Math 5Simplifying Fractions

Instructor: Mrs. Tew Turner

In this lesson we will learn how to recognize & write

fractions in simplest form.

Math Warm-up

Find all of the factors of 40. See if you can find all 8.

Math Warm-up - ANSWER

Find all of the factors of 40. See if you can find all 8.

1, 2, 4, 5, 8, 10, 20, 40

Pause to work.

In this lesson we will answer the question:

How can you write a fraction in Simplest Form?

Vocabulary

Greatest Common Factor: The greatest number that is a factor of 2 or more given numbers.Example: 18=2 x 3 x 3

24=2 x 2 x 2 x3Find the prime numbers!Benchmark fraction: Common fractions used for estimating, such as ½, ¼, ⅓, ⅔, & ¾.

Vocabulary REVIEW

Multiple: the result of multiplyingtwo numbers. Prime: a number that can bedivided evenly only by 1 or itself.Composite: a number that can bedivided evenly by numbers otherthan 1 or itself.

REVIEW Equivalent FractionsConnection to Level 4 Math

Some fractions are written differently as in this picture, but they each

represent the same amount of pizza!

REVIEW Equivalent Fractions: Looking for a pattern.

Fractions in Simplest Form

A fraction is in simplest form when its numerator and denominator have no common factor other than 1.Examples:½, ⅓, ⅔, ¼, ¾, ⅕, ⅜, ⅞

Fractions in Simplest Form

To write 12/20 in simplest form, find a common factor of the numerator and the denominator. Since 12 and 20 are even numbers, we know this fraction is NOT in simplest form. What do you know about EVEN numbers? They are divisible by 2, right?

Fractions in Simplest Form

12/20 in both the numerator and the denominator the factor of 2 is shared. 2 is a common factor. Divide both12 and 20 by 2.

12 ÷ 2 = 620 ÷ 2 10

Is this fraction 6/10 in simplest form?

No

12 ÷ 2 = 620 ÷ 2 10

Both 6 and 10 are even. We need to divide them by 2 again! 6 ÷ 2 = 310 ÷ 2 5

We need to change the fraction again until it cannot be divided any more?

Yes, since 3 and 5 share no more common factors.

Is 3/5 in simplest form?

Fractions in Simplest FormIf a number is a factor of two numbers, it is called a common factor.

The greatest common factor (GCF), of 2 numbers is the greatest number that is a factor of both numbers.4 was the greatest common factor for both 12 & 20. 2 is a factor but we still did NOT have simplest form until we divided it by 4.

Simplify the fraction. common factor = common

multiple

4 ÷ 2 = 2 10 2 5

3 (Is this fraction in simplest form?) 5 Can the numerator & denomInator

be divided by a whole number?

Simplest Form

YES

(It was not in simplest form as it could be divided by ‘2’ for both the numerator & denominator.)

NO

Greatest Common Factor

The greatest common factor (GCF), of 2 numbers: 20 & 3020: 1, 2, 4, 5, 10, 2030: 1, 2, 3, 5, 6, 10, 15, 30The GCF of 20 & 30 is 10. Or 10 is a multiple of both numbers.

Document Camera

Get your notebook

and pencil ready.

Make sure you

have the Lesson #

and date on your

page.

Simplest Form

Fractions in Simplest FormGuided Practice

In your Math NotebookIndependent Practice

1.

4.

2.

3.

In your Math NotebookIndependent Practice ANSWERS

1.

4.

2.

3.

Quick CheckSome of the following fractions

CANNOT be simplified. Simplify the ones you can.

1. 2. 3. 4.

In your Math Notebook

Explain why some cannot be simplified, while others can be.

Quick Check Answers

1. No2. No3. YES…8/22 = 4/11 (÷ by 2)4. Yes…14/28 = 2/4 (÷ by 7)

Suggested Explanation: #1 and #2 fractions can’t be simplified because they do not share factors other than 1.

ConclusionSimplifying fractions , also known as, reducing or putting into lowest terms, means to make the fraction as simple as possible. They are still the same or equivalent but written with a different fraction name, as ½ = 2/4.To simplify a fraction, divide the top and bottom by the highest number that can divide into both numbers exactly.

Today you learned how to write a fraction in Simplest Form.

Good Work with this

lesson.