Adding Fractions With Unlike Denominators

Adding Fraction with Unlike Denominators 101: A Comprehensive Guide

Adding fractions with similar denominators is pretty simple. Just add the numerators, and you're done! But the problem arises when dealing with unlike denominators.

Suppose you have two fractions: 2/3 and 4/5

As you can see, the first fraction has the denominator 3 and the second fraction has a denominator 5. If both the denominators had been 3, then the sum would have been 2/3 + 4/3 = 6/3 = 2

However, since the second fraction doesn’t have a denominator 3, you’ll have to approach this sum from a different angle.

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Introduction to Adding Fractions with Unlike Denominators

Finding the sum of fractions with similar denominators is quite simple. However, you cannot add the numerator and denominators separately when you have different denominators. Instead, you must use equivalent fractions with similar denominations to figure out their sum. For this, you need to find the LCM or the least common multiple of the fractions.

Steps for Adding Fractions with Unlike Denominators

When adding fractions with unlike denominators, you have to follow a few simple steps:

Step 1: Find the least common multiple of the denominators

Step 2: Multiply the numerator and denominator to get the like denominator

Step 3: Transform the original fractions into equivalent fractions

Step 4: Add the numerators, leaving the denominators unchanged

Step 5: Simplify the resultant fraction if required

Now, let's go through some examples to understand the process entirely.

Example 1: Add two fractions 1/3 and 2/5

Now, in these fractions, the denominators are 3 and 5. So, accordingly, you have to find the LCM of the two numbers.

LCM of 3 and 5 = 3x5 = 15

To make the denominator 15 in the first fraction, you have to multiply it with 5. So, naturally, you need to multiply the numerator by 5 too. Therefore, the resultant equivalent fraction is 5/15.

Similarly, to make the denominator 15 in the second fraction, you must multiply the numerator and denominator by 3.

Hence the resultant equivalent fraction is 6/15.

Now, all you have to do is add the equivalent fractions:

5/15 + 6/15 = 11/15

Example 2: 5/8 Add 3/10 and

The denominators in these fractions are 8 and 10 respectively. Now, the first step is to find their LCM.

LCM of 8 and 10 = 8 x 10 = 80

Therefore, to make the denominators 80 for both, you must multiply the first fraction by 10 and the second by 8.

The resultant fractions are 50/80 and 24/80.

On adding them, you get:

Now, since the numerator and denominator are even numbers, you can divide the numerator and denominator by 2 to reduce the fraction. Hence, the final result will be

Example 3: Add, and Add 1/2, 3/5, and 4/7

When you have three fractions with unlike denominators, you have to find the LCM for all three: 2, 5, and 7.

LCM of 2, 5, 7 = 2 x 5 x 7 = 70

To change the first fraction's denominator into 70, you must multiply it by 35.

Hence, the first fraction becomes: 35/70

To change the second fraction's denominator into 70, you must multiply it by 14.

Hence, the second fraction becomes: 42/70

To change the third fraction's denominator into 70, you must multiply it by 10.

Hence, the third fraction becomes: 40/70

Now, the sum of the equivalent fractions is:

Converting this to a mixed fraction, you’ll get.

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How to Add and Subtract Fractions?

When you have the same denominator infractions, adding and subtracting becomes simpler. All you have to do is add or subtract the numerators to get the solutions.

Example 1: Add 1/5 and 2/5

In this case, the denominator is 5 for both fractions, with the numerators being 1 and 2, respectively. Now, if you want to add the fractions, the resultant denominator remains unchanged, while the numerator will be a sum of the numerators of the two fractions, i.e., 1+2 = 3

Therefore, the resultant fraction is: 1/5 + 2/5 = 3/5

Example 2: Subtract 1/5 from 2/5

Similar to adding like fractions, the denominator, in this case, remains the same while you have to subtract the numerators.

Therefore, the equation becomes:

However, if you want to add or subtract fractions including unlike denominators, you have to follow the steps:

Find out the LCM of the unlike denominators
Calculate the equivalent fraction with the same denominator
Add or subtract the numerators keeping the denominator unchanged
Simplify the resultant fraction

For example, let’s take the example of the fractions 3/5 and 4/7

Now, the LCM of the unlike denominators 5 and 7 is 35. Therefore, to find the equivalent fractions, multiply the first fraction by 7 and the second by 5.

Therefore, the resultant fractions are:

Now, adding the fractions, you get:

Subtracting the fractions, you get:

Working with Improper Fractions

Fractions where the numerator is greater than or equal to the denominator, are called improper fractions. For example, 5/2 and 8/3 are improper fractions.

The rules for adding or subtracting improper fractions are the same as those for proper fractions. If the denominators are the same, add the numerators. However, if the denominators are different, the steps to follow are:

Find LCM of the denominators
Calculate the equivalent fraction to get like denominators
Add or subtract the numerators keeping the denominator unchanged
If the answer is an improper fraction, change it to a mixed fraction

Example:

Adding Mixed Numbers

Suppose you have to add the mixed fractions:

In this case, you have to follow the steps:

Change the mixed fractions to improper fractions
If the denominator is the same, add the numerators to get the resultant fraction and simplify if needed
If the denominators are different, find their LCM
Convert to the equivalent fraction of the same denominator
Add the numerators, keeping the denominator unchanged
Simplify the fraction

The final, simplified result is.

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Most Popular Questions Searched By Students:

Q. How do you add fractions with unlike denominators?

Ans. To add fractions with unlike denominators, you have to make the denominators the same. For this, you need to find the LCM of the unlike denominators and calculate the equivalent fractions for which they'll have similar denominators. Then, finally, you have to add the numerators to get the result.

Q. How do you add fractions with different denominators in KS2?

Ans. Since KS2 refers to Years 3 to 6, students are already familiar with the key mathematical functions of addition, subtraction, multiplication and division. Therefore, they can follow the usual steps to add fractions with different denominators without issues.

Q. How do you add fractions with different denominators from math antics?

Ans. With 2.53M subscribers on YouTube, Math Antics is one of the popular channels where you can find informative video content to help you with your maths papers. For example, their video on how to add fractions with different denominators is a treat for students who are visual learners.

Q. How do you add and subtract fractions with unlike denominators?

Ans. When you have unlike denominators, the first step is to convert them to like denominators. Then, once that is complete, you can add or subtract the numerators to get the resultant fraction.

Q. How do you add fractions with multiple denominators?

Ans. In the two fractions, 4/7 and9/14, 14 is a multiple of 7. In this case, you have to multiply the first fraction with 2 to convert the denominator to 14. So, the first fraction will be.