Q: Add the numerators (top numbers).

\[\frac{1}{8}+\frac{5}{8}=\frac{1+5}{8}=\frac{6}{8}\]

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

The answer is \[\frac{6}{8}\] This fraction is not in its simplest form as it can be simplified. Both 6 and 8 are multiples of 2, so 2 is a common factor and can be cancelled. \[\frac{6}{8}=\frac{2\times3}{2\times4}=\frac{3}{4}\] The final answer is \[\frac{3}{4}\]

Q: Add the numerators (top numbers).

\[\frac{5}{20}+\frac{8}{20}=\frac{5+8}{20}=\frac{13}{20}\]

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

The final answer is \[\frac{13}{20}\] 13 and 20 do not have a common factor. The fraction cannot be simplified. This fraction is in its simplest form. Alternatively, this question could have been solved by using decimals. \[\frac{1}{4}+\frac{2}{5}=0.25+0.4=0.65=\frac{65}{100}=\frac{13}{20}\]

Q: Add the numerators (top numbers).

\[\frac{5}{8}+\frac{4}{8}=\frac{5+4}{8}=\frac{9}{8}\]

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

The answer is \[\frac{9}{8}\] 9 and 8 do not have a common factor to cancel. BUT - This fraction is an improper fraction . It is usually expected that improper fractions are written as mixed numbers. \[\frac{9}{8}=\frac{8+1}{8}=\frac{8}{8}+\frac{1}{8}=1+\frac{1}{8}=1\frac{1}{8}\] The final answer is \[1\frac{1}{8}\] Alternatively, you could have chosen 16 as a common denominator and cancelled by the common factor of 2 to simplify. \[\frac{5}{8}+\frac{1}{2}=\frac{10}{16}+\frac{8}{16}=\frac{10+8}{16}=\frac{18}{16}=\frac{2\times9}{2\times8}=\frac{9}{8}=1\frac{1}{8} \]

Question 1

Ensure the fractions have a common denominator.

Accepted Answer

8 is the denominator for both fractions, so 8 is the common denominator.

Question 2

Add the numerators (top numbers).

Accepted Answer

$$\frac{1}{8}+\frac{5}{8}=\frac{1+5}{8}=\frac{6}{8}$$

Question 3

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

Accepted Answer

The answer is

$$\frac{6}{8}$$

This fraction is not in its simplest form as it can be simplified.
Both 6 and 8 are multiples of 2, so 2 is a common factor and can be cancelled.

$$\frac{6}{8}=\frac{2\times3}{2\times4}=\frac{3}{4}$$

The final answer is

$$\frac{3}{4}$$

Question 4

Ensure the fractions have a common denominator.

Accepted Answer

4 is the denominator of the first fraction and 5 is the denominator of the second fraction. These fractions do not have a common denominator.

To be able to add the fractions they need to have a common denominator.

4 and 5 have a Lowest Common Multiple of 20, so we need to change both fractions so that they have a common denominator of 20.
(Lowest Common Multiple is sometimes called LCM or Least Common Multiple.)

$$\frac{1}{4}=\frac{1}{4}\times\frac{5}{5}=\frac{1\times5}{4\times5}=\frac{5}{20}$$

$$\frac{2}{5}=\frac{2}{5}\times\frac{4}{4}=\frac{2\times4}{5\times4}=\frac{8}{20}$$

We have converted fractions so that they have a common denominator and can now be added.

$$\frac{1}{4}+\frac{2}{5}=\frac{5}{20}+\frac{8}{20}$$

Question 5

Add the numerators (top numbers).

Accepted Answer

$$\frac{5}{20}+\frac{8}{20}=\frac{5+8}{20}=\frac{13}{20}$$

Question 6

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

Accepted Answer

The final answer is

$$\frac{13}{20}$$

13 and 20 do not have a common factor. The fraction cannot be simplified. This fraction is in its simplest form.

Alternatively, this question could have been solved by using decimals.

$$\frac{1}{4}+\frac{2}{5}=0.25+0.4=0.65=\frac{65}{100}=\frac{13}{20}$$

Question 7

Ensure the fractions have a common denominator.

Accepted Answer

8 is the denominator of the first fraction and 2 is the denominator of the second fraction. These fractions do not have a common denominator.

To be able to add the fractions they need to have a common denominator.

8 and 2 have a Lowest Common Multiple of 8, so we make sure that both fractions have a common denominator of 8.
(Lowest Common Multiple is sometimes called LCM or Least Common Multiple.)

$$\frac{1}{2}=\frac{1}{2}\times\frac{4}{4}=\frac{1\times4}{2\times4}=\frac{4}{8}$$

We have converted the fractions so that they have a common denominator and can now be added.

$$\frac{5}{8}+\frac{1}{2}=\frac{5}{8}+\frac{4}{8}$$

Question 8

Add the numerators (top numbers).

Accepted Answer

$$\frac{5}{8}+\frac{4}{8}=\frac{5+4}{8}=\frac{9}{8}$$

Question 9

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

Accepted Answer

The answer is

$$\frac{9}{8}$$

9 and 8 do not have a common factor to cancel. BUT - This fraction is an improper fraction.
It is usually expected that improper fractions are written as mixed numbers.

$$\frac{9}{8}=\frac{8+1}{8}=\frac{8}{8}+\frac{1}{8}=1+\frac{1}{8}=1\frac{1}{8}$$

The final answer is

$$1\frac{1}{8}$$

Alternatively, you could have chosen 16 as a common denominator and cancelled by the common factor of 2 to simplify.

$$\frac{5}{8}+\frac{1}{2}=\frac{10}{16}+\frac{8}{16}=\frac{10+8}{16}=\frac{18}{16}=\frac{2\times9}{2\times8}=\frac{9}{8}=1\frac{1}{8} $$

Question 10

Ensure the fractions have a common denominator.

