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# Fractions in Simplest Form

## Dividing top and bottom of a fraction by their GCF

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Fractions in Simplest Form
License: CC BY-NC 3.0

Tessa made a pan of brownies for the sixth grade social. She cut the brownie pan into sixteen brownies. She sold 12 out of 16 brownies at the bake sale.

What fraction of the brownies did she sell? What fraction did she not sell?

In this concept, you will learn to write a fraction in simplest form.

### Finding Fractions in Simplest Form

Some fractions can describe large quantities. Simplifying a fraction can make it easier to understand its value. To simplify a fraction, divide the numerator and the denominator by a common factor. Sometimes you will also hear simplifying called reducing a fraction. A fraction that has been simplified by the greatest common factor is in simplest form. Remember that the greatest common factor (GCF) is the greatest factor that two or more numbers have in common.

Here is a fraction.

4860\begin{align*}\frac{48}{60}\end{align*}

Simplify the fraction to better understand its value.

First, find a common factor for the numerator and denominator.

48 – 1, 2, 3, 4, 6, 8, 12, 16, 24, 48

60 – 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60

Then, divide by the GCF common factor. The GCF for 48 and 60 is 12

48÷1260÷12=45\begin{align*}\frac{48 \div 12}{60 \div 12} = \frac{4}{5}\end{align*}

The simplest form of 4860\begin{align*}\frac{48}{60}\end{align*} is 45\begin{align*}\frac{4}{5}\end{align*}.

Comparing fractions with different denominators can be difficult. Some fraction may look similar, but not be equivalent fractions. You can compare fractions with different denominators by comparing them in their simplest form.

Here are two fractions.

36\begin{align*}\frac{3}{6}\end{align*} and 48\begin{align*}\frac{4}{8}\end{align*}

Let’s simplify 36\begin{align*}\frac{3}{6}\end{align*}. To do this, divide the numerator and denominator by the GCF. The GCF of 3 and 6 is 3.

3÷36÷3=12\begin{align*}\frac{3 \div 3}{6 \div 3} = \frac{1}{2} \end{align*}

Let’s simplify 48\begin{align*}\frac{4}{8}\end{align*}. To do this, divide the numerator and the denominator by the GCF. The GCF of 4 and 8 is 4.

4÷48÷4=12\begin{align*}\frac{4 \div 4}{8 \div 4} = \frac{1}{2}\end{align*}

Both 36\begin{align*}\frac{3}{6}\end{align*} and 48\begin{align*}\frac{4}{8}\end{align*} are equivalent to 12\begin{align*}\frac{1}{2}\end{align*}. Therefore, 36\begin{align*}\frac{3}{6}\end{align*} and 48\begin{align*}\frac{4}{8}\end{align*} are also equivalent fractions.

### Examples

#### Example 1

Earlier, you were given a problem about Tessa and her brownies.

Tessa sold 12 out of 16 brownies at the bake sale. Simply the fraction for the number brownies she sold and did not sell.

First, write the fraction for the number of brownies that was sold.

1216\begin{align*}\frac{12}{16}\end{align*}

Then, simplify the fraction by dividing both by the GCF. The GCF is 4.

1216=34\begin{align*}\frac{12}{16} = \frac{3}{4}\end{align*}

She sold 34\begin{align*}\frac{3}{4}\end{align*} of the brownies

Now, write the fraction for the number of brownies that was not sold.

416\begin{align*}\frac{4}{16}\end{align*}

Then, simplify the fraction by dividing both by the GCF. The GCF is 4.

416=14\begin{align*}\frac{4}{16} = \frac{1}{4}\end{align*}

She did not sell 14\begin{align*}\frac{1}{4}\end{align*} of the brownies.

#### Example 2

Simplify the fraction.

2736\begin{align*}\frac{27}{36}\end{align*}

First, find the GCF of 27 and 36. The GCF for 27 and 36 is 9.

27 – 1, 3, 9, 27

36 – 1, 2, 3, 4, 6, 9, 12, 18, 36

Then, divide both the numerator and the denominator by 9.

27÷936÷9=34\begin{align*}\frac{27\div 9}{36\div 9} = \frac{3}{4}\end{align*}

The simplest form of 2736\begin{align*}\frac{27}{36}\end{align*} is 34\begin{align*}\frac{3}{4}\end{align*}.

#### Example 3

Simplify the fraction.

420\begin{align*}\frac{4}{20}\end{align*}

First, find the GCF of 4 and 20. The GCF for 4 and 20 is 4

Then, divide both the numerator and the denominator by 4.

The simplest form of 420\begin{align*}\frac{4}{20}\end{align*} is 15\begin{align*}\frac{1}{5}\end{align*}.

Solution: 15\begin{align*}\frac{1}{5}\end{align*}

#### Example 4

Simplify the fraction.

816\begin{align*}\frac{8}{16}\end{align*}

First, find the GCF of 8 and 16. The GCF for 8 and 16 is 8

Then, divide both the numerator and the denominator by 8.

The simplest form of 816\begin{align*}\frac{8}{16}\end{align*} is 12\begin{align*}\frac{1}{2}\end{align*}.

#### Example 5

Simplify the fraction.

515\begin{align*}\frac{5}{15}\end{align*}

First, find the GCF of 5 and 15. The GCF for 5 and 15 is 5

Then, divide both the numerator and the denominator by 5.

The simplest form of 515\begin{align*}\frac{5}{15}\end{align*} is 13\begin{align*}\frac{1}{3}\end{align*}.

### Review

Simplify each fraction. If the fraction is already in simplest form write simplest form for your answer.

1. 810\begin{align*}\frac{8}{10}\end{align*}
2. 410\begin{align*}\frac{4}{10}\end{align*}
3. 210\begin{align*}\frac{2}{10}\end{align*}
4. 212\begin{align*}\frac{2}{12}\end{align*}
5. 312\begin{align*}\frac{3}{12}\end{align*}
6. 49\begin{align*}\frac{4}{9}\end{align*}
7. 520\begin{align*}\frac{5}{20}\end{align*}
8. 1224\begin{align*}\frac{12}{24}\end{align*}
9. 1236\begin{align*}\frac{12}{36}\end{align*}
10. 1144\begin{align*}\frac{11}{44}\end{align*}
11. 2045\begin{align*}\frac{20}{45}\end{align*}
12. 1820\begin{align*}\frac{18}{20}\end{align*}
13. 1230\begin{align*}\frac{12}{30}\end{align*}
14. 2240\begin{align*}\frac{22}{40}\end{align*}
15. 3563\begin{align*}\frac{35}{63}\end{align*}

### Review (Answers)

To see the Review answers, open this PDF file and look for section 5.8.

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### Vocabulary Language: English

Denominator

The denominator of a fraction (rational number) is the number on the bottom and indicates the total number of equal parts in the whole or the group. $\frac{5}{8}$ has denominator $8$.

Equivalent

Equivalent means equal in value or meaning.

fraction

A fraction is a part of a whole. A fraction is written mathematically as one value on top of another, separated by a fraction bar. It is also called a rational number.

Numerator

The numerator is the number above the fraction bar in a fraction.

Reducing

Reducing is another way to say simplifying, most often with respect to fractions.

Simplify

To simplify means to rewrite an expression to make it as "simple" as possible. You can simplify by removing parentheses, combining like terms, or reducing fractions.

### Image Attributions

1. [1]^ License: CC BY-NC 3.0

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