Fractions in Simplest Form

Lesson Plan - Get It!

Audio:

• 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.

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

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.

• 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.

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. Ryan’s mom said ½ of the pizza was left. Who is correct?

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.