How do you add Fractions?
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Example 1) Work out \[{3 \over 11} + {5 \over 11} \]

Step 1)

You will notice that the two denominators are identical (they are both 11), so we can move straight on to step 2).

Step 2)

With equal denominators, we can just add the numerators together.

This gives us: \[{3 \over 11} + {5 \over 11} = {3 + 5 \over 11} = {8 \over 11} \]

Step 3)

This fraction is already in simplest form so we have our answer.

Final answer: \[{3 \over 11} + {5 \over 11} \; = \; {8 \over 11} \]

Example 2) Work out \[{2 \over 5} + {4 \over 15} \]

Step 1)

You will notice that the second denominator (15) is a multiple of the first denominator (5) so we need to follow Step 1a)

So we need to multiply the numerator and denominator of the first fraction by 3.

\[{2 \over 5} = {2 \times 3 \over 5 \times 3} = {6 \over 15} \]

So we now have: \[{2 \over 5} + {4 \over 15} \; = \; {6 \over 15} + {4 \over 15} \]

Step 2)

Now the denominators are equal, all we need to do now is to add the numerators together.

This gives us: \[{6 \over 15} + {4 \over 15} = {6 + 4 \over 15} = {10 \over 15} \]

Step 3)

We need to write this answer in simplest form, so divide the numerator and denominator by a common factor of 5!

\[{10 \over 15} \; = \; {10 ÷ 5 \over 15 ÷ 5} \; = \; {2 \over 3}\]

Final answer: \[{2 \over 5} + {4 \over 15} \; = \; {2 \over 3} \]

Example 3) Work out this fraction sum, giving your answer as a mixed number. \[{2 \over 7} + {3 \over 4} \]

Step 1)

The denominator of the first fraction is 7. The denominator of the second fraction is 4. These numbers are not multiples of one another.

We need to use Step 1b)

So we multiply the numerator and denominator of the first fraction by the second fraction's denominator (4).

This gives us: \[{2 \over 7} = {2 \times 4 \over 7 \times 4} = {8 \over 28} \]

Next we multiply the second fraction's numerator and denominator by the first fraction's denominator (7).

This gives us: \[{3 \over 4} = {3 \times 7 \over 4 \times 7} = {21 \over 28}\]

We have now converted the two fractions into fractions with like denominators, and changed our sum to: \[{2 \over 7} + {3 \over 4} = {8 \over 28} + {21 \over 28}\]

Step 2)

Now we have converted the two fractions into fractions with equal denominators, all we need to do now is to add the numerators together.

This gives us: \[{8 \over 28} + {21 \over 28} = {8 + 21 \over 28} = {29 \over 28}\]

Step 3)

This fraction is already in simplest form.

Now we need to convert the answer into a mixed number: \[{29 \over 28} = 1 {1 \over 28}\]

Final answer: \[{2 \over 7} + {3 \over 4} \; = \; 1 {1 \over 28}\]

Example 4) Work out this fraction sum, giving your answer as an improper fraction. \[{5 \over 3} + {7 \over 8} \]

Step 1)

The denominator of the first fraction is 3. The denominator of the second fraction is 8. These numbers are not multiples of one another so we need to use Step 1a)

So we need to multiply the numerator and denominator of the 1st fraction by 8 and the numerator and denominator of the 2nd fraction by 3..

This gives us: \[{5 \over 3} + {7 \over 8} = {5 \times 8 \over 3 \times 8} + {7 \times 3 \over 8 \times 3} = {40 \over 24} \; + \; {21 \over 24} \]

Step 2)

Now we have converted the two fractions into fractions with equal denominators, all we need to do now is to add the numerators together.

This gives us: \[{40 \over 24} + {21 \over 24} = {40 + 21 \over 24} = {61 \over 24}\]

Step 3)

This fraction is already in simplest form.

Final answer: \[ {5 \over 3} + {7 \over 8} = {61 \over 24} \]