Ratios
What is a ratio?
It is a comparison of two things by division
In the United States 2 out of every 5
people have brown eyes.
To write this as a ratio we write:
2 to 5 or
2/5 or 2:5
RATIOS
What does it mean when it says:
The ratio of men to women in this
class is 1 to 3?
It means that 1 out of every 4 people in the
room are men
Uses of ratios
Comparing a part to another part
part
black
3
= white = 2
part
Uses of ratios
Comparing a part to a whole
part
=
whole
black
3
= 5
total
Uses of ratios
Comparing a whole to a part
whole
total
5
= black = 3
part
Writing ratios in simplest form
Write the ratio 32:68 in simplest form
Step one: write ratio as a fraction
32/68
Step two: reduce fraction
8/17
Step three: write reduced fraction as ratio
8:17
RATIOS
• What does it mean when it says:
– The ratio of the lengths of the sides of a
rectangle are 2:3 (Remember that a rectangle
only has two dimensions)
• It means that for every 2 units of length
on the shorter side of the rectangle, there
are 3 of those same units of length on the
longer side.
The ratio of the lengths are 2:3
Find the missing length.
2
?
a) 3
b) 4
c) 6
Answer:
a) 3
The ratio of the lengths are 2:3
Find the missing length.
14
?
a) 7
b) 21
c) 42
Answer:
b) 21
Area (space inside)
• What happens to the area of a rectangle
when each side is increased by a factor of
2? (by a factor of 2 means multiply each
side by 2)
Length of sides were
doubled, and area
quadrupled (x4)
Ratio of corresponding sides vs.
ratio of corresponding areas
Given that these rectangles are similar:
A = 24
Ratio of
corresponding sides
is 4:8 which reduces
to 1:2 (or 6:12 which
reduces to 1:2)
4
6
A = 96
12
8
Ratio of areas of
the two rectangles
is 24:96 which
reduces to 1:4
Ratios
•
There are 4 boys to every 6 girls in Mr. Jung’s
class. If there are 30 students in the class, how
many of those students are boys?
4 boys for every 6 girls means 4
boys out of 10 kids
4/10 = x/30
x = 12