1.
7-1 Ratio and Proportion
Objectives
Write and simplify ratios.
Use proportions to solve problems.
Holt McDougal Geometry
2.
7-1 Ratio and Proportion
Vocabulary
ratio
proportion
extremes
means
cross products
Holt McDougal Geometry
3.
7-1 Ratio and Proportion
A ratio compares two numbers by division. The ratio
of two numbers a and b can be written as a to b, a:b,
or
, where b ≠ 0. For example, the ratios 1 to 2,
1:2, and
all represent the same comparison.
Holt McDougal Geometry
4.
7-1 Ratio and Proportion
Remember!
In a ratio, the denominator of the fraction cannot be
zero because division by zero is undefined.
Holt McDougal Geometry
5.
7-1 Ratio and Proportion
A proportion is an equation stating that two ratios
are equal. In the proportion
, the values
a and d are the extremes. The values b and c
are the means. When the proportion is written as
a:b = c:d, the extremes are in the first and last
positions. The means are in the two middle positions.
Holt McDougal Geometry
6.
PROPORTION
TWO EQUAL RATIOS
a = c
b
d
MEANS: b,c
EXTREMES: a,d
7.
Use the proportion
given to complete
each statement
a. 5 y
b.
x
5
y
2
x
y
y
c.
2
5
?
?
d.
?
?
x
?
5
?
8.
Cross Products Property
The product of the
means equals the
product of the
extremes.
15.
Properties of Proportions
a
c
=
b
d
a+b
b
=
c+d
d
16.
7-1 Ratio and Proportion
Example 3A: Solving Proportions
Solve the proportion.
7(72) = x(56)
504 = 56x
x=9
Holt McDougal Geometry
Cross Products Property
Simplify.
Divide both sides by 56.
17.
7-1 Ratio and Proportion
Example 3B: Solving Proportions
Solve the proportion.
(z – 4)2 = 5(20)
Cross Products Property
(z – 4)2 = 100
Simplify.
(z – 4) = 10
Find the square root of both sides.
(z – 4) = 10 or (z – 4) = –10 Rewrite as two eqns.
z = 14 or z = –6
Holt McDougal Geometry
Add 4 to both sides.
18.
7-1 Ratio and Proportion
Check It Out! Example 3a
Solve the proportion.
3(56) = 8(x)
168 = 8x
x = 21
Holt McDougal Geometry
Cross Products Property
Simplify.
Divide both sides by 8.
19.
7-1 Ratio and Proportion
Check It Out! Example 3b
Solve the proportion.
2y(4y) = 9(8)
8y2 = 72
Cross Products Property
Simplify.
y2 = 9
Divide both sides by 8.
y= 3
Find the square root of both sides.
y = 3 or y = –3
Holt McDougal Geometry
Rewrite as two equations.
20.
7-1 Ratio and Proportion
Check It Out! Example 3c
Solve the proportion.
d(2) = 3(6)
2d = 18
d=9
Holt McDougal Geometry
Cross Products Property
Simplify.
Divide both sides by 2.
21.
7-1 Ratio and Proportion
Check It Out! Example 3d
Solve the proportion.
(x + 3)2 = 4(9)
Cross Products Property
(x + 3)2 = 36
Simplify.
(x + 3) = 6
Find the square root of both sides.
(x + 3) = 6 or (x + 3) = –6 Rewrite as two eqns.
x = 3 or x = –9
Holt McDougal Geometry
Subtract 3 from both sides.
22.
7-1 Ratio and Proportion
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Holt McDougal Geometry
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