Download 8.1 Ratio and Proportion

8.1 Ratio and Proportion
Slide #1
Computing Ratios

If a and b are two quantities that are measured
in the same units, then the ratio of a to be is
a/b. The ratio of a to be can also be written as
a:b. Because a ratio is a quotient, its
denominator cannot be zero. Ratios are
usually expressed in simplified form. For
instance, the ratio of 6:8 is usually simplified
to 3:4. (You divided by 2)
Slide #2
Ex. 1: Simplifying Ratios

a.
Simplify the ratios:
12 cm
b. 6 ft
4 cm
18 ft
Slide #3
c. 9 in.
18 in.
Ex. 1: Simplifying Ratios

a.
Simplify the ratios:
12 cm
b. 6 ft
4m
18 in
Solution: To simplify the ratios with unlike
units, convert to like units so that the units
divide out. Then simplify the fraction, if
possible.
Slide #4
Ex. 1: Simplifying Ratios

a.
Simplify the ratios:
12 cm
4m
12 cm
12 cm
4m
4∙100cm
12
400
Slide #5
3
100
Ex. 1: Simplifying Ratios

Simplify the ratios:
b. 6 ft
18 in
6 ft
6∙12 in
18 in
18 in.
72 in.
18 in.
Slide #6
4
1
4
Using Proportions

An equation that
equates two ratios is
called a proportion.
For instance, if the
ratio of a/b is equal to
the ratio c/d; then the
following proportion
can be written:
Means
Slide #7
Extremes
=
The numbers a and d are the
extremes of the proportions.
The numbers b and c are the
means of the proportion.
Properties of proportions
1.
CROSS PRODUCT PROPERTY. The
product of the extremes equals the product of
the means.
If
 = , then ad = bc
Slide #8
Properties of proportions
2.
RECIPROCAL PROPERTY. If two ratios
are equal, then their reciprocals are also
equal.
If
 = , then
b
a
=
To solve the proportion, you find the
value of the variable.
Slide #9
Ex. 5: Solving Proportions
4
x
4 x
4
x
=
=
=
5
7
Write the original
proportion.
7
5
Reciprocal prop.
28
5
4
Multiply each side by
4
Simplify.
Slide #10
Ex. 5: Solving Proportions
3
2
=
y+2 y
3y = 2(y+2)
3y = 2y+4
y
=
4
Write the original
proportion.
Cross Product prop.
Distributive Property
Subtract 2y from each
side.
Slide #11