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.

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

Step 1: Identify unlike denominators of the fractions you want to subtract.

Denominators are 5 and 3, which are unlike.

Step 2: 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

Step 3: 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

Step 4: Subtract the numerators of the fractions, keeping the LCM as the denominator.

9/15 – 5/15 = 4/15

Step 5: Simplify the result, if possible.

4/15 cannot be simplified any further, so the final answer is 4/15.

Let’s consider one more example for better understanding.

Example: Consider two numbers 1/3 and 4/5. Subtract a smaller fraction from the larger one.

Given two fractions: 1/3 and 4/5

To perform Subtraction or even to compare the two numbers, we will need to have a common denominator for both of them

Given First Fractional Number: 1/3

Given Second Fractional Number: 4/5

Numbers in Denominator: 3 for the first number and 5 for the second number.

We will find LCM of the numbers 3 and 5

LCM of 3 and 5 is 15.

So, to attain 15 as denominator, the multiplying factor for numerator and denominator for first fractional number is 5 and for second fractional number is 3

First Fractional Number: (1×5)/(3×5) = 5/15

Second Fractional Number: (4×3)/(5×3) = 12/15

Since denominator is same, we will compare numerators. Clearly, 12/15 is greater than 5/15. So, we will subtract 5/15 from 12/15

Second Fractional Number > First Fractional Number

Second Fractional Number – First Fractional Number

= (12/15) – (5/15)

= (12 – 5)/15

= 7/15

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 as follows:

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.

To subtract fractions, first check and find the common denominator, then subtract the numerators and simply the resultant fraction if possible. Subtracting fractions involves making the denominators (bottom number) same by finding the lowest common multiple of them and subtracting the numerators (top number) and finally simplifying the fraction if possible.

In this article, we will learn about, subtracting fractions, examples, and others in detail.