*Contributor: Erika Wargo. Lesson ID: 12406*

Which is easier, adding 12/144 + 1/12 or adding 1/12 + 1/12? They're both the same, only the second time, the large fraction was simplified! Learn how easy it is to make fraction simplification easy!

categories

subject

Math

learning style

Visual

personality style

Otter

Grade Level

Intermediate (3-5)

Lesson Type

Quick Query

Ryan’s family ordered a pizza with eight slices for lunch. After everyone ate, Ryan noticed that ^{4}⁄_{8} of the slices were left. Ryan’s mom said ½ of the pizza was left.

- Who is correct?

- Does
^{263}⁄_{526}seem like a pretty hairy fraction?

- Did you know that fractions can be simplified?

*Simplify* means to make something easier to understand. Simplifying, or reducing, fractions means to rewrite the fraction in a simpler form, without changing the value of the fraction.

As you watch *Math Antics - Simplifying Fractions*, write down the two methods that are used to simplify fractions:

- What is a common factor?
- How does finding the greatest common factor (GCF) help simplify fractions?

There are two methods used to simplify fractions.

**Method 1**

Choose a whole number that evenly divides into both the numerator and the denominator. Start with 2, 3, 5, or 7 and continue dividing until either the numerator or the denominator is a prime number.

- The numerator is the top number of a fraction.
- The denominator is the bottom number of a fraction.
- Prime numbers can only be divided by 1 and the number itself.

Example: Simplify the fraction |
12 |

20 |

Since 12 and 20 are both even numbers, start by dividing by 2.

12 | ÷ | 2 | = | 6 | |

20 | 2 | 10 |

The new fraction is | 6 | , which can be divided by 2 again. |

10 |

6 | ÷ | 2 | = | 3 | |

10 | 2 | 5 |

3 | is our solution because both 3 and 5 are prime numbers. |

5 |

There is no other number that can divide into both besides one.

**Method 2**

Now, look at that same problem, but simplify using the greatest common factor.

12 |

20 |

- First, list the factor pairs of each number. Factors are the numbers that multiply together to give us the number.

12: 1 x 12, 2 x 6, 3 x 4

20: 1 x 20, 2 x 10, 4 x 5

- Now, rewrite the factors for each number in order from least to greatest. Circle or highlight the common factors.

12: 1, 2, 3, 4, 6, 12

20: 1, 2, 4, 5, 10, 20

- Find the highest number in the common factors. 4 is the greatest common factor of 12 and 20. After dividing both fractions by 4, we get the same answer, 3/5.

12 | ÷ | 4 | = | 3 | |

20 | 4 | 5 |

Simplifying or reducing fractions can help us understand fractions a little easier. Look back at the problem from the beginning of the lesson. Discuss with a parent or teacher who is correct and how you figured out your answer.

*Ryan’s** family ordered a pizza with **eight **slices for lunch. After everyone ate, **Ryan** noticed that ^{4}⁄_{8} of the slices were left. *

The two fractions are ^{4}/_{8} and ^{1}/_{2}.

Can either fraction be simplified?

^{4}/_{8} can be simplified by dividing by the greatest common factor of 4.

^{4}/_{8} simplifies to ^{1}/_{2}.

Both Ryan and his mom were correct! Referring to fractions in their simplest form helps people understand situations better. It may be easier to understand that ½ of the pizza is left, instead of ^{4}⁄_{8}.

Both answers are correct, but answers are usually simplified when working with fractions.

Explain outloud the steps in each method used to simply fractions.

- Which method do you like the most?

In the *Got It?* section, you will practice identifying the greatest common factors of numbers and simplifying fractions.