Title: LESSON: Adding and Subtracting Fractions with Unlike Denominators
Course: Mathematics Essentials Q1 > Section: Week 8

Add and subtract fractions with unlike denomiators

INTRODUCTION

Adding and Subtracting Fractions with Different Denominators

READ: Add Fractions With Different Denominators

Add Fractions With Different Denominators

Not all fractions have common or like denominators. When we have fractions with unlike denominators, we can still add them, but we will need to rename the fractions before we can add them. How do we add fractions with different denominators?

To add fractions that have different denominators, we have to rename the fractions so that they are alike. We rename them by changing the different denominators of the fractions to like denominators.

Example

In this example, we are trying to add halves and fourths. If something is divided into halves, it is divided into two pieces. If something is divided into fourths, it is divided into four pieces. We are trying to add fourths and halves. They are different quantities. You can see that although the bar is the same size, the parts are different sizes. We have to rewrite these fractions so that they have common denominators.

How do we rewrite fractions to have a common denominator?

The first step in doing this is to the find the least common multiple of both of the denominators. This LCM will become the lowest common denominator.

Let’s look at 2 and 4.

First, name the multiples of 2: 2, 4, 6, 8, 10 . . . .

Next, name the multiples of 4: 4, 8, 12, 16

The least common multiple of 2 and 4 is 4.

Our next step is to rewrite each fraction as an equivalent fraction that has four as a denominator.

to name one-half in terms of fourths, we need to multiply the numerator and denominator by the same number. 2 2 4, so we multiply the numerator by 2 also. 1 2 2.

Our second fraction is already written in terms of fourths so we don’t need to change it at all.

Next, we can add the renamed fractions.

Our answer is . This answer is in simplest form, so our work is complete.

As long as you rename fractions with the lowest common denominator, you can add any number of fractions with unlike denominators.

READ: Subtract Fractions with Different Denominators

Subtract Fractions with Different Denominators

Just as we can add fractions with different denominators by renaming them with the lowest common denominator, we can also subtract fractions with different denominators by doing the same thing.

First, remember that to subtract two fractions with different denominators, we have to make them fractions with the same denominator. We do this by finding the least common multiple and then we rename each fraction as an equivalent fraction with that least common multiple as the lowest common denominator.

Example

First, find the least common multiple of 4 and 8. It is 8.

Next, rename each fraction in terms of eighths. Remember that renaming is another way of saying that we create an equivalent fraction in terms of eighths.

is already in terms of eighths. We leave it alone.

Now we can rewrite the problem and find the difference.

We can simplify four-eighths by dividing the numerator and the denominator by the GCF. The GCF is 4.

WATCH: Unlike Denominators

READ: Adding and Subtracting Mixed Number with Unlike Denominators

Adding and Subtracting Mixed Numbers with Unlike Denominators

Do you remember adding mixed numbers with like denominators? Adding & subtracting mixed numbers with unlike denominators is very similar, but with one extra step. When we add mixed numbers with different denominators, we need to rename the fraction part of the mixed number with a common denominator FIRST. Then we can add the mixed numbers.

Example

Our first step here is to rename both fractions with a common denominator. The common denominator for 8 and 4 is 8.

can stay the same. It already has a denominator of 8.

Let’s rewrite the problem.

When we add these two fractions now, we get an improper fraction. Seven eighths and four-eighths is equal to Eleven-eighths.

Now we can change .

This is the first part of the answer. Now we can add the whole numbers and then find the sum of both quantities.

This is our final answer.

EXAMPLE 1

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CHECK Yourself! Adding and Subtracting Fractions with Unlike Denominators

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