# 6.8: Differences of Fractions with Different Denominators

**At Grade**Created by: CK-12

**Practice**Differences of Fractions with Different Denominators

Have you ever made a plaque? Take a look at this dilemma.

Travis is working on a piece of wood for a plaque on the front of the house. The wood is \begin{align*} \frac{6}{8}\end{align*} of an inch thick. He has shaved off \begin{align*} \frac{1}{2}\end{align*} of an inch.

Given this work, what is the new thickness of the wood plaque?

**Pay attention to this Concept and you will learn how to subtract fractions with different denominators. Then you will know how to figure out the new thickness of the wood.**

### Guidance

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 rename them with a common 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.

\begin{align*}\frac{6}{8} - \frac{1}{4} = \underline{\;\;\;\;\;\;\;\;\;}\end{align*} **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.

\begin{align*}\frac{6}{8}\end{align*} is already in terms of eighths. We leave it alone.

\begin{align*}\frac{1}{4} = \frac{2}{8}\end{align*}

**Now we can rewrite the problem and find the difference.**

\begin{align*}\frac{6}{8} - \frac{2}{8} = \frac{4}{8}\end{align*}

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

\begin{align*}\frac{4 \div 4}{8 \div 4} = \frac{1}{2}\end{align*}

**Our final answer is** \begin{align*}\frac{1}{2}\end{align*}.

Subtract the following fractions. Be sure that your answer is in simplest form.

#### Example A

\begin{align*}\frac{5}{6} - \frac{1}{3} = \underline{\;\;\;\;\;\;\;\;\;}\end{align*}

**Solution: \begin{align*}\frac{3}{6} = \frac{1}{2}\end{align*}**

#### Example B

\begin{align*}\frac{1}{2} - \frac{4}{9} = \underline{\;\;\;\;\;\;\;\;\;}\end{align*}

**Solution: \begin{align*}\frac{1}{18}\end{align*}**

#### Example C

\begin{align*}\frac{4}{5} - \frac{1}{4} = \underline{\;\;\;\;\;\;\;\;\;}\end{align*}

**Solution: \begin{align*}\frac{11}{20}\end{align*}**

Now back to Travis and the wood plaque. Here is the original problem once again.

Travis is working on a piece of wood for a plaque on the front of the house. The wood is \begin{align*} \frac{6}{8}\end{align*} of an inch thick. He has shaved off \begin{align*} \frac{1}{2}\end{align*} of an inch.

Given this work, what is the new thickness of the wood plaque?

To figure this out, we can write the following problem.

\begin{align*}\frac{6}{8} - \frac{1}{2} = \underline{\;\;\;\;\;\;\;\;\;}\end{align*}

First, we can rename these two fractions with the common denominator 8.

\begin{align*}\frac{6}{8} - \frac{4}{8}\end{align*} = \begin{align*}\frac{1}{4}\end{align*}

**This is our answer.**

### Vocabulary

Here are the vocabulary words in this Concept.

- Renaming fractions
- renaming fractions means rewriting them with a different denominator, but not changing the value of the fraction.

- Least Common Multiple
- the lowest multiple that two or more numbers have in common.

- Lowest Common Denominator
- the least common multiple becomes the lowest common denominator when adding or subtracting fractions with different denominators.

### Guided Practice

Here is one for you to try on your own.

\begin{align*}\frac{3}{4} - \frac{6}{12} = \underline{\;\;\;\;\;\;\;\;\;}\end{align*}

**Answer** First, we rename the fractions in terms of twelfths, then we subtract.

\begin{align*}\frac{9}{12} - \frac{6}{12} = \frac{3}{12} = \frac{1}{4}\end{align*}

**This is our answer.**

### Video Review

Here are videos for review.

Jame Sousa Subtracting Fractions

Jame Sousa Example of Subtracting Fractions with Unlike Denominators

### Practice

Directions: Subtract the following fractions. Be sure that your answer is in simplest form.

1. \begin{align*}\frac{4}{8} - \frac{1}{8} = \underline{\;\;\;\;\;\;\;\;\;}\end{align*}

2. \begin{align*}\frac{9}{10} - \frac{1}{2} = \underline{\;\;\;\;\;\;\;\;\;}\end{align*}

3. \begin{align*}\frac{10}{10} - \frac{1}{3} = \underline{\;\;\;\;\;\;\;\;\;}\end{align*}

4. \begin{align*}\frac{15}{16} - \frac{2}{8} = \underline{\;\;\;\;\;\;\;\;\;}\end{align*}

5. \begin{align*}\frac{9}{10} - \frac{1}{3} = \underline{\;\;\;\;\;\;\;\;\;}\end{align*}

6. \begin{align*}\frac{3}{5} - \frac{1}{3} = \underline{\;\;\;\;\;\;\;\;\;}\end{align*}

7. \begin{align*}\frac{9}{10} - \frac{1}{4} = \underline{\;\;\;\;\;\;\;\;\;}\end{align*}

8. \begin{align*}\frac{20}{30} - \frac{1}{5} = \underline{\;\;\;\;\;\;\;\;\;}\end{align*}

9. \begin{align*}\frac{18}{19} - \frac{2}{19} = \underline{\;\;\;\;\;\;\;\;\;}\end{align*}

10. \begin{align*}\frac{4}{6} - \frac{1}{8} = \underline{\;\;\;\;\;\;\;\;\;}\end{align*}

11. \begin{align*}\frac{7}{8} - \frac{4}{9} = \underline{\;\;\;\;\;\;\;\;\;}\end{align*}

12. \begin{align*}\frac{1}{2} - \frac{1}{3} = \underline{\;\;\;\;\;\;\;\;\;}\end{align*}

13. \begin{align*}\frac{4}{5} - \frac{1}{3} = \underline{\;\;\;\;\;\;\;\;\;}\end{align*}

14. \begin{align*}\frac{7}{9} - \frac{2}{5} = \underline{\;\;\;\;\;\;\;\;\;}\end{align*}

15. \begin{align*}\frac{11}{12} - \frac{2}{3} = \underline{\;\;\;\;\;\;\;\;\;}\end{align*}

16. \begin{align*}\frac{6}{7} - \frac{4}{5} = \underline{\;\;\;\;\;\;\;\;\;}\end{align*}

Least Common Multiple

The least common multiple of two numbers is the smallest number that is a multiple of both of the original numbers.Lowest Common Denominator

The lowest common denominator of multiple fractions is the least common multiple of all of the related denominators.Renaming fractions

Renaming fractions means rewriting fractions with different denominators, but not changing the value of the fraction.### Image Attributions

Here you'll learn how to subtract fractions with different denominators.

Least Common Multiple

The least common multiple of two numbers is the smallest number that is a multiple of both of the original numbers.Lowest Common Denominator

The lowest common denominator of multiple fractions is the least common multiple of all of the related denominators.Renaming fractions

Renaming fractions means rewriting fractions with different denominators, but not changing the value of the fraction.