Year 6

Add and subtract fractions with different denominators and mixed numbers, using the concept of equivalent fractions

Add and subtract fractions by rewriting them with a common denominator.

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Lesson overview

Number - fractions, decimals and percentages

Fractions with different denominators cannot be combined directly. We rewrite them as equivalent fractions with the same denominator first, then add or subtract the numerators.

Add with sixths

1/2 + 1/3 becomes 3/6 + 2/6.

Original	Equivalent
1/2	3/6
1/3	2/6
Total	5/6

Make the denominators match first.

Subtract with twelfths

3/4 - 1/6 becomes 9/12 - 2/12.

Then subtract the numerators.

Worked example

Work out 1/2 + 1/3.

Fraction	In sixths
1/2	3/6
1/3	2/6

Find a common denominator of 6.
1/2 is 3/6 and 1/3 is 2/6.
Add 3/6 and 2/6.
The total is 5/6.

Try it

Find the common denominator before you try to combine the fractions.

Question 1

1/2 + 1/3 =

1/2	1/3
3/6	2/6

Question 2

3/4 - 1/6 =

Question 3

Which is the common denominator of 1/2 and 1/5?

Question 4

2/3 + 1/6 =

2/3	1/6
4/6	1/6

Question 5

1 and 1/2 + 1/4 =

\frac{1}{2}

$\frac{2}{4}$

\frac{1}{4}

$\frac{1}{4}$

Common mistakes

Watch for these when working through the lesson.

Adding denominators together.
Forgetting to rewrite the fractions as equivalent fractions.
Not simplifying after the calculation when possible.

Add and subtract fractions with different denominators and mixed numbers, using the concept of equivalent fractions

Lesson overview

Worked example

Try it

Common mistakes

Related topics

Independent practice will plug in here