Ratios

Ratio?

Ratio is a way of comparing two or more quantities

Examples:

◦Number of oranges to apples

◦Number of girls in a class compared to boys

There are 3 ways to express ratios:

As a fraction - ¾Using a colon - 3:4Using the word “to” - 3 to 4

What is the ratio of cats to mice?

Number of Cats: 3

Number of Mice: 6

Express the ratio as a fraction:

Express the ratio in words:

Express the ratio with a colon:

3 to 6

3:6

63

Team Wins Losses

S.D. Padres 16 11

L.A. Dodgers 18 13

Chicago Cubs 17 14

2001 Spring Training

List the wins to losses by the Cubs : 17 to 14

Wins to games played by the Cubs: 17 to 31

List the losses to wins by the Padres: 11/16

Losses to games played by the Padres : 11/27

Team Wins Losses

S.D. Padres 16 11

L.A. Dodgers 18 13

Chicago Cubs 17 14

2001 Spring Training

List the Dodgers wins to total games: 18 : 31

List the Dodgers losses to wins: 13 : 18

Your face uses about 13 muscles to smile and about 43 muscles to frown. Write the ratio of muscles used for frowning to muscles used for smiling in three different ways.

43:13

43/13

43 to 13

Comparing Ratios Seth and Nathan compared their CD

collections. To determine who has a greater ratio of rock CDs to pop CDs, write the ratios.

Rock Pop Hip-hop

Seth 9 23 16

Nathan 42 70 25

Seth:

= .375

Nathan: = 0.6

Write ratios as fractions.

Write fractions as decimals to compare.

Nathan has a greater ratio of rock to pop CDs.

Pop

Rock

23

9

Pop

Rock

70

42

How do you change a fraction into a decimal?

Divide the denominator into the numerator

OR on your calculator hit 9 divided by 24 = .375

24

9

RED & BLUE Smarties

6 BLUE 3 RED

“The Ratio of BLUE to RED Smarties is 6 to 3

Blue : Red

6 : 3

Which symplifies to 2 : 1

“The Ratio of BLUE to RED Smarties is 6

Ratio Example Problems

…. Or… We can compare Red to Blue Smarties!

RED & BLUE Smarties

6 BLUE 3 RED

“The Ratio of RED to BLUE Smarties is 3 to 6”

Red : Blue

3 : 6

1 : 2

“The Ratio of RED to BLUE Smarties is 1:2”

“For every RED Smartie, there are 2 BLUES”

Simplifying Ratios

In the Smarties example, we changed 6:3 to 2:1

This is called Simplifying a ratio

We did it by dividing each number by 3

3 was the largest common factor

Try to simplify these

8:218:34:85:255:2

4:16:11:21:55:2 !!

Sharing an amount in a given ratio“Bart and Maggie share a bag of 16 life savers with the ratio of 3:1”

This means “for every 3 life savers Bart gets, Maggie gets 1”4

Lifesavers for Maggie

12Lifesavers for Bart

What is a ratio?

Example: There are 300 computers and 1200 students in our school. What is the ratio of computers to students?

Express the ratio in words:

Express the ratio as a fraction:

A ratio is a comparison

of two quantities.

Express the ratio with a colon:300 computers : 1200 students

How many students are there for one computer?

300 computers to 1200 students

𝟑𝟎𝟎𝒄𝒐𝒎𝒑𝒖𝒕𝒆𝒓𝒔𝟏𝟐𝟎𝟎𝒔𝒕𝒖𝒅𝒆𝒏𝒕𝒔

Equivalent ratios make

the same comparison.

What is an Equivalent Ratio?

1.There are 300 computers for 1200 students

Express the ratio as a fraction:

1200300

2.There is 1 computer for every 4 students

OR

Bring the fraction to lowest terms:

1200300

41

=

Practice With Equivalent Ratios

Find an equivalent ratio by dividing:

9030

Divide by 3031

= # 1

# 2 1215

45

= Divide by 3

# 3300125

125

= Divide by 25

30903030

÷÷

=

312315

÷÷

=

2530025125

÷÷

=

Practice With Equivalent Ratios

Find an equivalent ratio by multiplying:

410

Multiply by 554510

x x

= # 4

# 5

# 6

2050

=

37

12 x 312 x 7

=3684

= Multiply by 12

2011

6 x 206 x 11

=12066

= Multiply by 6

Practice:Ratios worksheet