# Fractions Simplified: Adding and Subtracting

Now that your child clearly understands the relationships between the types of fractions, they are ready to start adding and subtracting fractions. As always, start with lots of pictures and hands on activities to show how adding and subtracting fractions works. When your child is ready to move past the pictures, here are some easy ways to teach these concepts.

## Working with Like Fractions

Like fractions are two fractions that are split into the same number of equal pieces. In other words they have the same denominator. ( Like ^{3}⁄_{5} and ^{1}⁄_{5}) These fractions are simple to add and subtract because they already have the same denominator. You only have to add or subtract the numerators. The denominator stays the same throughout the entire problem. For ^{3}⁄_{5} + ^{1}⁄_{5}, simply add 3 + 1 = 4. You answer will then be ^{4}⁄_{5}. To subtract ^{3}⁄_{5} – ^{1}⁄_{5}, just subtract 3 – 1 = 2. Your answer is ^{2}⁄_{5}.

## Working with Unlike Fractions

Unfortunately, not all fractions are going to have the same denominators. Fractions with different denominators cannot be easily added and subtracted. Therefore, the first step in working with unlike fractions is to get a common denominator. You find a common denominator by multiplying one or both of the fractions by a fraction equal to one (like ^{5}⁄_{5}). For example:

^{1}⁄_{4} and ^{3}⁄_{8} – You can multiply ^{1}⁄_{4} x ^{4}⁄_{4} to get ^{4}⁄_{16}. You can then multiply ^{3}⁄_{8} x ^{2}⁄_{2} to get ^{6}⁄_{16}. (Notice you are just multiplying the numerators and then multiplying the denominators for each equation.)

The goal is to choose the smallest number possible to multiply by so that your numbers are not huge. Once your fractions have the same denominator, you can add and subtract the numerators. ^{4}⁄_{16} + ^{6}⁄_{16} = ^{10}⁄_{16}. ^{6}⁄_{16} – ^{4}⁄_{16} = ^{2}⁄_{16}.

## Adding and Subtracting Mixed Numbers

Working with mixed numbers only adds one small step to the process. You can add and subtract the fraction part the same as you always do. (Remember to find a common denominator if necessary.) Then add or subtract the whole number to finish the problem. Here are a few examples:

- 2
^{3}⁄_{5}+ 7^{1}⁄_{5}= 9^{4}⁄_{5}Add the fractions first.^{3}⁄_{5}+^{1}⁄_{5}=^{4}⁄_{5}. Then add your whole numbers. 2 + 7 = 9. You end up with 9^{4}⁄_{5}. - 6
^{7}⁄_{8}– 3^{2}⁄_{8}= 3^{5}⁄_{8}Subtract the fractions.^{7}⁄_{8}–^{2}⁄_{8}=^{5}⁄_{8}. Now subtract the whole numbers. 6 – 3 = 3. Your answer then is 3^{5}⁄_{8}. - 4
^{3}⁄_{5}+ 2^{1}⁄_{3}= 6^{14}⁄_{15}Change the fractions into like fractions^{3}⁄_{5}x^{3}⁄_{3}=^{9}⁄_{15}.^{1}⁄_{3}x^{5}⁄_{5}=^{5}⁄_{15}. Add the new fractions.^{9}⁄_{15}+^{5}⁄_{15}=^{14}⁄_{15}. Now add the whole numbers. 4 + 2 = 6. Your answer is 6^{14}⁄_{15}. - 9
^{1}⁄_{2}– 4^{1}⁄_{3}= 5^{1}⁄_{6}Change the fractions into like fractions.^{1}⁄_{2}x^{3}⁄_{3}=^{3}⁄_{6}.^{1}⁄_{3}x^{2}⁄_{2}=^{2}⁄_{6}. Subtract the new fractions.^{3}⁄_{6}–^{2}⁄_{6}=^{1}⁄_{6}. Now subtract the whole numbers. 9 – 4 = 5. You end up with 5^{1}⁄_{6}.

Don’t forget to simplify each answer by putting the fraction into the lowest terms possible! Adding and subtracting fractions doesn’t have to be hard. Teach your child to follow these simple steps, and they will be flying through those fraction problems in no time. How do you make adding and subtracting fractions easier for your children?