Whether you’re learning to add and subtract fractions for the first time, preparing for a standardized test, or looking to get ahead in your math class, you’re in the right place!
In this complete, kid-friendly guide, we’ll walk you through simple steps to add and subtract fractions with like denominators. You’ll find easy-to-follow instructions, practical examples, and a quick practice test to help you master this math topic.
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Simply put, a fraction is a part of a whole. Fractions consist of a numerator and a denominator.
The top number is called the numerator, and it tells us how many parts we have.
The bottom number is called the denominator, and it shows us how many equal parts the whole is divided into.
For example, in the fraction \(\Large\frac{3}{4}\), the numerator (3) means we have 3 parts, while the denominator (4) tells us that the whole is divided into 4 equal parts.
Imagine you are going on a four-day field trip. To budget your allowance, you decide to split it into four equal amounts – one for each day. If all goes according to plan, by the end of day 3, you will have spent \(\Large\frac{3}{4}\) of your total allowance.
If two fractions have the same denominator, such as \(\Large\frac{1}{4}\) and \(\Large\frac{2}{4}\), it means they’re divided into the same number of equal parts—just like cutting a cake into 4 equal slices or splitting your total allowance into 4 equal amounts.
If you ate 1 slice (\(\Large\frac{1}{4}\)) of the cake and your friend ate 2 slices (\(\Large\frac{2}{4}\)), how many slices of the cake have you eaten together?
Together, you have eaten \(\Large\frac{3}{4}\) of the cake, or 3 out of the 4 slices!
Let’s visualize this!
The circle below represents our cake cut into 4 slices.
Let’s shade in your slice and the two slices your friend ate:
To add these fractions, all we need to do is combine the shaded pieces.
\(\Large\frac{1}{4}\) + \(\Large\frac{2}{4}\) = \(\Large\frac{1+2}{4}\) = \(\Large\frac{3}{4}\)
What can we conclude based on this example?
When adding fractions with like denominators, we simply add the numerators (the top numbers) and keep the denominator (the bottom number) the same.
Let’s see this in action and add \(\Large\frac{3}{10}\) and \(\Large\frac{4}{10}\).
We keep the bottom number unchanged and simply add the top numbers (3 and 4) together.
\(\Large\frac{3}{10}\) + \(\Large\frac{4}{10}\) = \(\Large\frac{3+4}{10}\) = \(\Large\frac{7}{10}\)
As simple as that!
Subtracting fractions with like denominators is just as easy as adding them!
Let’s start with a visual example to see how it works.
Imagine we want to subtract \(\Large\frac{2}{8}\) from \(\Large\frac{6}{8}\).
Let’s illustrate!
We’ll draw a rectangle and divide it into 8 equal parts like so:
\(\Large\frac{6}{8}\) represents 6 equal parts of that rectangle, while \(\Large\frac{2}{8}\) represents 2 parts.
Let’s shade these in like so:
To subtract, we take away the 2 parts (\(\Large\frac{2}{8}\)) of the grid on the right from the 6 parts (\(\Large\frac{6}{8}\)) of the grid from the left like so:
In math terms, when subtracting fractions with like denominators, we subtract numerators (top numbers) and keep the denominators (bottom numbers) unchanged.
Let’s see this in action with another example: \(\Large\frac{5}{9}\) - \(\Large\frac{3}{9}\).
So, we will keep the bottom numbers unchanged and simply subtract the top numbers.
\(\Large\frac{5}{9}\) - \(\Large\frac{3}{9}\) = \(\Large\frac{5-3}{9}\) = \(\Large\frac{2}{9}\)
And that’s all there is to it.
Wasn’t that easy?
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Now that you understand the principle, let’s explore a few more examples of adding and subtracting fractions with like denominators:
Let’s solve -\(\Large\frac{3}{8}\) + \(\Large\frac{2}{8}\).
We just have to keep the bottom numbers the same and add the numerators.
-\(\Large\frac{3}{8}\) + \(\Large\frac{2}{8}\) = \(\Large\frac{-3+2}{8}\)
\(\Large\frac{-3+2}{8}\) = \(\Large\frac{-1}{8}\) or -\(\Large\frac{1}{8}\).
Let’s try another example!
