Warm UpWrite each fraction in lowest terms.

1416

1.

972

3.

2464

2.78

38

18

Unit 1: Ratios and Propotional Unit 1: Ratios and Propotional ReasoningReasoning

Lesson 1: Lesson 1: ““Ratios”Ratios”

Vocabulary

fraction

rational numberratioequivalent ratios

A fraction is an equal part of a whole

The top number is the

numerator... 3 4

The bottom number is the

denominator...

for example...

...this tells you how

many equal pieces

there are present.

...this tells you how many

equal pieces the fraction

is broken into.

4 equal pieces...

3 are present

nd

Any fraction can be written as a decimal by dividing the numerator by the denominator.

1 2 1 ÷ 2

A rational number is any number that can be written as a fraction, as long as both the numerator and denominator are integers and d 0 (because you can't divide anything by zero).

=

= 0.5

for example...

A ratio is a comparison of two quantities.

Ratios can be written in three ways.

7 5

Each of these name the same ratio!

First number “ to” second 7 to 5

First number “:” second 7:5

As a fraction, with the first number over second

Class Example: Writing Ratios in Simplest Form

Write the ratio 15 bikes to 9 skateboards in simplest form.

159

53

The ratio of bikes to skateboards is , 5:3, or 5 to 3.

15 ÷ 39 ÷ 3

Write the ratio as a fraction.

= = Simplify.

53

bikes

(Start by writing the words as a fraction; the first is the numerator, the second is the denominator.)

skateboards

Partner Example: Writing Ratios in Simplest Form

Write the ratio 24 shirts to 9 jeans in simplest form.

249

83

The ratio of shirts to jeans is , 8:3, or 8 to 3.

=shirtsjeans

24 ÷ 39 ÷ 3

Write the ratio as a fraction.

= = Simplify.

83

Ratios that make the same comparison are equivalent ratios. Equivalent ratios represent the same point on the number line.

One way to check whether two ratios are equivalent is to write both in simplest form.

Partner Example: Determining Whether Two Ratios Are Equivalent

Simplify to tell whether the ratios are equivalent.

1215

B. and 2736

327

A. and 218

Since ,

the ratios are

equivalent.

19

= 19

19

=3 ÷ 327 ÷ 3

327

=

19

=2 ÷ 218 ÷ 2

218

=

45=

12 ÷ 315 ÷ 3

1215

=

34=

27 ÷ 936 ÷ 9

2736

=

Since ,

the ratios are not

equivalent.

45 3

4

Individual Practice: Determining Whether Two Ratios Are Equivalent

Simplify to tell whether the ratios are equivalent.

1449

B. and 1636

Since ,

the ratios are

equivalent.

15

= 15

15

=3 ÷ 315 ÷ 3

315

=

15

=9 ÷ 945 ÷ 9

945

=

27

=14 ÷ 749 ÷ 7

1449

=

49=

16 ÷ 436 ÷ 4

1636

=

Since ,

the ratios are not

equivalent.

27 4

9

315

A. and 945