Three ways to write the same value
A fraction, a decimal and a percentage are three different ways of writing the same quantity, and being able to switch between them quickly is essential. To convert a fraction to a decimal, divide the numerator by the denominator; to make a percentage, multiply the decimal by 100. To turn a percentage back into a fraction, write it over 100 and cancel down to its lowest terms.
Key idea
fraction → decimal: divide
decimal → percentage: × 100
percentage → fraction: write over 100 and simplify
Calculating with fractions
To add or subtract fractions, first rewrite them with a common denominator, then combine the numerators. To multiply, multiply the numerators together and the denominators together. To divide, multiply by the reciprocal of the second fraction. Always simplify the final answer.
Worked example
Work out ⅝ ÷ ¼.
Multiply by the reciprocal: ⅝ × 4/1 = 20/8 = 5/2 = 2.5.
Check as a decimal: 0.625 ÷ 0.25 = 2.5. ✓
Comparing and ordering
The safest way to compare mixed forms is to convert them all to decimals and then line them up. For example 3/5 = 0.6, 65% = 0.65, ⅔ ≈ 0.667 and 0.7, so the largest value is 0.7.
Remember
- Always give a fraction in its lowest terms.
- 0.75 = ¾ = 75%.
- The recurring decimal 0.444… = 4/9.