Understanding Proportion
Ratio

A ratio is the comparison of two numbers
by division.

A classroom has 16 boys and 12 girls.
Also written as 16 boys , 16:12 or 16 to 12
12 girls
 Generally, ratios are in lowest terms:
16 = 16/4 = 4
12 12/4 3

Ratio, continued

Ratios can compare two unlike things:
Joe earned $40 in five hours
 The ratio is 40 dollars or 8 dollars
5 hours
1 hour


When the denominator is one, this is called
a unit rate.
Ratio, continued
Let’s look at a classroom:
 Ratios can be part-to-part


16 boys
15 girls
Ratios can be part-to-whole

16 boys
31 students
Ratio, continued

If a ratio is part-to-whole, you can divide
and find a decimal or a percent.

16 boys
31 students
31/16.00 = .516, or 51.6% are boys
Proportion

Proportion is a statement that says two ratios
are equal.

In an election, Damon got three votes for each two
votes that Shannon got. Damon got 72 votes. How
many votes did Shannon get?

Damon 3 = 72 so 3 x 24 = 72
Shannon 2
n
2 x 24 48
n = 48, so Shannon got 48 votes.
Proportion, continued

Tires cost two for $75. How much will
four tires cost?

# of tires 2 = 4 so 2 x 2 = 4 tires
cost
75 n
75 x 2
$150
n = 150, so four tires cost $150
Proportion, continued

One more way to solve proportions:

2=6
8 n
2xn=6x8
n = 24
2n = 48
2
2
Proportion, continued
Now you try!
 Three cans of soup costs $5. How much
will 12 cans cost?


# of cans 3 = 12 3 x 4 = 12 cans
cost
5
n 5x4
20 dollars
n = 20, so 12 cans cost $20