Simplifying Fractions

In this section, we learn how to simplify fractions. This is sometimes referred to as reducing a fraction to its lowest terms. Fractions that look different but have the same value are known as equivalent fractions. We can simplify a fraction by dividing both numerator and denominator by the GCF. Recall that dividing a non-zero number by itself results in 1 and multiplication by 1 leaves the number unchanged.
Simplifying Fractions:

1. Factor the numerator and denominator completely
2. Cancel all common factors

Example 1: Simplify each fraction
$$\frac{2}{6}$$ -factor the numerator and denominator completely $$\require{cancel}\frac{2}{3 \cdot 2}$$ -Cancel all common factors $$\frac{\cancel{2}}{3 \cdot \cancel{2}}$$ -When the numerator cancels completely, we write it as 1:
$$\frac{2}{6}=\frac{1}{3}$$