7
Ratio and
Proportion
Functions
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7.2
Proportion
Copyright © Cengage Learning. All rights reserved.
Proportion
A proportion states that two ratios or two rates are equal.
Thus,
and
are proportions.
A proportion has four terms.
In the proportion
the first term is 2, the second term
is 5, the third term is 4, and the fourth term is 10.
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Proportion
The first and fourth terms of a proportion are called the
extremes, and the second and third terms are called the
means of the proportion.
This is more easily seen when the proportion
written in the form
is
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Example 1
Given the proportion
a. The first term is 2.
b. The second term is 3.
c. The third term is 4.
d. The fourth term is 6.
e. The means are 3 and 4.
f. The extremes are 2 and 6.
g. The product of the means = 3  4 = 12.
h. The product of the extremes = 2  6 = 12.
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Proportion
Proportion
In any proportion, the product of the means equals the
product of the extremes.
That is, if
, then bc = ad.
To determine whether two ratios are equal, put the two
ratios in the form of a proportion.
If the product of the means equals the product of the
extremes, the ratios are equal.
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Example 3
Determine whether or not the ratios
and
are equal.
If the product of the means (36  29) = the product of the
extremes (13  84), then
.
However, 36  29 = 1044 and 13  84 = 1092.
Therefore,
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Proportion
To solve a proportion means to find the missing term. To
do this, form an equation by setting the product of the
means equal to the product of the extremes.
Then solve the resulting equation.
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Proportion
We have studied percent, using the formula P = BR, where
R is the rate written as a decimal.
Knowing this formula and knowing the fact that percent
means “per hundred,” we can write the proportion
where R is the rate written as a percent. We can use this
proportion to solve percent problems.
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Example 9
A student answered 27 out of 30 questions correctly. What
percent of the answers were correct?
P (part) = 27
B (base) = 30
R (rate) = x
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Example 9
30x = 2700
cont’d
The product of the means equals the
product of the extremes.
x = 90
Therefore, the student answered 90% of the questions
correctly.
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Kitchen Ratios
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Kitchen Ratios
The kitchen ratio is a very common term in the culinary
field. It is used to express the relationship as a ratio among
all the ingredients that are used in a recipe.
This allows one to take any recipe and make more or less
of the given recipe. Some recipes are given in terms of the
number of parts of each ingredient.
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Example 14
Cheese balls are formed using the kitchen ratio of 1, 1, 2
for blue cheese, cream cheese, and cheddar cheese. How
much of each cheese is needed to make forty 2-oz cheese
balls?
First, 40  2 oz = 80 oz of cheese is needed in the ratio of
1 : 1 : 2.
Let x = the number of ounces of blue cheese
x = the number of ounces of cream cheese
2x = the number of ounces of cheddar cheese
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Example 14
cont’d
The total amount of cheese needed is
x + x + 2x = 80
4x = 80
x = 20
Thus, we need 20 oz of blue cheese, 20 oz of cream
cheese, and 40 oz of cheddar cheese.
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