Pre-Algebra Chapter 6 - Ramsey School District

Using Proportions
Vocabulary
• proportion
• cross products
• Solve proportions.
• Use proportions to solve real-world problems.
are proportions used in recipes?
For many years, Phyllis Norman
was famous in her neighborhood for
making her flavorful fruit punch.
The recipe is shown at the right.
a. For each of the first four
ingredients, write a ratio that
compares the number of ounces
of each ingredient to the number
of ounces of water.
12 oz frozen lemonade concentrate
12 oz frozen grape juice concentrate
12 oz frozen orange juice concentrate
40 oz lemon-lime soda
84 oz water
Yields: 160 oz of punch
b. Double the recipe. (Hint: Multiply each number of ounces by 2.)
Then write a ratio for the ounces of each of the first four ingredients
to the ounces of water as a fraction in simplest form.
c. Are the ratios in part a and b the same? Why or why not?
PROPORTIONS To solve problems that relate to ratios, you can use a
proportion. A proportion is a statement of equality of two ratios.
• Words
A proportion is an equation stating that two ratios are equal.
• Symbols b
a d
c • Example
2
3 6 9
Proportion
Consider the following proportion.
a c
d b
Study Tip
Properties
When you multiply each
side of an equation by
bd, you are using the
Multiplication Property
of Equality.
1
1
a c
bd bd Multiply each side by bd to eliminate the fractions.
b d
1 1
ad cb Simplify.
The products ad and cb are called the cross products of a proportion.
Every proportion has two cross products.
12(168) is one
cross product.
1 2 24
84
1 68
12(168) 84(24)
2016 2016
The cross products are equal.
84(24) is another
cross product.
Concept Check
Write a proportion whose cross products are equal to 18.
270 Chapter 6 Ratio, Proportion, and Percent