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:
- Add and subtract fractions (find a common denominator)
- Compare fractions
- Simplify fractions
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.