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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

Have you ever had to cut a pan of brownies evenly? It can be more challenging than one would think.

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?

To identify each fraction, you will need to know how to simplify. This Concept will teach you how to write each fraction and then how to simplify each of them.

### Guidance

One of the trickiest skills involving equivalent fractions is being able to determine whether or not they are equivalent.

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

This is tricky because we can’t tell if the numerator and denominator were multiplied by the same number. These fractions look like they might be equal, but how can we tell for sure? This is where simplifying fractions is important.

How do we simplify fractions? You can think of simplifying fractions as the opposite of creating equal fractions. When we created equal fractions we multiplied. When we simplify fractions, we divide.

What do we divide? To simplify a fraction, we divide the top and the bottom number by the Greatest Common Factor.

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

The GCF of 3 and 6 is 3.

3÷36÷3=12

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

The GCF of 4 and 8 is 4.

4÷48÷4=12

We can see that 36\begin{align*}\frac{3}{6}\end{align*} and 48=12\begin{align*}\frac{4}{8} = \frac{1}{2}\end{align*}. They are equivalent fractions.

We can use simplifying to determine if two fractions are equivalent, or we can just simplify a fraction to be sure that it is the simplest it can be. Sometimes you will also hear simplifying called reducing a fraction.

Simplify the following fractions by dividing by the GCF of the numerator and the denominator.

#### Example A

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

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

#### Example B

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

Solution: 12\begin{align*}\frac{1}{2}\end{align*}

#### Example C

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

Solution: 13\begin{align*}\frac{1}{3}\end{align*}

Do you understand how to write the brownie fractions and simplify them? Here is the original problem once again.

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?

First, let's write the fraction that she sold and simplify it. Tessa sold 12 out of 16 brownies.

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

She did not sell 4 out of 16 brownies.

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

This is the solution to the problem.

### Vocabulary

Fraction
a part of a whole.
Equivalent
means equal
Numerator
the top number in a fraction
Denominator
the bottom number in a fraction
Simplifying Fractions
dividing a numerator and a denominator by the GCF to create a fraction that is in simplest form. An equivalent fraction is created.
Reducing
another way to say simplifying

### Guided Practice

Here is one for you to try on your own.

Simplify the following fraction.

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

To start, we have to find the GCF of both 48 and 60. The GCF of 48 and 60 is 12.

We can divide both the numerator and the denominator by 12.

45\begin{align*}\frac{4}{5}\end{align*} is our simplified fraction.

### Video Review

http://www.mathplayground.com/howto_fractions_reduce.html – a blackboard style video on reducing/simplifying fractions

### Practice

Directions: 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*}

### Vocabulary Language: English

Denominator

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

Equivalent means equal in value or meaning.
fraction

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

Numerator

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

Reducing

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

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.