Add and subtract fractions

Key Rules:

• 1. To add or subtract fractions, rewrite them over a common denominator, then add or subtract the numerators only; the denominator stays the same.
• 2. Give every answer in its simplest form, as a proper fraction or a mixed number.

Remember:

• •Common denominator to add or subtract, straight across to multiply, flip the divisor to divide.

Don’t Forget...

• •Adding the denominators as well as the numerators, so 14 + 24 becomes 38. The denominator names the size of the parts, not an amount to add: one quarter and two quarters make three quarters, 34.
• •Flipping the first fraction instead of the second when dividing. Only the divisor is replaced by its reciprocal: 23 divided by 45 means 23 x 54, and flipping the 23 instead asks a different question with a different answer.
• •Finding a common denominator before multiplying. Multiplication works directly on the numerators and denominators, so a common denominator is never needed and usually creates larger numbers that hide the cancelling.

Worked Example:

Work out 34 + 56.

The denominators 4 and 6 differ, so find their lowest common multiple: 12.

Rewrite both fractions in twelfths: 34 = 912 and 56 = 1012.

Add the numerators and keep the denominator: 9 + 10 = 19, giving 1912.

1912 is greater than 1, so write it as the mixed number 1 712.

Answer: 1 712

Why It Works:

Multiplying the numerator and denominator of a fraction by the same number does not change its value, so 34 and 912 are the same number written differently. Once both fractions count parts of the same size, twelfths here, adding the numerators simply counts those parts, which is exactly what addition means.

Another Example:

Find 56 of 84 kg.

Divide the amount by the denominator to find one sixth: 84 divided by 6 is 14.

Multiply that by the numerator to make five sixths: 14 x 5 = 70.

Answer: 70 kg