Transcript Proportions and Ratios

PROPORTIONS AND
RATIOS
EQ: How can finding equivalent
ratios help us solve proportions?
WHAT IS A RATIO?

A ratio is a comparison of two numbers by division

In other words, a ratio looks like a fraction

Example: How many blue colored pencils do I have
compared to my total number of colored pencils?

Right! I have 5 to 13 or 5/13 or 5:13.
WHAT IS A PROPORTION?

A proportion is an equation that says that two
ratios are equivalent (equal)

For example, 4/8 = 2/4
=
HOW CAN WE USE CROSS PRODUCTS?

For two ratios to form a proportion, their cross
products must be equal.
CROSS PRODUCTS
Cross products in proportions are equal
4 =
__
8
8•2=
2
__
4
4•4
16 = 16
3 = ___
9
__
5
15
5 • 9 = 3 • 15 6
45 = 45
9 =
__
6
• 3 =
3
14
2
__
__ = __
2
7
1
9 • 2 7 • 2 = 14 • 1
18 = 18
14 = 14
HOW CAN WE USE CROSS PRODUCTS TO
SOLVE A PROPORTION?

Example #1: Find the missing value
n
5
__
__
=
6
18
6 • n = 5 • 18
6n = 90
90
6n
___
= ___
6
6
n = 15
Find the cross products.
The cross products are equal.
n is multiplied by 6.
Divide both sides by 6 to undo the
multiplication.
HOW CAN WE USE CROSS PRODUCTS TO
SOLVE A PROPORTION?

Example #2: Find the missing value.
n
3
__
__
=
5
15
5 • n = 3 • 15
5n = 45
5n
45
___
___
=
5
5
n=9
Find the cross products.
The cross products are equal.
n is multiplied by 5.
Divide both sides by 5 to undo the
multiplication.
ON YOUR OWN:

Find the missing value.
25
5__ __
=
7
m
HOW TO SOLVE PROBLEMS USING
PROPORTIONS?

Out of 32 students, 24 prefer dogs as pets. Based
on these results, how many of the 500 students in
the school prefer dogs as pets?
Prefer dogs
Total students in class
s
__
24
__
=
32 500
Prefer dogs
Total students in school
32 • s = 24 • 500
32s = 12,000
32s
___ = 12,000
______
32
32
s = 375
So, 375 out of 500 students prefer to have a dog as a pet.
ON YOUR OWN:

At West High Middle School, the teacher to
student ratio if 3 to 78. If there are 468 students
enrolled at the school, how many teachers are
there at the school?
ON YOUR OWN:

Barbara’s goal is to practice piano 20 minutes for
every 5 minutes of lesson she takes. If she takes
a 20 minute piano lesson this week, how many
minutes should she practice?
TOD:
 On

a sheet of paper answer the following:
In your own words, explain how you would
use cross products to find the missing
value in a proportion.