Here we will learn about adding fractions including how to add fractions with the same denominators and with unlike denominators (different denominators) and how to add mixed numbers.

There are also fractions worksheets based on Edexcel, AQA and OCR exam questions, along with further guidance on where to go next if you’re still stuck.

Adding fractions is when we add two or more fractions together or when we calculate the total of several numbers written as fractions.
To do this the fractions must have a common denominator (bottom number). Then we can add the fractions by adding the numerators (top numbers).

The method for adding fractions can be modified to subtract fractions.

E.g.

1. Ensure the fractions have a common denominator.
2. Add the numerators (top numbers).
3. Write your answer as a fraction, making sure it is in its simplest form.

### Related lessons on fractions

Adding fractions is part of our series of lessons to support revision on fractions. You may find it helpful to start with the main fractions lesson for a summary of what to expect, or use the step by step guides below for further detail on individual topics. Other lessons in this series include:

### Example 1: adding fractions with a common denominator

Work out:

$\frac{1}{5}+\frac{1}{5}$

1. Ensure the fractions have a common denominator.

5 is the denominator for both fractions, so 5 is the common denominator.

$\frac{1}{5}+\frac{1}{5}=\frac{1+1}{5}=\frac{2}{5}$

3Write your answer as a fraction, making sure it is in its simplest form.

$\frac{2}{5}$

2 and 5 do not have a common factor so the fraction cannot be simplified. This fraction is in its simplest form.

### Example 2: adding fractions with a common denominator

Work out:

$\frac{1}{8}+\frac{5}{8}$

Ensure the fractions have a common denominator.

Write your answer as a fraction, making sure it is in its simplest form.

### Example 3: adding fractions with different denominators

Work out:

$\frac{1}{4}+\frac{2}{5}$

Ensure the fractions have a common denominator.

Write your answer as a fraction, making sure it is in its simplest form.

### Example 4: adding fractions with different denominators

Work out:

$\frac{5}{8}+\frac{1}{2}$

Ensure the fractions have a common denominator.

Write your answer as a fraction, making sure it is in its simplest form.

### Example 5: adding mixed numbers

Work out:

$2\frac{1}{2}+1\frac{1}{3}$

Ensure the fractions have a common denominator.

Write your answer as a fraction, making sure it is in its simplest form.

### Example 6: adding mixed numbers

Work out:

$2\frac{3}{4}+1\frac{2}{5}$

Ensure the fractions have a common denominator.

Write your answer as a fraction, making sure it is in its simplest form.

### Common misconceptions

• To be able to add fractions they must have common denominators

When fractions are added together they must have the same denominator. If not, they must be converted to an equivalent fraction with a common denominator.

• Adding the correct parts of the fraction together
When adding fractions with a common denominator we only add the numerators.
$\frac{1}{2}+\frac{1}{2}=\frac{1+1}{2}=\frac{2}{2}=1$

1. Work out:

\frac{3}{9}+\frac{4}{9}

\frac{7}{9}

\frac{7}{18}

\frac{8}{8}

\frac{11}{18}
\frac{3}{9}+\frac{4}{9}=\frac{3+4}{9}=\frac{7}{9}

2. Work out – give your answer as a fraction in its simplest form:

\frac{5}{12}+\frac{3}{12}

\frac{8}{12}

\frac{8}{24}

\frac{1}{3}

\frac{2}{3}
\frac{5}{12}-\frac{3}{12}=\frac{5+3}{12}=\frac{8}{12}=\frac{2}{3}

3. Work out:

\frac{3}{5}+\frac{1}{4}

\frac{4}{9}

\frac{17}{20}

\frac{4}{20}

\frac{19}{20}
\frac{3}{5}+\frac{1}{4}=\frac{12}{20}+\frac{5}{20}=\frac{12+5}{20}=\frac{17}{20}

4. Work out:

\frac{3}{5}+\frac{1}{3}

\frac{4}{8}

\frac{14}{15}

\frac{4}{15}

\frac{11}{15}
\frac{3}{5}+\frac{1}{3}=\frac{9}{15}+\frac{5}{15}=\frac{9+5}{15}=\frac{14}{15}

5. Work out: 2\frac{1}{2}+1\frac{2}{5}

1\frac{1}{2}

3\frac{13}{15}

1\frac{8}{15}

3\frac{9}{10}
2\frac{1}{2}+1\frac{2}{5} =\frac{5}{2}+\frac{7}{5} =\frac{25}{10}+\frac{14}{10} =\frac{25+14}{10} =\frac{39}{10} =3\frac{9}{10}

6. Work out:

1\frac{1}{6}+1\frac{1}{5}

2\frac{11}{30}

2\frac{2}{11}

2\frac{7}{30}

1\frac{17}{30}
1\frac{1}{6}+1\frac{1}{5} =\frac{7}{6}+\frac{6}{5} =\frac{35}{30}+\frac{36}{30} =\frac{35+36}{30} =\frac{71}{30} =2\frac{11}{30}

1. Work out:

\frac{5}{12}+\frac{1}{6}

(2 marks)

\frac{1}{6}=\frac{2}{12}
For using a correct common denominator of 12 (or 36)

(1)

\frac{5}{12}+\frac{2}{12}=\frac{7}{12}

(1)

2. Calculate:

\frac{4}{5}+\frac{5}{7}

(3 marks)

\frac{4}{5}+\frac{5}{7}=\frac{28}{35}+\frac{25}{35}
For writing fractions with a common denominator of 35

(1)

\frac{28+25}{35}

(1)

\frac{53}{35}=1\frac{18}{35}
For writing the final answer as a mixed number

(1)

3. Work out:

2\frac{1}{8}+1\frac{1}{3}

(2 marks)

2\frac{1}{8}+1\frac{1}{3}=\frac{17}{8}+\frac{4}{3}=\frac{51}{24}+\frac{32}{24}

OR

2\frac{1}{8}+1\frac{1}{3}=2\frac{3}{24}+1\frac{8}{24}
For a method to add fractions with a correct common denominator

(1)

\frac{51}{24}+\frac{32}{24}=\frac{83}{24}

OR

2\frac{3}{24}+1\frac{8}{24}=3\frac{11}{24}

(1)

## Learning checklist

You have now learned how to:

• Add fractions with the same denominator
• Add fractions with different denominators