The document discusses ratios, proportions, and solving proportions. It defines a ratio as comparing two numbers by division and a proportion as two equal ratios. Properties of proportions are explored, including the cross products property, exchange property, reciprocal property, and "add one" property. Examples are provided of setting up and solving proportions using these properties.

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.

9. Properties of Proportions
a
c
=
b
d
1. ad = bc

10. PROPERTIES OF
PROPORTION
Exchange Property
You may
exchange the means
or the extremes.

11. Properties of Proportions
a
c
=
b
d
a
c
=
b
d

12. PROPERTIES OF
PROPORTION
Reciprocal Property
Take the reciprocal of
both ratios.

13. Properties of Proportions
a
c
=
b
d
b
a
=
d
c

14. PROPERTIES OF
PROPORTION
“Add One” Property

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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