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Math 300
Basic College Mathematics
Chapter 5
Ratio and Proportion
Math 300 M-G Chapter 5; Rev: Jan 2009
Page 1 of 8
5.1 Ratios
Ratios
 A ratio is the quotient of two quantities.
Ratio Notation as a Fraction
 The ratio of a to b is given by the fraction notation a , where a
b
is the numerator and b is the denominator.
Example: Write each ratio using fractional notation. Do not
simplify.
1. 7 to 12
2. 14 to 5
Example: Write each ratio as a ratio of whole numbers using
fractional notation. Write the fraction in simplest form.
3. 25 to 150
4. 18 quarts to 30 quarts
Math 300 M-G Chapter 5; Rev: Jan 2009
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5.2 Rates
Rates
 When a ratio is used to compare different kinds of quantities.
Example: Write each rate as a fraction in simplest form.
1. 14 lab tables for 28 students
Writing a Rate as a Unit Rate
 To write a rate as a unit rate, divide the numerator of the rate
by the denominator.
Example: Write the rate as a unit rate.
2. 275 miles in 11 hours
Unit Price
 The unit price is the ratio of price to the number of units.
 Formula for unit price: unit price 
price
number of units
Example: Find the unit price.
3. $0.87 for 3 apples
Math 300 M-G Chapter 5; Rev: Jan 2009
Page 3 of 8
5.2 Rates (cont)
Example: Find the unit price and decide which is the better buy.
Round 3 decimal places. Assume that we are comparing different
sizes of the same brand.
4. Pickles: $1.89 for 32 ounces
$0.89 for 18 ounces
Math 300 M-G Chapter 5; Rev: Jan 2009
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5.3 Proportions
 When 2 ratios or rates are equal. For example:
a proportion. We sometimes read
3 6

2 4
3 6

2 4
is called
as “3 is to 2” as “6 is
to 4.”
Example: Write this sentence as a proportion.
1. 4 hit songs is to 16 releases as 1 hit song is to 4 releases.
2. 1 1 cups milk is to 10 bagels as
2
Math 300 M-G Chapter 5; Rev: Jan 2009
3
4
cup milk is to 5 bagels.
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5.3 Proportions (cont)
Determining Whether Proportions Are True
 If the cross products are equal, then the proportion is true.
 If the cross products are not equal, then the proportion is
false.
Example: Determine whether the proportion is a true proportion.
3.
8 20

6 15
4.
7 4

12 7
Finding an Unknown Value n in a Proportion
Method 1: Simple Proportion Method
1. Multiply the two number values which are diagonal to one
another.
2. Divide the product above by the third (unused) number in the
proportion
Method 2: Algebra Method
1. Set the cross products equal to each other.
2. Divide both sides of the equation by the number that is
multiplied by n.
Math 300 M-G Chapter 5; Rev: Jan 2009
Page 6 of 8
5.3 Proportions (cont)
Example: For each proportion, find the unknown number n.
1.
n 12

3 9
2.
25 7

100 n
3.
12 n

10 16
Math 300 M-G Chapter 5; Rev: Jan 2009
Page 7 of 8
Math 300 Chapter 5
Glossary
Ratio – a quotient of two quantities. It is exactly like a fraction.
Rate – are used to compare different kinds of quantities. For
example, miles/minute.
Proportion - a statement that 2 ratios or rates are equal. For
example, 3/4 = 6/8.
Properties
Use cross products to determine whether proportions are true or
false.
Finding an unknown value “n” in a proportions
1) Set the cross products equal to each other.
2) Divide the number not multiplied by “n” by the number that
is multiplied by “n”.
Hints
Be careful when writing ratios. A ratio of 12/7 is not the same as
7/12.
Ratios are not written as mixed numbers. Always write them as
proper or improper fractions.
In the context of ratios, the word “per” means division. For
example, miles per hour.
When you properly set up your proportions, you should check that
the numerators all have the same units. Also check the
denominators to ensure that they have the same units as well.
Math 300 M-G Chapter 5; Rev: Jan 2009
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