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Subtracting Fractions

Updated on by sue

Subtracting Fractions: Subtraction and addition are inverse operations of one another and whatever rules applies for addition of fractions would apply to subtraction of fraction as well. The focal point of fraction subtraction are as follows:

  • Fraction with same denominators.
  • Related denominators of fractions.
  • Relatively prime denominators of fractions.
  • Fraction denominators that are not relatively prime or related.
  • Mixed numbers

How to Subtract Fractions

Subtraction is one of the arithmetic operations. Subtract fractions is nothing but it is perform subtraction operation between two or more fractions.

To subtract two fractions, they need to have a common denominator. To find the common denominator, we need to know least common multiples. LCM is the smallest number that the denominators of each of the fractions will divide into evenly.

There are two kinds of Subtracting fractions:

  • Subtract fractions with like (same) denominators.
  • Subtract fractions with unlike (different) denominator.
Table of Contents
  1. Like Denominators
  2. Unlike Denominators
  3. Variables
  4. Whole Numbers
  5. Examples
  6. Calculator

Subtract Fractions Examples

Below you can see the examples of how do you subtract fractions which are having same(like) and different (unlike) denominators-

Solved examples for Subtracting Fractions:

Question 1: Subtracting fraction 3/4 and 1/4

Solution:

  • Step 1: Bottom denominators are same. So, move to step 2.
  • Step 2: Subtract the numerator and place the value over the same denominator 3/4 – 1/4 = 3−1/4 = 2/4
  • Sep 3: Simplify the fraction 2/4

Correct answer is 1/2

Question 2: Subtracting fraction 18/7 and 6/7

Solution:

  • Step 1: Bottom denominators are same. So, move to step 2.
  • Step 2: Subtract the numerator and place the value over the same denominator (18/7) – (6/7) = 18−6/7 = 12/7
  • Step 3: Simplify the fraction 12/7

Correct answer is 12/7

Question 3: Subtracting fraction 15/3 and 6/3

Solution:

Bottom numbers are different. We have to make them same,

  • Step 1: Bottom denominators are same. So, we can move to step 2.
  • Step 2: Subtract the numerator and place the value over the same denominator (15/3) – (6/3) = 15−6/3 = 9/3
  • Step 3: Simplify the fraction 9/3

Correct answer is 3

Question 4: Subtract the fraction 1/2 from 1/10

Solution:

  • Step 1: Multiply denominator and numerator of 1/2 by 5. So that bottom numbers are the same: Now its 5/10 – 1/10
  • Step 2: Now subtract top numbers and place the value over the same denominator: 5−1/10 = 4/10
  • Step 3: Simplify the fraction 4/10

Correct answer is 2/5

Question 5: Subtract the fraction 2/7 from 3/14

Solution:

Bottom numbers are different. We have to make them same.

  • Step 1: Multiply denominator and numerator of 2/7 by 2 we get 4/14. Now bottom numbers are the same: Now its 4/14 – 3/14
  • Step 2: Now subtract top numbers and place the value over the same denominator: 4−3/14

Correct answer is 1/14

Subtract Fractions with like Denominators

Subtracting fractions with denominators deals with the common fraction denominator. The fractions may consist of numerator and denominator, one or more fractions with same denominators is said to be like denominators. A fraction involves two numbers. The top number is said to be numerator and the bottom number is said to be denominator.

Fraction = Numerator of a Fraction/Denominator of a Fraction

To subtract the fractions with the common denominator, first subtract the numerators and then put that difference over that common denominator.

How to Subtract Fractions with Like Denominators

Here are the steps for subtracting fractions with like denominators:

  1. The denominators should be same.
  2. We subtract the numerators, when the denominators are same.
  3. Now simplify the fractions.

Subtract Fractions with Like Denominators Examples

Below are the examples on how to subtract fractions with like denominators:

Question 1: Simplify the given fraction, 5/3 – 7/3

Solution:

= 5/3 – 7/3

Here the two fractions have same denominator, we can easily add the variables in numerator without changing the values of denominator.

= (5−7)/3

= (−2)/3

Correct answer is −2/3

Question 2: Simplify the given fraction, 10/7 – 9/7

Solution:

= 10/7 – 9/7

Here the two fractions have same denominator, we can easily add the variables in numerator without changing the values of denominator.

= (10−9)/7

= (1)/7

Correct answer is 1/7

Question 3: Simplify the given fraction, 13/9 – 10/9

Solution:

= 13/9 – 10/9

Here the two fractions have same denominator, we can easily add the variables in numerator without changing the values of denominator.

= (13−10)/9

= (3)/9

Equivalent fraction is 1/3

Correct answer is 1/3

Question 4: Simplify the given fraction, 7/9 – 3/9

Solution:

= 7/9 – 3/9

Here the two fractions have same denominator, we can easily add the variables in numerator without changing the values of denominator.

