Simplifying Fractions

Lesson 1

1. List the factors of 21.

2. List the factors of 12.

3. What fraction is represented by the model?

4. Write two fractions that are equivalent to .2

1

Targets: Write fractions in simplest form.

Fraction: A number that represents a part of a whole number.

Equivalent Fractions: Fractions that represent the same number but have different numerators and denominators.

Greatest Common Factor: Greatest factor that is common to two or more numbers.

Simplest Form: When a numerator and denominator’s only common factor is 1.

Divide the numerator and denominator by the greatest common factor (GCF).

- OR -

Divide the numerator and denominator by common factors until the only common factor is 1.

Find two fractions that are equivalent to .

Multiply the top and bottom by the same number.

Divide the top and bottom by the same number.

14

10

Find the GCF of 10 and 15.

Prime factorizations:◦10 = 2 · 5◦15 = 3 · 5

The only common factor is 5. GCF = 5.

Find the GCF of 24 and 36.

Prime factorizations:◦24 = 2 · 2 · 2 · 3◦36 = 2 · 2 · 3 · 3

Common factors: 2 · 2 · 3 = 12. GCF = 12.

Write the fraction in simplest form:

Find GCF of 20 and 50.

Prime factorization:◦20 = 2 · 2 · 5◦50 = 2 · 5 · 5

Greatest Common Factor: 2 · 5 = 10

Divide the numerator and denominator by the GCF.

50

20

Write the fraction in simplest form:

One common factor is 5.

A remaining common factor of 9 and 12 is 3.

One is the only remaining common factor. is in simplest form.

60

45

4

3

Find two fractions that are equivalent to .

Find the GCF of 32 and 48.

Write each fraction in simplest form.

a. b.

12

3

18

15

80

30

Describe a situation where you might see a fraction that is not in simplest form.