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 .

SEPTEMBER 4, 2015

Warm-Up:

2

1

1, 2, 3, 4, 6, 12

1, 3, 7, 21

45

, ,2 6

Ex: ...4 12

TONIGHT’S HOMEWORK

Worksheet 1.1** This is on a handout, or on my teacher website

Sign Syllabus!

WRITE THE OBJECTIVE IN YOUR OWN WORDS IN YOUR MATH JOURNAL:

SWBAT write fractions in simplest form.

Lesson 1.1

VOCABULARYFractionA number that represents a part of a whole number.

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

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

Simplest FormWhen a numerator and denominator’s only common factor is 1.

EXAMPLE 1

Find two fractions that are equivalent to .

Multiply the top and bottom bythe same number.

Divide the top and bottom bythe same number.

1014

Explore! Fraction Tiles

Each large rectangle below represents one whole. Each rectangle is divided into equal parts. It is called a fraction bar.

Step 1 Write a fraction to representnumber of shaded sectionstotal number of sections

for each fraction bar.

Step 2 Match each fraction in the left column with its equivalent fraction in the right column. Write the pair of equivalent fractions.

For example, .1 2

5 10

Step 3 Write a third equivalent fraction for each pair in Step 2.

Explore! Fraction Tiles

Step 5 The fractions in the left column are in simplest form. Look at the fractions in the left column compared to those in the right column and explain what simplest form means.

Step 4 Draw two fraction bars to show and . Are these equivalent fractions? Explain. If so, write a third equivalent fraction to and .

34

68 3

468

EXAMPLE 2

Find the GCF of 24 and 36.

Look at the prime factorization of 24 and 36.

The common prime factors of24 and 36 are 2, 2 and 3.

The GCF can be found my multiplyingthese factors together.

2 2 3 12

GCF = 12

A factor tree may help.

36

4 9

2 2 3 3

36 2 2 3 3 24 2 2 2 3

WRITING FRACTIONS IN SIMPLEST FORMDivide 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.

EXAMPLE 3a. Write the fraction in simplest form:

Find GCF of 20 and 50. 20 = 2 2 5 50 = 2 5 5

The common prime factors GCF = 2 5 = 10of 20 and 50 are 2 and 5.

Divide the numerator anddenominator by the GCF.

in simplest form is

2050

2050

25

EXAMPLE 3 CONTINUED…

b. Write the fraction in simplest form:

One common factor of 45 and 60 is 5.

Divide the numerator anddenominator by 5.

A common factor of 9 and 12 is 3.

Divide the numerator anddenominator by 3.

in simplest form is

4560

4560

34

COMMUNICATION PROMPT

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

EXIT PROBLEMS

1. Find two fractions that are equivalent to .

2. Find the GCF of 32 and 48.

3. Write each fraction in simplest form.

a. b.

312

18

15

80

30

16

, , , , ,1 2 4 5 6

Ex: ...4 8 16 20 24

56

38