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Supplemental Math: Study Aid1 chapters | 19 lessons

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Lesson Transcript

Instructor:
*Jennifer Beddoe*

Simplifying fractions requires you to reduce a fraction to its smallest form. This lesson will give two methods for simplifying fractions, and a quiz at the end will allow for some practice.

Have you ever eaten a whole pizza? Maybe not, but if you've ever eaten part of a pizza and saved the rest for later, you've eaten a fraction of a pizza. Say this was your pizza, sliced into 5 even pieces. What if you eat 3 of the 5 pieces? You can relate the amount of pizza you ate as a fraction, 3/5, which means that there are 2/5 of the pizza leftover for lunch tomorrow.

A fraction represents part of a whole number. The **numerator** (or top number) tells you how many pieces you are talking about, and the **denominator** (the bottom number) is how many pieces make up the whole. As for your pizza, you ate 3 pieces, so for this fraction the numerator is 3, and there were 5 pieces in total, so the denominator is 5. There are three types of fractions:

**Proper fractions**, where the numerator is less than the denominator**Improper fractions**, where the numerator is higher than (or equal to) the denominator**Mixed fractions**, a whole number and proper fraction combined

**Simplifying fractions** is the process of reducing the numerator and denominator to their smallest whole numbers so the fraction is in its simplest form. In mathematics, it is always important to make sure everything is in its simplest form. This helps other mathematicians or scientists to easily interpret data and can also help avoid confusion when numbers and equations become large and complex.

There are two methods for simplifying fractions. The first method is to divide the numerator and denominator until you can't simplify any further. It's very important when you are dividing that at each step you divide the numerator and denominator by the same number. This will keep the fraction equivalent. The second method is to divide each number by the **greatest common factor** (GCF). The GCF is the largest number that will divide into both numbers evenly. It is calculated by listing the factors of each number and determining which is the greatest.

**1.** Use the first method described to simplify 120/180.

Divide both the numerator and denominator by 2 to get 60/90.

Divide both the numerator and denominator of 60/90 by 3 to get 20/30.

Divide both the numerator and denominator of 20/30 by 5 to get 4/6.

Divide both the numerator and denominator of 4/6 by 2 to get 2/3.

The fraction 2/3 is in its simplest form.

**2.** Find the GCF of 36 and 54.

The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36.

The factors of 54 are 1, 2, 3, 6, 9, 18, 27, and 54.

The common factors of 36 and 54 are 1, 2, 3, 6, 9, and 18.

These numbers are all common factors of 36 and 54, but the greatest is 18. Therefore, 18 is the greatest common factor of 36 and 54.

**3.** Simplify the following fraction: 24/40.

First, find the GCF of 24 and 40.

The factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24.

The factors of 40 are 1, 2, 4, 5, 8, 10, 20, and 40.

The greatest common factor (GCF) is 8.

Divide both sides of the fraction by 8 and you get 3/5.

Fractions are in the **simplest form** when there is no common number that can be divided into both the **numerator** and **denominator** evenly. There are two methods for **simplifying fractions**. The first is to divide both the numerator and denominator by common numbers until there are no more numbers in common. The second option is to find the **greatest common factor** of the two numbers and then divide each by this number.

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Supplemental Math: Study Aid1 chapters | 19 lessons

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