Subtracting Fractions

Subtraction of Fractions is a process in which we find the difference between the values of two fractions. A fraction represents a ratio or a part of whole In this article, we will learn about, subtracting fractions, examples, and others in detail.

Steps for subtracting fractions

1. Identify the denominators: Check if the fractions have the same denominators.
2. Find the common denominator: If the fractions have different denominators, find the smallest common denominator. This can be done by identifying the least common multiple of the two denominators.
3. Making denominators equal: Multiply the numerator and denominator with number to make the denominators of the fraction same .
4. Subtract the numerators: Subtract the top numbers (the numerators). Put the answer over the same denominator.

Here's an example of subtracting fractions with the same denominator:

\frac{5}{7} - \frac{2}{7} = \frac{(5 - 2)}{7} = \frac{3}{7}

Fractions can be like fractions and unlike fractions and they can be easily subtracted using the steps explained ahead.

Subtracting Fractions with Like Denominators

Fractions with the same denominator, are also called like fractions.

We can easily subtract these fractions using the following formula,

a/b - c/b = (a-c)/b

To subtract fractions with the same denominators we simply subtract the numerators specified in the fraction and use the same denominator to obtain the result.

Let's understand this with the help of an example. The image added below shows 3/4 of a whole and 1/4 of a whole.

When the denominators are the same, there's no need to find the Least Common Multiple (LCM), Now the only thing we have to do is to subtract the numerators while keeping the denominators the same to get the desired result. Hence, our result will be (3 - 1)/4 = 2/4 = 1/2 which is shown in the figure below.

Subtracting Fractions With Like Denominators Example

Example: Find the difference between 5/4 and 3/4

Solution:

Given fractions : 5 /4and 3/4

Here 5 and 5 are the denominator of the given fractions, As both denominators are the same.
Since, the Denominators are the same we can simply subtract the numerators.

5/4 + 3/4 = (5 - 3) /4 = 2/4

Our numerators are 5 and 3 by subtracting them (5 - 3 = 2) and hence we got 2/4. Simplify it and the result will be 1/2.

Subtracting Fractions with Unlike Denominators

When subtracting dissimilar fractions with unlike denominators we need to use the following steps:

Step 1: Identify the unlike denominators of the fractions you want to subtract.
Step 2: Find least common multiple (LCM) of the denominators i.e., the smallest number that is divisible by all denominators.
Step 3: Multiply numerator and denominator by the factor of LCM to make denominators equal.
Step 4: Subtract the numerators of the fractions, keeping the LCM as the denominator. 
Step 5: Simplify the result, if possible.

Let's consider an example of 2/3 - 1/4 for this illustration.

To subtract the 1/4 from 2/3, we take the LCM of the denominators which can be represented by partitioning the circle into equal parts. Now, each partition of both circles represents an equal area, thus we can subtract them as a single unit.

Therefore, 8/12 - 3/12 = 5/12 i.e., 5 parts out of 12 equal parts.

Example of Subtracting Fractions with Unlike Denominators

Let's consider some solved examples of subtraction of dissimilar fractions with different denominators to understand the concept and method better.

Example: Subtract 3/5 from 1/3

Identify unlike denominators of the fractions you want to subtract.
Denominators are 5 and 3, which are unlike.

Find least common multiple (LCM) of the denominators.
Multiples of 5: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, ...
Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60, ...
LCM of 5 and 3 is 15

Multiply numerator and denominator by the factor of LCM to make denominators equal.

• 1/3 = (1 × 5)/(3 × 5) = 5/15
• 3/5 = (3 × 3)/(5 × 3) = 9/15

Subtract the numerators of the fractions, keeping the LCM as the denominator.
9/15 - 5/15 = 4/15

So, the final answer is 4/15.

Subtracting Fractions With Whole Numbers

We can easily subtract a fraction with whole numbers in the same way we subtract two fractions . Mathematically whole number is noting but a fraction with denominator 1. So we simply put 1 as the denominator for the whole number and subtract the formed fraction normally.

Example: Subtract 7 from 19/2

Solution:

Given numbers are, 7 and 19/2
by putting 1 as denominator for 7
We get, 7/1 and 19/2

Now, subtracting them normally,
= 19/2 - 7
= 19/2 - 7/1
= 19/2 - 14/2
= (19 - 14)/2
= 5/2

Also, Read

• Addition of fractions
• Multiplication of Fractions

Sample Problems on Subtracting Fractions

Various problems on subtracting fractions are,

Problem 1: Subtract 1/3 from 1/2.
Solution:

Find LCM of numbers 3 & 2
LCM of 3 & 2 is 6

So, to attain 6 as denominator, the multiplying factor for numerator and denominator for first fractional number is 2 and for second fractional number is 3
First Fractional Number: (1×2)/(3×2) = 2/6
Second Fractional Number: (1×3)/(2×3) = 3/6

= (1×3)/(2×3) - (1×2/3×2)
= (3/6) - (2/6)
= 1/6

Problem 2: Subtract 1/4 from 1/3.
Solution:

Find LCM of the numbers 4 & 3
LCM of 4 & 3 is 12

So, to attain 12 as denominator, the multiplying factor for numerator and denominator for first fractional number is 3 and for second fractional number is 4
First Fractional Number: (1×3)/(4×3) = 3/12
Second Fractional Number: (1×4)/(3×4) = 4/12

= [(1×4)/(3×4) - (1×3)/(4×3)]
= (4/12) - (3/12) 
= 1/12

Problem 3: Subtract 1/4 from 1/2.
Solution:

Find LCM of the numbers 4 & 2
LCM of 4 & 2 is 4.

So, to attain 4 as denominator, the multiplying factor for numerator and denominator for first fractional number is 1 and for second fractional number is 2
First Fractional Number: (1×1)/(4×1) = 1/4
Second Fractional Number: (1×2)/(2×2) = 2/4

= [(1×2)/(2×2) - (1×1)/(4×1)]
= (2/4) - (1/4)
= 1/4

Problem 4: Subtract 1/5 from 1/2.
Solution:

Find LCM of the numbers 5 & 2

LCM of 5 & 2 is 10

So, to attain 10 as denominator, the multiplying factor for numerator and denominator for first fractional number is 2 and for second fractional number is 5

First Fractional Number: (1×2)/(5×2) = 2/10
Second Fractional Number: (1×5)/(2×5) = 5/10

= (5/10) - (2/10)
= 3/10