Subtracting mixed numbers with like denominators

In this lesson, I will show you how to subtract mixed numbers with the same denominator. We have some examples and exercises.

Content:

• Example 1
• Steps for subtracting mixed numbers with like denominators
• Example 2
• Example 3
• Videos
• References

Before getting into this topic, don’t forget that a proper fraction is a fraction where the numerator is less than the denominator. Also, a mixed number is the sum of a whole number and a proper fraction. Look at the image below.

1) Subtract 9⁴/₅ – 2¹/₅:

To find the difference between these mixed numbers, first, we subtract the whole numbers (9 – 2).

Next, we subtract the fractions (⁴/₅ – ¹/₅). Given that these fractions have the same denominators, we start by subtracting the denominators ( 4 – 1) and then we keep the denominator the same.

Finally, we add the difference of the fractions (³/₅) to the difference of the whole numbers (7).

The final answer is 7³/₅.

Steps for subtracting mixed numbers with like denominators

To subtract mixed numbers with the same denominator, follow these simple steps:

• Subtract the whole numbers.
• Subtract the fractions (simplify, if possible).
• Add the difference of the fractions to the difference of the whole numbers.

2) Subtract 8³/₄ – 5¹/₄:

First, we are going to subtract the whole numbers (8 – 5).

Then, we subtract the fractions (³/₄ – ¹/₄). Don’t forget to simplify the resulting fraction, in this case, we can simplify the resulting fraction by dividing the numerator and the denominator by 2.

Lastly, we add the difference of the fractions (¹/₂) to the difference of the whole numbers (3).

The resulting mixed number is 3¹/₂. We leave the result as a mixed number.

3) Subtract 8¹/₃ – 3²/₃:

The can follow the same steps we saw in the previous examples, however, if we subtract the fractions, ¹/₃ – ²/₃, we are going to get in trouble because we can not subtract 2 from 1. The second fraction (²/₃) is greater than the first one (¹/₃), this is a special case and we need a different procedure to find the difference.

We could also subtract mixed numbers by converting them to improper fractions. So first, we rewrite the mixed numbers as improper fractions.

Then, we subtract these 2 fractions with like denominators. We start by subtracting the numerators, and then, we keep the same denominator.

Finally, we write the resulting improper fraction (¹⁴/₃) as a mixed number.

The answer is 4²/₃.

Videos

In this video, we will see more examples.

And here, a few more examples of subtracting mixed numbers with the same denominator.

Let’s continue with another example with regrouping:

Finally, an example where the fraction of the second mixed number is greater than the fraction of the first mixed number.

References

For this lesson, we have used these books:

• Tussy, K., Gustafson, D. y Koenig, D. (2013). Prealgebra (4th ed.; pp. 378-380). Cengage Learning.
• OpenStax (2020). Prealgebra 2e (pp. 372-374). Rice University.