Subtracting Fractions

Subtracting fractions include the subtraction of two or more fractions with the same or different denominators. Like fractions can be subtracted directly but for unlike fractions we need to make the denominators same first and then subtract them.  In Mathematics, a fraction is a portion of a quantity out of the whole. The whole quantity can be any number, special value or item. We can perform different arithmetic operations on fractions such as addition, subtraction, multiplication and division.

In this article, we will learn what are subtracting fractions and subtracting fractions with like denominators, unlike denominators, and whole numbers. Also, learn the subtraction of mixed fractions with many solved examples.

Introduction to Fractions

A fraction is a numerical value that represents the parts of the whole. A fraction consists of two parts, namely the numerator and the denominator. The upper part of the fraction is called the numerator and the lower part of the fraction is called the denominator. For example, 7/9 is a fraction. Here, 7 is the numerator and 9 is the denominator. Based on the numerator and the denominator, there are different types of fractions. They are:

Proper Fraction: In a proper fraction, the numerator is less than the denominator. Example: ⅗, ⅖, etc.

Improper Fraction: In improper fractions, the numerator is greater than the denominator. Example, 9/7, 11/9, etc.

Mixed Fraction: The mixed fraction is the combination of the proper fraction and a whole number. Example 2 ⅘, 4 ⅔, etc.

Unit Fraction: In unit fraction, the numerator should be equal to 1. For example, ⅓, ¼, ⅕, etc.

Equivalent Fractions: The equivalent fractions are the fractions that represent the same value. If we multiply or divide the numerator and the denominator by the same value, we get the equivalent fractions. Example, 2/4, 4/8, 8/16, etc

Like Fractions: Fractions with the same denominators are called the like fractions. Example: 3/2, 5/2, 7/2, etc

Unlike Fractions: Fractions with different denominators are called unlike fractions. Example: 2/7, 2/9, 3/11, and so on.

What is Meant by Subtracting Fractions?

In Mathematics, subtracting fractions means the process of the subtraction of two fractional values. We have learned to subtract the whole numbers. For example, the subtraction of 3 from 5 results in 2. (i.e. 5-3 = 2). Similarly, we can perform subtraction operations on fractions. Subtracting Fractions include:

• Subtracting Fractions with Like Denominators
• Subtracting Fractions with Unlike Denominators
• Subtracting Mixed Fractions
• Subtracting Fractions with Whole Numbers

Now, let us discuss all these subtracting fractions in detail with examples.

Subtracting Fractions with Like Denominators

Subtracting fractions with like denominators means the subtraction of fractions with the same denominator values. Follow the below steps to subtract the like fractions.

Step 1: Keep the denominator values as it is and subtract the numerator value, which will give the result.

Step 2: If required, simplify the fraction.

Example 1:

Subtract 7/12 from 9/12.

Solution:

Given: (9/12) – (7/12)

Here, the denominator values are the same and keep the value as it is.

Now, subtract the numerator values

(9/12) – (7/12) = (9-7)/12

(9/12) – (7/12) = 2/12

Simplify the fraction, and we get

(9/12) – (7/12) = 1/6.

Therefore, (9/12) – (7/12) = 1/6.

Subtracting Fractions with Unlike Denominators

Subtracting fractions with unlike denominators means the subtraction of fractions with the different denominator values. Go through the below steps to subtract the unlike fractions.

Step 1: Determine the LCM of the denominator values.

Step 2: Convert the denominator to the LCM value by multiplying the numerator and denominator using the same number.

Step 3: Subtract the numerators, once the fractions have the same denominator values.

Step 4: Simplify the fraction, if required.

Example 2:

Subtract 2/3 from 3/5.

Solution:

Given: (3/5) – (2/3)

Find the LCM of 3 and 5. The LCM of 3 and 5 is 15.

To make the denominators equal, convert the denominators to the LCM value.

Thus, (3/5) – (2/3) = (9/15) – (10/15)

Now, the denominators are equal and we can subtract the numerator values.

(3/5) – (2/3) = (9/15) – (10/15)

= (9-10)/15

= -1/15

Therefore, (3/5) – (2/3) = -1/15.

Subtracting Mixed Fractions

While subtracting mixed fractions, go through the following steps:

Step 1: Convert mixed fractions into the improper fraction.

Step 2: Now, check the denominator values

• If the fractions are like fractions, follow the procedure of subtracting fractions with like denominators.
• If the fractions are unlike fractions, follow the procedure of subtracting fractions with unlike denominators.

Example 3:

Subtract 8 ⅚ from 15 ¾.

Solution:

Given: (15 ¾) – (8 ⅚ )

Now, convert mixed fractions into improper fractions.

(15 ¾) – (8 ⅚ ) = (63/4)- (53/6)

Now, find the LCM of 4 and 6 and make the denominators equal.

Thus, LCM of 4 and 6 is 12

(63/4)- (53/6) = (189/12) – (106/12)

(63/4)- (53/6) = 83/12

Therefore, (15 ¾) – (8 ⅚ ) = 83/12

Note:

We can convert improper fractions into mixed fractions if required.

Subtracting Fractions with Whole Numbers

Follow the below steps while subtracting the fractions with whole numbers:

Step 1: Convert the whole number into the fractional form. For example, if 4 is a whole number, convert it into a fraction as 4/1

Step 2: Now, follow the procedure of subtracting fractions with unlike denominators.

Step 3: Simplify the fraction, if required.

Example 4:

Subtract: 2 – (½)

Solution:

Given: 2- (½)

Convert the whole number “2” into the fractional form as “2/1”.

Therefore, 2 – (½) = (2/1)- (½)

Now, take the LCM of 1 and 2.

The LCM of 1 and 2 is 2.

(2/1) – (1/2) = (4/2) – (1/2)

(2/1) – (1/2) = (4-1)/2

(2/1) – (1/2) = 3/2

Therefore, 2 – (1/2) = 3/2.

Video Lesson on Fractions

Also, check: Subtracting Fractions Calculator.

Practice Problems on Subtracting Fractions

Solve the following problems related to subtracting fractions:

• Subtract ⅘ from 10/5.
• Subtract 9/2 from 11/3.
• Subtract: 5 – (4/3).
• Subtract: (6 ½) – (2 ⅘)
• Subtract: (2/7) – 4.