Ratio of a to b
Simplifying Ratios: 



a
b
 a:b
1 m = 100 cm
16 oz= 1 lb
5, 280 ft = 1 mi
1,760 yd = 1 mi
denominators cannot be zero
must have the same units
must be simplified
12 in = 1 ft
3 ft = 1 yd
Converting:
1.
12cm
4m
2.
6ft
18in
3.
6. The area of a rectangle is 108 cm2.
The ratio of the width to the length is 3:4.
Find the length and the width.
24oz
2lb
4.
14ft
6yd
5.
7. If the measures of the angles in a triangle
have the ratio of 4:5:6, classify the triangle
as right, obtuse or acute.
Proportion: equation that equates two ratios
Properties:
a. Cross Products
a c
If  , then
b d
a c

b d
b. Reciprocal Property
a c
If  , then
b d
c. Interchange Property
a c
a
 , then
If
.

b d
c
Practice: Complete each statement.
8. If
6 5
6
 , then

x y
5
10. If
.
x 7
 , then xy  ____ .
4 y
440yd
2mi
9. If
x
y
x

, then

12 26
y
.
9 x
2
 , then

2 y
9
.
11. If
Decide whether the statement is True or False.
12. If
x 8
y 3
 , then
 .
y 3
x 8
15. If
x 8
x y
 , then
 .
y 3
8 3
13. If
x 8
3 y
 , then
 .
y 3
x 8
14. If
x 8
x 3
 , then
 .
y 3
8 y
Solve for x.
16.
x
9

6 24
17.
4
3

x 3 x 3
18.
5
3

2x  7 x  3
Solve for the variable.
19. MN:MO is 3:4
M
x
O
20. SU:UT = PR:RQ
S
P
5
x
9
N
U
R
36
T
Use the diagram and the given information to find the unknown length.
AB AE
AB AE
21. Given
22. Given

, find BC.

, find BC.
BC ED
BC ED
.
12
Q
Geometric Mean:
The geometric mean of two positive numbers a, b is the
positive number x such that:
2

so x  ab
Geometric mean: x  a  b
23. Find the geometric mean of 3 and 12.
24. Find the geometric mean of 6 and 12.
25. 8 is the geometric mean of 4 and what number?