DO NOW (not later):

1
DO NOW (not later)

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

Free powerpoints at http//www.worldofteaching.com
2

• The number of boys
• The number of girls
• If we compare boys to girls we get
• ___ boys to _____ girls.

3
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.
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AIM

• What is a ratio?

5
Its 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?
6
How many basketballs to footballs are there?

• For every 4 basketballs there are 6 footballs.
• The ratio is 4 to 6.

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What are some other ways we can write the ratio
of basketball to footballs?
Every ratio can be written in 3 ways

• 4 to 6
• 4 6
• 4
• 6

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

• 68 , 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.
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Equivalent Ratios

• Simplify the following ratios
• 4 to 8
• 10 to 8
• 8 to 10

• 4 / 4 1 1 to 2
• 8 8 / 4 2

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
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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)
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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 124.
• This means that there is one cup of milk for
  every two cups of sugar and four cups of batter.

12
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?
• How many yellow marbles are there?

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.
4 2 can be simplified to 2 1
4 3
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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?

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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

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Practice Word Problems

1. 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.

• 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.

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Practice Word Problems

• Mindy has 72 candy bars. If the ratio of Mars to
  Snickers is 84, Find the number of each type of
  candy.
• Explain what this ratio tell us.

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Challenge Question

• The perimeter of a rectangle is 500 feet. The
  ratio of the base and height is 32. What is the
  measure of the height?