= (7−3)/9

= (4)/9

Equivalent fraction is 4/9

Correct answer is 4/9

Question 5: Simplify the given fraction, 8/7 – 3/7

Solution:

= 8/7 – 3/7

Here the two fractions have same denominator, we can easily add the variables in numerator without changing the values of denominator.

= (8−3)/7

= (5)/7

Equivalent fraction is 5/7

Correct answer is 5/7

Question 6: Simplify the given fraction, 8/13 – 5/13

Solution:

= 8/13 – 5/13

Here the two fractions have same denominator, we can easily add the variables in numerator without changing the values of denominator.

= (8−5)/13

= (3)/13

Equivalent fraction is 3/13

Correct answer is 3/13

Subtract Fractions with Unlike Denominators

Fractions are denoted by a/b where a and b are whole numbers and b not equals to 0. For comparing and ordering of unlike fractions, first convert them into like fractions and then compare or rearrange them in the order as desired. When the numerator and denominator of fraction which are multiplied or divided by same number, we get its own equivalent fractions.

How to Subtract Fractions with Unlike Denominators

Below are the steps for how to subtract fractions with different denominators –

  1. Find out Lowest Common Denominator(LCD) of the fractions.
  2. Rename fractions to have LCD.
  3. Now subtract the numerators of the given fractions.
  4. The difference will be the numerator and the LCD will be the denominator of the answer.
  5. Simplify the Fraction if needed.

Subtract Fractions with Unlike Denominators Examples

Below are the solved examples on subtracting fractions with different denominators –

Question 1: Subtract 5/12 from 13/24

Solution:

Here we have unlike fractions, so we have to take LCM for 12 and 24 is 24

5/12 = 5×2/12×2 = 10/24

13/24 – 5/12 = 13/24 – 10/24

= 3/24

Correct answer is 1/8

Question 2: 7/10 – 8/15

Solution:

Here we have unlike fractions, so we have to take LCM for 10 and 15 = 30.

7/10 – 8/15 = 7×3/10×3 – 8×2/15×2

= 21/30 – 16/30

= 21−16/30 = 5/30

Correct answer is 1/6

Question 3: Subtract 3 2/5 – 2 3/8

Solution:

Given fraction is unlike mixed fractions take LCM, LCM for 5 and 8 is 40

3 2/5 – 2 3/8 = 17/5 – 19/8

= 17×8/5×8 – 19×5/8×5

= 136/40 – 95/40

= 41/40

Correct answer is 1 1/40

Subtracting Fractions with Whole Numbers

Subtracting the whole numbers to fractions is just attaching the whole number in face of the fraction without any type of signs between them.

The units of the denominators have to be similar then subtract only the numerators, and keep that same denominator. If the denominators are not similar then we have to take LCM and we perform the process of subtraction for the values of numerator when the denominators are same.

Below you could see subtracting fractions from whole numbers

Subtracting Fractions with Whole Numbers Examples

Question 1: Subtract 18/5 – 3

Solution:

Here the first number is given in the fraction format. And the second number is a whole number. So the second number is written in improper fraction

18/5 – 3/1

Now find LCM of 5 and 1= 5

= 18×1/5×1 – 3×5/1×5

= 18/5 – 15/5

= 18−15/5

= 3/5 .

Question 2: Subtract 17/4 – 3

Solution:

Here the first number is given in the fraction format. And the second number is a whole number. So the second number is written in improper fraction

17/4 – 3/1

Now find LCM of 3 and 1= 3

= 17×1/4×1 – 3×4/1×4

= 17/4 – 12/4

= 17−12/4

= 5/4 .

Subtracting Fractions with Variables

Question 1: Find the fraction with variable 7×5 – 3×5

Solution:

Given 7×5 – 3×5

The above two fractions as same denominators. So we subtract numerators of two fractions by keeping denominators same.

= 7x/5 – 3x/5

= 7x−3x/5

= 4x/5

So the final answer is 4x/5

Question 2: Find the fraction with variable 16x/7 – 5x/7

Solution:

Given 16x/7 – 5x/7

The above two fractions as same denominators. So we can subtract numerators of two fractions by keeping denominators same.

= 16x/7 – 5x/7

= 16x−5x/7

= 11x/7

So the final answer is 11x/7

Subtracting Fractions Calculator

Use our Subtract fractions calculator for subtracting simple and mixed fractions. Enter values in fraction calculator, then select subtract(-) operation and click on calculate button. It shows step by step solution along with final result.

Subtract Fractions Calculator

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About Sue

Sue is a content maker and web perf analyst at IBPS Recruitment. She authors in-depth guides on SSC, UPSC, MBA, Engineering, Govt Jobs, Bank exams and Financial Calculators. You can find her on Pinterest or directly contact via e-mail.