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Ratios Notes
Essential Question:

What does it mean if two different ratios
describe the same situation? How can being
able to describe a situation in multiple ways
help you to solve problems?
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?
RATIO
We just found the
RATIO of boys to
girls.
Is the ratio of
girls to boys
the same ?
No, when writing a ratio, ORDER matters.
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?
Every ratio can be written in 3 ways:



4 to 6
First quantity to Second quantity
4:6
First quantity : Second quantity
4
6
First quantity divided by the second
quantity (as a fraction).
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
4 = 4/4
8
8/4
=1
= 1 to 2
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
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.
Write the ratio of yellow to blue marbles in
Yellow
: Blue form.
: Red is4 : 24 can
: 2 be
: 3
simplest
simplified to 2 : 1
2)Since
What
the ratio
of yellow
to red marbles?
any is
multiple
of this
is an equivalent
ratio, this 4 : 3
can also be written as 4x : 2x: 3x
3) How many yellow marbles are there?
1)
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,
b) Write the ratio in simplest form.
2
3
20
30
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
You go to a party where
the ratio of boys to girls
is 28 to 56. Express the
ratio of boys to girls in
(1)28 / 56 = 1 / 2
simplest form.
The ratio of boys to girls is 1 to 2
2) Explain what this ratio
(2) For
every
1 boy there are 2
tells
us.
1)
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?
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