Math Lesson 3.4.4 - Subtraction of Fractions

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Welcome to our Math lesson on Subtraction of Fractions, this is the fourth lesson of our suite of math lessons covering the topic of Operations with Fractions, you can find links to the other lessons within this tutorial and access additional Math learning resources below this lesson.

Subtraction of Fractions

Since subtraction is the inverse operation of addition, there is nothing special to add in subtraction of fractions. Everything we have said for addition of fractions (proper and improper) or mixed numbers is also true for subtraction of fractions and mixed numbers. The only difference is in the methodology, i.e. subtraction is carried out by borrowing a unit (in subtraction of mixed numbers) when necessary. Let's consider some examples in this regard.

Example 4

Do the following operations:

8/11 - 3/11
17/6 - 4/9
5 1/4 - 2/9
17/2 - 1 2/3
6 1/4 - 1 4/5

Solution 4

This is the simplest case of fractions subtraction where both fractions have the same denominator, so no extra arrangements are required. We have:

8/11 - 3/11 = (8 - 3)/11 = 5/11

Now, we have a situation where we must first transform both fractions to have the same denominator. Thus, since LCM of 6 and 9 is 18, we obtain

17/6 - 4/9 = 51/18 - 8/18 = 43/18

We can also write this result as a mixed number if we want. Thus,

43/18 = 43 ÷ 18 = 2 (7) = 2 7/18

We can do this subtraction in two ways:

5 1/4 - 2/9 = (5 × 4 + 1)/4 - 2/9= 21/4 - 2/9
= (21 × 9)/(4 × 9) - (2 × 4)/(9 × 4)
= 189/36 - 8/36
= 181/36
= 181 ÷ 36
= 5 (1)
= 5 1/36
5 1/4 - 0 2/9 = (5 - 0)(1/4 - 2/9)
= 5((1 × 9)/(4 × 9) - (2 × 4)/(9 × 4))
= 5(9/36 - 8/36)
= 5 1/36

As you see, the result is the same with both methods. Again, we can use the two methods of the previous case, but now we will save time and use only one of them, as the approach is similar. Moreover, both methods give the same result. We have

17/2 - 1 2/3 = 17/2 - (1 × 3 + 2)/3
= 17/2 - 5/3
= (17 × 3)/(2 × 3) - (5 × 2)/(3 × 2)
= 51/6-10/6
= 41/6
= 41 ÷ 6
= 6 (5)
= 6 5/6

We have

6 1/4 - 1 4/5 = (6 - 1)(1/4 - 4/5)
= 5(5/20 - 16/20)
= 4((20 + 5)/20 - 16/20)
= 4((25 - 16)/20)
= 4 9/20

When a whole number is added or subtracted to a fraction, we write the whole number as a fraction with the same denominator for the given fraction. For example,

5 + 3/4 = 20/4 + 3/4 = 23/4

and

8 - 1/3 = 24/3 - 1/3 = 23/3

More Operations with Fractions Lessons and Learning Resources

Fractions Learning Material
Tutorial ID	Math Tutorial Title	Revision Notes	Revision Questions
3.4	Operations with Fractions
Lesson ID	Math Lesson Title	Lesson	Video Lesson
3.4.1	Addition of Fractions
3.4.2	Addition of fractions with different denominators
3.4.3	Addition of improper fractions and/or mixed numbers
3.4.4	Subtraction of Fractions
3.4.5	Multiplication of Fractions
3.4.6	Division of Fractions
3.4.7	Power of Fractions
3.4.8	Application of PEMDAS Rule in Operations with Fractions
3.4.9	Applications of Operations with Fractions in Practice

Whats next?

Enjoy the "Subtraction of Fractions" math lesson? People who liked the "Operations with Fractions lesson found the following resources useful:

Subtraction Feedback. Helps other - Leave a rating for this subtraction (see below)
Fractions Math tutorial: Operations with Fractions. Read the Operations with Fractions math tutorial and build your math knowledge of Fractions
Fractions Video tutorial: Operations with Fractions. Watch or listen to the Operations with Fractions video tutorial, a useful way to help you revise when travelling to and from school/college
Fractions Revision Notes: Operations with Fractions. Print the notes so you can revise the key points covered in the math tutorial for Operations with Fractions
Fractions Practice Questions: Operations with Fractions. Test and improve your knowledge of Operations with Fractions with example questins and answers
Check your calculations for Fractions questions with our excellent Fractions calculators which contain full equations and calculations clearly displayed line by line. See the Fractions Calculators by iCalculator™ below.
Continuing learning fractions - read our next math tutorial: Converting Fractions to Decimals and Vice-versa

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