Equivalent fractions
- Multiply or divide the top (numerator) and bottom (denominator) by the same number: 2/3 = 4/6 = 8/12.
- To simplify, divide both by their HCF: 12/18 = 2/3.
- Mixed numbers and improper fractions: 2 3/4 = 11/4 (2 × 4 + 3 = 11), and 17/5 = 3 2/5.
- To order fractions, give them a common denominator or change them to decimals.
Adding and subtracting
- Use a common denominator: 1/3 + 1/4 = 4/12 + 3/12 = 7/12.
- 5/6 − 1/3 = 5/6 − 2/6 = 3/6 = 1/2.
Multiplying and dividing
- Multiply the numerators and multiply the denominators: 2/3 × 3/5 = 6/15 = 2/5.
- To divide, flip the second fraction and multiply: 2/3 ÷ 4/5 = 2/3 × 5/4 = 10/12 = 5/6.
- Change mixed numbers into improper fractions first.
Fractions of amounts
- Divide by the denominator, then multiply by the numerator: 3/5 of 40 = 40 ÷ 5 × 3 = 24.
- To write one number as a fraction of another, put it over the total and simplify: 15 out of 60 = 15/60 = 1/4.
Key terms
- Numerator
- The top number of a fraction.
- Denominator
- The bottom number of a fraction.
- Equivalent fractions
- Fractions that have the same value, such as 1/2 and 2/4.
- Simplify
- Divide the numerator and denominator by a common factor.
- Improper fraction
- A fraction whose numerator is bigger than its denominator, such as 7/4.
- Mixed number
- A whole number and a fraction, such as 1 3/4.
- Common denominator
- A denominator shared by two or more fractions.
- Reciprocal
- A fraction turned upside down: the reciprocal of 4/5 is 5/4.