Systematic Ways of Subtracting Fractions With Unlike Denominators

Amruta Deshpande May 6, 2019
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Subtracting fractions with unlike denominators is not all that difficult if done in a systematic way. Here's an post on how to subtract fractions with unlike denominators.
Mathematics is about numbers and calculations. Addition and subtraction are the basic mathematical applications. But when it comes to subtracting fractions, it gets a little tougher, and that's especially if the fractions have different denominators.

Unlike Denominators and Whole Numbers

Subtracting fractions with whole numbers is pretty easy! These are simple steps that will help you in subtracting fractions with unlike denominators. Have a look at them.
Step 1: The first step for subtracting mixed fractions is to make them equivalent. They have to have the same denominator, only then can you subtract them. You can find the common denominator by the following method. Let us say you have to subtract 2÷3 from 4÷5.

i.e. : 4÷5 - 2÷3
Step 2: List all the multiples of both the denominators and find the lowest multiple that is common to both. This number is known as their least common multiple (LCM). It will be the new denominator for the fractions.

The common denominator for the two fractions will be 3×5 = 15
Step 3: Now, we have to find the new numerators for the fractions. For that, you need to divide the new denominator by the original denominator of the fractions. The answers obtained are then multiplied by the original numerators to get the new numerators.
For the first fraction, 15 ÷ 5 = 3, hence multiply the old numerator by 3,
i.e., 4 × 3 = 12, so 12 is the new numerator for the first fraction. Similarly, find the new numerator for the second fraction, 2÷3.
15÷3 = 5, multiply 2 by 5, 2×5 = 10

So, your new fractions have the same denominators and are equivalent. They are 12÷15 and 10÷15.
Step 4: You get two equivalent fractions, that is, fractions with the same denominators. Now, subtract the new numerator of the second fraction from that of the first. This number upon the new denominator is your final answer. You may have to reduce the fraction if possible.

12÷15 - 10÷15 = (12 - 10)÷15 = 2÷15
Wasn't that easy! This was about subtracting fractions with different denominators and whole numbers. But do you know how to go about subtracting fractions with mixed numbers, or simply, mixed fractions? Now, that can be a little difficult. But if you get the basics right, you will have fun with these mixed fractions.

Unlike Denominators and Mixed Numbers

We're sure you know what mixed fractions are! Subtracting mixed fractions can be done in two different ways. You can either convert the mixed fractions into improper fractions, and then use the given method for subtracting, or you could subtract the whole numbers and fractions individually, and then combine them. Let us see the first method in detail.
Step 1: Suppose you have to subtract two mixed fractions 3¼ and 1⅔. The first step is to convert them into improper fractions. For that, you need to multiple the whole number by the denominator. Now, add the numerator to the answer to get your new numerator.
3¼ is the mixed fraction, where 3 is the whole number, 4 is the denominator, and 1 is the numerator. So, 3×4 = 12+1 = 13, is your new numerator, and the 1¾ is the new fraction.
Similarly, 1⅔ can be simplified as, 1×3 = 3+2 = 5, 5÷3 is the new second fraction.
Step 2: Now, as described in step 1, find the lowest common multiple for the two fractions.

The new denominator is 3×4 = 12
Step 3: The new numerators will be 39 and 20, as calculated by the given method.

Step 4: So, now your fractions are 39÷12 and 20÷12.

39÷12 - 20÷12 = (39 - 20)÷12 = 19÷12.
So, now when you have to subtract fractions, be it whole numbers or mixed, just follow these simple steps, and you will get the numbers right.