RATIOS

DO NOW (not later):

Compare the number of boys to girls in the class.

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.

Essential Question:

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)

Now you try…1.There are 6 goldfish and 5 mollys in the fish

tank. What is the ratio of goldfish to all fish in the tank?

2.Brad has 2 brothers and 4 sisters. What is the ratio of boys to girls in his family?

3.Julie has 8 cats, 5 dogs, 4 pigs, and 7 horses on her farm.a)What is the ratio of cats to dogs?b)What is the ratio of dogs to horses?c)What is the ratio of pigs to cats?d)What is the ratio of cats to all animals on the

farm?