Transcript Ratios and Unit Rates

Ratios and Unit Rates
Ratios
 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.
Ratios
 What
do we call a comparison between
two numbers???
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
What is a ratio?


How many basketballs to footballs are there?
For every 4 basketballs there are 6 footballs.
 The ratio is 4 to 6
Ratios

What are some other ways we can write the
ratio of basketballs to footballs???
 4 to 6 First quantity to Second quantity

4:6

4
6

First quantity : Second quantity
First quantity divided by the
second quantity (as a fraction)
Every ratio can be written in these 3 ways!
Ratios
 Careful…..Order
DOES matter in a ratio!

4 to 6 is NOT the same as 6 to 4!!!

4:6 is NOT the same as 6:4!!!

4 is NOT the same as 6
6
4
Ratios

Write the ratio of sandwiches to coke bottle in 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.
To write an equivalent ratio by
simplifying follow these steps:
 Step

Example: 4 to 8 = 4
8
 Step

1 - Write the ratio as a fraction
2 - Simplify the fraction
Example: 4 ÷ 4 = 1
8÷4 2
 Step
3 - Write the equivalent ratio in the
same form as the question.

Example: 1 = 1 to 2
2
Equivalent Ratios
 Equivalent
ratios can also 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)
Practice Problem
 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.
 Explain what this ratio tells us.
Unit Rates
 In
a ratio, if the numerator and denominator
are measured in different units then the ratio
is called a rate
 A unit
rate is a rate per one given unit, like
60 miles per 1 hour.
 To
change a rate into a unit rate, divide both
the numerator and denominator by the
number in the denominator.
Unit Rates Examples
 Example:
75 miles= 75 mi ÷ 3 = 25 mi
3 hours
3 hr ÷ 3 1 hr
 The
unit rate is 25 miles per hour
Unit Rates Examples
 Example:


Find the unit rate…
Belinda biked 36 miles in 4 hours.
36 mi ÷ 4 = 9 mi
4 hr ÷ 4 1 hr
 She
rode 9 miles per hour
Try one on your own…
 Find
the unit rate. Joe scores 96 points in
8 games.
 Kendra
spends $21 for 3 CD’s.