\(\Large\frac{2}{7}\) + (-\(\Large\frac{1}{7}\))
Keep the denominator the same and simply follow the rules of adding with one negative number:
\(\Large\frac{2}{7}\) + (-\(\Large\frac{1}{7}\))
= \(\Large\frac{2+(-1)}{7}\)
= \(\Large\frac{2-1}{7}\)
= \(\Large\frac{1}{7}\)
We will add -\(\Large\frac{4}{6}\) + (-\(\Large\frac{1}{6}\)).
We keep the denominators the same and add the numerators.
-\(\Large\frac{4}{6}\) + (-\(\Large\frac{1}{6}\) = \(\Large\frac{-4+(-1)}{6}\)
When adding two negative numbers (such as -4 and -1), you combine them just like adding positive numbers, but the result keeps the negative sign because both are below zero. So:
\(\Large\frac{-4+(-1)}{6}\) = -\(\Large\frac{5}{6}\)
Let’s solve \(\Large\frac{5}{7}\) - (-\(\Large\frac{1}{7}\)).
\(\Large\frac{5}{7}\) - (-\(\Large\frac{1}{7}\)) = \(\Large\frac{5-(-1)}{7}\)
We’ll follow the rules of subtracting with negative numbers where two minuses become a plus like so:
\(\Large\frac{5-(-1)}{7}\) = \(\Large\frac{5+1}{7}\) = \(\Large\frac{6}{7}\)
Let’s solve \(\Large\frac{3}{5}\) - \(\Large\frac{4}{5}\).
As usual, we keep the denominators unchanged and subtract the numerators:
\(\Large\frac{3}{5}\) - \(\Large\frac{4}{5}\) = \(\Large\frac{3-4}{5}\)
= \(\Large\frac{-1}{5}\)
or
= -\(\Large\frac{1}{5}\)
When subtracting fractions results in a negative numerator, the fraction as a whole becomes negative. This happens because you’re subtracting a larger value from a smaller one.
Ready to put what you’ve learned into practice? Try solving these tasks by yourself.
\(\Large\frac{2}{7}\) + \(\Large\frac{3}{7}\)
\(\Large\frac{5}{8}\) + (-\(\Large\frac{-2}{8}\))
-\(\Large\frac{4}{9}\) + (-\(\Large\frac{1}{9}\))
\(\Large\frac{3}{10}\) - \(\Large\frac{7}{10}\)
\(\Large\frac{6}{11}\) - (-\(\Large\frac{2}{11}\))
Once you’re ready, check your answers at the bottom of the page.
Here are some common questions our students often have about adding and subtracting fractions with like denominators, along with simple and clear answers to help you out.
The denominator tells us how many equal parts the whole is divided into.
When fractions have the same denominator that means that we are working with parts of equal sizes, so we only need to combine or subtract the numerators to find the total number of parts.
Imagine cutting a pizza into 8 equal slices. If you eat 3 slices and your friend eats 2 slices, you’ve eaten 5 slices or \(\Large\frac{5}{8}\) of the pizza. The size of the slices you are “working with” remains unchanged, the only thing that changes is how much of the pizza you have eaten and how much you have left.
To simplify the fraction, divide the numerator and denominator by their greatest common factor (GCF).
For example, we can simplify \(\Large\frac{12}{16}\). The GCF for 12 and 16 is 4, so \(\Large\frac{12÷4}{16÷4}\) = \(\Large\frac{3}{4}\).
If the numerator is larger than the denominator, the fraction becomes an improper fraction. You can leave it as is, or convert the improper fraction to a mixed number by dividing the numerator by the denominator.
For example, we can convert \(\Large\frac{7}{5}\) to a mixed number.
Divide the numerator by the denominator:
7 ÷ 5 = 1 with a remainder of 2 (also written as 1 R2)
Write the whole number:
The whole number from the division is 1.
Write the remainder as a fraction:
The remainder 2 becomes the new numerator, and the denominator stays the same. So, the fraction part is \(\Large\frac{2}{5}\).
Combine the whole number and the fraction:
\(\Large\frac{7}{5}\) = 1\(\Large\frac{2}{5}\)
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If you’ve given our exercises a try, check your answers here:
\(\Large\frac{5}{7}\)
\(\Large\frac{3}{8}\)
-\(\Large\frac{5}{9}\)
-\(\Large\frac{4}{10}\)
\(\Large\frac{8}{11}\)
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