Year 6 Maths reasoning (SATs) · Fractions and decimals reasoning · Lesson 2.3

Year 6 Maths reasoning (SATs): Adding, subtracting and mixed numbers

Part of the Year 6 Maths reasoning (SATs) fractions and decimals reasoning chapter. Chapter overview · whole chapter on one page

2.3

Adding, subtracting and mixed numbers

Year 6
Add and subtract fractions with different denominators and mixed numbers (Year 6)

Story. Tom walks 3/8 of a kilometre to the shop, then 1/4 of a kilometre to the park. Later, a jug holds 2 1/2 litres and the juice bottle has 1 3/4 litres in it, so the class must work out how much is left.

Rule

To add or subtract fractions, first write them with the same denominator. Add or subtract the numerators only.

For a mixed number, add or subtract the whole numbers and the fractions separately, then simplify.

Key ideas

Common denominator first, then add or subtract the tops.
Write the answer in simplest form.
If the fraction part adds to more than 1 whole, carry it into the whole numbers.

Worked example 2.3.1

Work out 1/4 + 1/6. Give your answer in its simplest form.

Method. Use a common denominator, add or subtract the tops, then simplify.

Write both with the same bottom number. The bottoms are 4 and 6, so use 12.
1/4 = 3/12 and 1/6 = 2/12
Work out the tops. 3 + 2 = 5.
5/12
Simplify, or write as a mixed number. Divide the top and bottom by any common factor, or by the bottom if the top is bigger.
5/12
Write the answer.
5/12

Check. 5/12 is the same as 5/12. ✓

Watch out. Add or subtract the tops only. The bottom number stays the same.

Worked example 2.3.2

Work out 5/6 - 2/3. Give your answer in its simplest form.

Method. Use a common denominator, add or subtract the tops, then simplify.

Write both with the same bottom number. The bottoms are 6 and 3, so use 6.
5/6 = 5/6 and 2/3 = 4/6
Work out the tops. 5 - 4 = 1.
1/6
Simplify, or write as a mixed number. Divide the top and bottom by any common factor, or by the bottom if the top is bigger.
1/6
Write the answer.
1/6

Check. 1/6 is the same as 1/6. ✓

Watch out. Add or subtract the tops only. The bottom number stays the same.

Worked example 2.3.3

Work out 3 1/2 + 2 2/3. Give your answer as a mixed number in its simplest form.

Method. Add the whole parts and the fraction parts, then simplify.

Add the whole numbers. 3 + 2 = 5.
5
Add the fractions with a common denominator. Use 6 as the common bottom number.
1/2 + 2/3 = 1 1/6
Put the parts together. Add the whole number part to the whole part of the fraction total.
6 1/6
Write the answer.
6 1/6

Check. 6 1/6 is the total. ✓

Watch out. When the fraction parts add to more than 1, carry the whole number into the front.

Watch out

Watch out. 1/3 + 1/4 is not 2/7. Find a common denominator (12) first.

Exam tip

Practice guide. Write the common denominator above both fractions before you do any adding.