Accepted Answer

As the values are mixed numbers it is a good idea to write them as improper fractions (where the numerator is larger than the denominator.)

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

$$1\frac{1}{3}=\frac{3}{3}+\frac{1}{3}=\frac{3+1}{3}=\frac{4}{3}$$

So the question is

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

2 is the denominator of the first fraction and 3 is the denominator of the second fraction. These fractions do not have a common denominator.

To be able to add the fractions they need to have a common denominator.

2 and 3 have a Lowest Common Multiple of 6, so we change both fractions so that they have a common denominator of 6.

$$\frac{5}{2}=\frac{5}{2}\times\frac{3}{3}=\frac{5\times3}{2\times3}=\frac{15}{6}$$

$$\frac{4}{3}=\frac{4}{3}\times\frac{2}{2}=\frac{4\times2}{3\times2}=\frac{8}{6}$$

We have converted the fractions so that they have a common denominator and can now be added.

$$\frac{5}{2}+\frac{4}{3}=\frac{15}{6}+\frac{8}{6}$$

Question 11

Add the numerators (top numbers).

Accepted Answer

$$\frac{15}{6}+\frac{8}{6}=\frac{15+8}{6}=\frac{23}{6}$$

Question 12

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

Accepted Answer

The answer is

$$\frac{23}{6}$$

23 and 6 do not have a common factor to cancel. BUT - This fraction is an improper fraction.
It is usually expected that improper fractions are written as mixed numbers.

$$\frac{23}{6}=\frac{18+5}{6}=\frac{18}{6}+\frac{5}{6}=3+\frac{5}{6}=3\frac{5}{6}$$

The final answer is

$$3\frac{5}{6}$$

Alternatively, you could add the whole numbers together and then add the fractions together.

$$2\frac{1}{2}+1\frac{1}{3}\ =2+\frac{1}{2}+1+\frac{1}{3}\ =2+1+\frac{1}{2}+\frac{1}{3}\ =2+1+\frac{3}{6}+\frac{2}{6}\ =3+\frac{5}{6}\ =3\frac{5}{6}$$

Question 13

Ensure the fractions have a common denominator.

Accepted Answer

As the values are mixed numbers it is a good idea to write them as improper fractions (where the numerator is larger than the denominator.)

$$2\frac{3}{4}=\frac{8}{4}+\frac{3}{4}=\frac{8+3}{4}=\frac{11}{4}$$

$$1\frac{2}{5}=\frac{5}{5}+\frac{2}{5}=\frac{5+2}{5}=\frac{7}{5}$$

So the question is

$$2\frac{3}{4}+1\frac{2}{5}=\frac{11}{4}+\frac{7}{5}$$

4 is the denominator of the first fraction and 5 is the denominator of the second fraction. These fractions do not have a common denominator.

To be able to add the fractions they need to have a common denominator.

4 and 5 have a Lowest Common Multiple of 20, so we change both fractions so that they have a common denominator of 20.

$$\frac{11}{4}=\frac{11}{4}\times\frac{5}{5}=\frac{11\times5}{4\times5}=\frac{55}{20}$$

$$\frac{7}{5}=\frac{7}{5}\times\frac{4}{4}=\frac{7\times4}{5\times4}=\frac{28}{20}$$

We have converted the fractions so that they have a common denominator and can now be added.

$$\frac{11}{4}+\frac{7}{5}=\frac{55}{20}+\frac{28}{20}$$

Question 14

Add the numerators (top numbers).

Accepted Answer

$$\frac{55}{20}+\frac{28}{20}=\frac{55+28}{20}=\frac{83}{20}$$

Question 15

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

Accepted Answer

The answer is

$$\frac{83}{20}$$

83 and 20 do not have a common factor to cancel. BUT - This fraction is an improper fraction.
It is usually expected that improper fractions are written as mixed numbers.

$$\frac{83}{20}=\frac{80+3}{20}=\frac{80}{20}+\frac{3}{20}=4+\frac{3}{20}=4\frac{3}{20}$$

The final answer is

$$4\frac{3}{20}$$

Alternatively, you could add the whole numbers together and then add the fractions together.

$$2\frac{3}{4}+1\frac{2}{5}\ =2+\frac{3}{4}+1+\frac{2}{5}\ =2+1+\frac{3}{4}+\frac{2}{5}\ =2+1+\frac{15}{20}+\frac{8}{20}\ =3+\frac{15+8}{20}\ =3+\frac{23}{20}\ =3+1+\frac{3}{20}\ =4\frac{3}{20}$$

Adding Fractions

What is adding fractions?

How to add fractions

Adding fractions worksheet

Adding fractions worksheet

Related lessons on fractions

Adding fractions examples

Example 1: adding fractions with a common denominator

Example 2: adding fractions with a common denominator

Example 3: adding fractions with different denominators

Example 4: adding fractions with different denominators

Example 5: adding mixed numbers

Example 6: adding mixed numbers

Common misconceptions

Practice adding fractions questions

Adding fractions GCSE questions

Learning checklist

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