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Ratios. Compare the number of boys to girls in the class. Free powerpoints at http://www.worldofteaching.com. 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?.

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ratios
Ratios
  • Compare the number of boys to girls in the class.

Free powerpoints at http://www.worldofteaching.com

slide2
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
What do we call a comparison between two or more quantities?

We just found the RATIO of boys to girls.

RATIO

Is the ratio of girls to boys the same ?

No, when writing a ratio, ORDER matters.

slide4
AIM:

What is a ratio?

it s friday night and your friends are having a party
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
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
What are some other ways we can write the ratio of basketball to footballs?
  • 4 to 6
  • 4 : 6
  • 4

6

Every ratio can be written in 3 ways:

First quantity to Second quantity

Careful!!

Order matters in a ratio.

4 to 6

Is NOT the same as

6 to 4

First quantity : Second quantity

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

write the ratio of sandwiches to coke bottles 3 different ways
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
Equivalent Ratios
  • = 4 / 4 = 1 = 1 to 2
  • 8 8 / 4 2
  • Simplify the following ratios:
    • 4 to 8
    • 10 to 8
    • 8 to 10

GCF = 4

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

equivalent ratios can be formed by multiplying the ratio by any number
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
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
A bag contains 18 yellow, blue, and red marbles. The ratio of yellow to blue to red marbles is 4 : 2 : 3.
  • Write the ratio of yellow to blue marbles in simplest form.
  • What is the ratio of yellow to red marbles?

4 : 2 can be simplified to 2 : 1

4 : 3

practice problem 1
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
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

3

c) 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 problems
Practice Word Problems
  • 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.
  • Explainwhat this ratio tells us.
  • 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 problems16
Practice Word Problems
  • Mindy has 72 candy bars. If the ratio of Mars to Snickers is 8:4, Find the number of each type of candy.
  • Explain what this ratio tell us.
challenge question
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?