7-1 Ratio and Proportion
Toolbox
Pg. 458 (17-27; 35-38; 46 why4;
52-54; ch. 49)
Holt McDougal Geometry
7-1 Ratio and Proportion
Essential Questions
How do you write and simplify ratios?
How do you use proportions to solve
problems?
Holt McDougal Geometry
7-1 Ratio and Proportion
The Lord of the Rings movies transport viewers to
the fantasy world of Middle Earth. Many scenes
feature vast fortresses, sprawling cities, and
bottomless mines. To film these images, the
moviemakers used ratios to help them build
highly detailed miniature models.
Holt McDougal Geometry
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
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
7-1 Ratio and Proportion
Example 1: Writing Ratios
Write a ratio expressing the slope of l.
Substitute the
given values.
Simplify.
Holt McDougal Geometry
7-1 Ratio and Proportion
A ratio can involve more than two numbers. For
the rectangle, the ratio of the side lengths may
be written as 3:7:3:7.
Holt McDougal Geometry
7-1 Ratio and Proportion
Example 2: Using Ratios
The ratio of the side lengths of a triangle is
4:7:5, and its perimeter is 96 cm. What is the
length of the shortest side?
Let the side lengths be 4x, 7x, and 5x.
Then 4x + 7x + 5x = 96 . After like terms are
combined, 16x = 96. So x = 6. The length of the
shortest side is 4x = 4(6) = 24 cm.
Holt McDougal Geometry
7-1 Ratio and Proportion
In Algebra 1 you learned the Cross Products
Property. The product of the extremes ad and the
product of the means bc are called the cross
products.
Holt McDougal Geometry
7-1 Ratio and Proportion
Example 3A: Solving Proportions
Solve the proportion.
7(72) = x(56)
504 = 56x
x=9
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Cross Products Property
Simplify.
Divide both sides by 56.
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.
7-1 Ratio and Proportion
Example 4: Using Properties of Proportions
Given that 18c = 24d, find the ratio of d to c in
simplest form.
18c = 24d
Divide both sides by 24c.
Simplify.
Holt McDougal Geometry
7-1 Ratio and Proportion
Summary
D – What did we do?
L – What did you learn?
I – What was interesting?
Q – What questions do you have?
Holt McDougal Geometry