2. Ratio – a comparison of 2 numbers measured in the
same units
The ratio of x to y can be written:
x to y
x:y
Because a ratio is a quotient, its denominator cannot be zero.
Ratios are expressed in simplified form.
6:8 is simplified to 3:4.
y
x
3. Ex. 1: Simplifying Ratios
Simplify the ratios:
a. 12 cm b. 6 ft
4 m 18 in
4. Ex. 1: Simplifying Ratios
Simplify the ratios:
a. 12 cm
4 m
12 cm 12 cm 12 3
4 m 4∙100cm 400 100
5. Ex. 1: Simplifying Ratios
Simplify the ratios:
b. 6 ft
18 in
6 ft 6∙12 in 72 in. 4
18 in 18 in. 18 in. 1
6. Ex. 2: Using Ratios
The perimeter of
rectangle ABCD is 60
centimeters. The ratio
of AB: BC is 3:2. Find
the length and the
width of the rectangle
w
l
A
B
C
D
7. Ex. 2: Using Ratios
SOLUTION: Because
the ratio of AB:BC is
3:2, you can represent
the length of AB as 3x
and the width of BC as
2x.
w
l
A
B
C
D
8. Solution:
Statement
2l + 2w = P
2(3x) + 2(2x) = 60
6x + 4x = 60
10x = 60
x = 6
Reason
Formula for perimeter of a rectangle
Substitute l, w and P
Multiply
Combine like terms
Divide each side by 10
So, ABCD has a length of 18 centimeters and a width of 12 cm.
9. Ex. 3: Using Ratios
The measures of the angles in ∆JKL are in the
ratio 1:2:3. Find the measures of the angles.
10. Solution:
Statement
x°+ 2x°+ 3x° =
180°
6x = 180
x = 30
Reason
Triangle Sum Theorem
Combine like terms
Divide each side by 6
So, the angle measures are 30°, 2(30°) = 60°, and 3(30°) = 90°.
11. Ex. 4: Using Ratios
The ratios of the side
lengths of ∆DEF to the
corresponding side
lengths of ∆ABC are
2:1. Find the unknown
lengths.
8 in.
3 in.
F
D E
C
A B
12. Ex. 4: Using Ratios
SOLUTION:
DE is twice AB and DE = 8,
so AB = ½(8) = 4
Use the Pythagorean
Theorem to determine what
side BC is.
DF is twice AC and AC = 3,
so DF = 2(3) = 6
EF is twice BC and BC = 5,
so EF = 2(5) or 10
8 in.
3 in.
F
D E
C
A B
4 in
a2 + b2 = c2
32 + 42 = c2
9 + 16 = c2
25 = c2
5 = c
13.
14.
15. Using Proportions
Proportion - An
equation that sets two
ratios equal to one
another
=
Means Extremes
The numbers a and d are the
extremes of the proportions.
The numbers b and c are the
means of the proportion.
If using an extended
proportion –
a:b:c = d:e:f
16. Properties of proportions
1. CROSS PRODUCT PROPERTY. The
product of the extremes equals the product of
the means.
If = , then ad = bc
17. Properties of proportions
2. RECIPROCAL PROPERTY. If two ratios
are equal, then their reciprocals are also
equal.
If = , then =
b
a
