$\frac{1}{2} = \frac{2}{4} = \frac{5}{10} = \frac{50}{100}$$
Making equivalent fractions: $$\frac{3}{5} = \frac{?}{20} \implies 5 \times 4 = 20, \text{ so } 3 \times 4 = 12 \implies \frac{12}{20}$$
Why it matters: equivalent fractions are needed to:
Comparing fractions: convert to the same denominator, then compare numerators. $$\frac{3}{4} \text{ vs } \frac{5}{7}: \quad \frac{21}{28} \text{ vs } \frac{20}{28} \implies \frac{3}{4} > \frac{5}{7}$$
Common error: only multiplying the numerator or only the denominator — both must be multiplied by the same value.
Simplifying fractions Adding and subtracting fractions Lowest Common Multiple
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