Fractions: solved examples

Worked examples of fractions, from easy to hard, with every step written out. Try each one yourself first, then check the working.

✓ Every answer here is computed and checked by the math engine

Easy

Example 1. Simplify $\frac{21}{35}$ to its lowest terms.
1. Divide the numerator and denominator by 7. $\frac{21}{35} = \frac{21 \div 7}{35 \div 7} = \frac{3}{5}$
Answer: $\frac{3}{5}$
Example 2. Simplify $\frac{2}{4}$ to its lowest terms.
1. Divide the numerator and denominator by 2. $\frac{2}{4} = \frac{2 \div 2}{4 \div 2} = \frac{1}{2}$
Answer: $\frac{1}{2}$
Example 3. Simplify $\frac{18}{20}$ to its lowest terms.
1. Divide the numerator and denominator by 2. $\frac{18}{20} = \frac{18 \div 2}{20 \div 2} = \frac{9}{10}$
Answer: $\frac{9}{10}$

Example 4. Work out $\frac{1}{3} - \frac{1}{2}$ .
1. Use a common denominator, then combine the numerators. $\frac{1}{3} - \frac{1}{2} = -\frac{1}{6}$
Answer: $-\frac{1}{6}$
Example 5. Work out $\frac{1}{2} + \frac{2}{3}$ .
1. Use a common denominator, then combine the numerators. $\frac{1}{2} + \frac{2}{3} = \frac{7}{6}$
Answer: $\frac{7}{6}$
Example 6. Work out $\frac{8}{9} + \frac{1}{2}$ .
1. Use a common denominator, then combine the numerators. $\frac{8}{9} + \frac{1}{2} = \frac{25}{18}$
Answer: $\frac{25}{18}$

Example 7. Work out $\left(-\frac{5}{6}\right) \times \frac{1}{3}$ .
1. Multiply across and simplify. $\left(-\frac{5}{6}\right) \times \frac{1}{3} = -\frac{5}{18}$
Answer: $-\frac{5}{18}$
Example 8. Work out $\left(-\frac{7}{2}\right) \div \left(-3\right)$ .
1. Multiply by the reciprocal and simplify. $\left(-\frac{7}{2}\right) \div \left(-3\right) = \frac{7}{6}$
Answer: $\frac{7}{6}$
Example 9. Work out $\frac{3}{4} \times \frac{1}{2}$ .
1. Multiply across and simplify. $\frac{3}{4} \times \frac{1}{2} = \frac{3}{8}$
Answer: $\frac{3}{8}$

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