DO NOW (not later):

Compare the number of boys to girls in the class.

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The number of boys =

The number of girls =

If we compare boys to girls we get

___ boys to _____ girls.

What do we call a comparison between two or more quantities?

RATIOWe just found the RATIO of boys to girls.

Is the ratio of girls to boys the same ?

No, when writing a ratio, ORDER matters.

AIM:

What is a ratio?

It’s Friday night and your friends are having a party…… The ratio of girls to guys is 2 to 12.

Would you want to attend the party?

How many basketballs to footballs are there?

For every 4 basketballs there are 6 footballs.

The ratio is 4 to 6.

What are some other ways we can write the ratio of basketball to footballs?

4 to 6

4 : 6

4 6

First quantity to Second quantity

First quantity : Second quantity

First quantity divided by the second quantity (as a fraction).

Every ratio can be written in 3 ways:

Careful!!

Order matters in a ratio.

4 to 6

Is NOT the same as

6 to 4

Write the ratio of sandwiches to coke bottles 3 different ways.

6:8 , 6 to 8, and 6 8

Since a fraction can be simplified, We can simplify the ratio 6/8 to 3/4. The ratio of sandwiches to coke bottles can also be expressed as 3 : 4 or 3 to 4.

In other words, ratios can be simplified to form equivalent ratios.

Equivalent Ratios Simplify the following ratios:

4 to 8 10 to 8 8 to 10

Step 1 – Write the ratio as a fraction

Step 2 – Simplify the fraction (Find the greatest common factor (GCF) of both numbers and divide the numerator and denominator by the GCF).

Step 3 – Write the equivalent ratio in the same form as the question

4 = 4 / 4 = 1 = 1 to 2

8 8 / 4 2

GCF = 4

Equivalent Ratios can be formed by multiplying the ratio by any number.

For example, the ratio 2 : 3 can also be written as 4 : 6 (multiply original ratio by by 2) 6 : 9 (multiply original ratio by by 3) 8 : 12 (multiply original ratio by by 4)

The ratio 2 : 3 can be expressed as 2x to 3x (multiply the original ratio by any number x)

Compound Ratios

A ratio that compares more than 2 quantities is called a compound ratio.

Example: A cake recipe says the ratio of cups of milk, sugar,

and batter are 1:2:4. This means that there is one cup of milk for every

two cups of sugar and four cups of batter.

A bag contains 18 yellow, blue, and red marbles. The ratio of yellow to blue to

red marbles is 4 : 2 : 3. 1) Write the ratio of yellow to blue marbles in

simplest form.2) What is the ratio of yellow to red marbles?3) How many yellow marbles are there?

4 : 2 can be simplified to 2 : 1

4 : 3

Yellow : Blue : Red is 4 : 2 : 3

Since any multiple of this is an equivalent ratio, this can also be written as 4x : 2x: 3x

Let 4x = yellow, 2x = blue , 3x = red

4x + 2x+ 3x = 18

9x = 18

X= 2

Since the question asks for yellow marbles,

there are 4x or 4 (2) = 8 yellow marbles.

Practice problem # 1(1) You have 100 different shirts. The ratio

of blue to black shirts is 20 . 30

a) Write the ratio of blue to black shirts 3 different ways.

b) Write the ratio in simplest form. c) Explain what this ratio tells us.

d) How many black shirts do you have?

Solution - # 1 You have 100 different shirts. The ratio of blue to black shirts is 20 /

30 a) Write the ratio of blue to black shirts 3 different ways.

20 to 30 , 20 : 30, 20 30

b) Write the ratio in simplest form. 2 3c) Explain what this ratio tells us. For every two blue shirts, there are

3 black shirts.d) How many black shirts do you have?

2x + 3x = 100 5x = 100 x = 20

There are 2x black shirts so 2 (20) = 40 black shirts

Practice Word Problems1) You go to a party where

the ratio of boys to girls is 28 to 56. Express the ratio of boys to girls in simplest form.

2) Explain what this ratio tells us.

(1)28 / 56 = 1 / 2

The ratio of boys to girls is 1 to 2

(2) For every 1 boy there are 2 girls at the party.

Practice Word Problems

(1) Mindy has 72 candy bars. If the ratio of Mars to Snickers is 8:4, Find the number of each type of candy.

(2) Explain what this ratio tell us.

Challenge Question

The perimeter of a rectangle is 500 feet. The ratio of the base and height is 3:2. What is the measure of the height?