2-6 Ratios and Proportions

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2-6 Ratios and Proportions
Algebra 1 Glencoe McGraw-Hill Linda
Stamper
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A ratio is a comparison of two quantities
measured in the same unit.
A ratio compares two quantities by division!
You can write a ratio in different ways.
5 to 6
5 6
The order of the numbers in a ratio is very
important. The first number in a ratio always
names the quantity mentioned first.
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An equation that states that two ratios are equal
is a proportion.
Cross Product Property
If two ratios are equal then their cross products
are also equal.
Determine whether each pair of ratios forms a
proportion. Write yes or no (must show support
work).
yes
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Determine whether each pair of ratios forms a
proportion. Write yes or no (must show support
work).
Example 1
Example 2
no
no
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When a proportion involves a variable, solving
for the variable is called solving the proportion.
Solve the proportion.
Check
Write the cross products.
Multiply.
Solve
Do the arithmetic work off to the side or make a
separate column for this work!
?
6
Solve the proportion.
5
Check
/
Write the cross products.
/
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Multiply.
Solve
You can not cross cancel through an equal sign.
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Solve the proportion. If necessary, round to the
nearest hundredth.
Example 4
Example 3
Example 5
Do the arithmetic work off to the side or make a
separate column for this work!
You can simplify a fraction before you use cross
products.
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Solve the proportion.
Example 7
Example 6
Example 8
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Write a proportion for the problem. Then solve.
Mrs. Jones travels 140 miles in 2.5 hours. At
this rate, how far will she travel in 4 hours?
Start with a word ratio.
Mrs. Jones will travel 224 miles in 4 hours.
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Mrs. Jones travels 140 miles in 2.5 hours. At
this rate, how long will it take her to travel
224 miles?
Write word ratio.
Mrs. Jones will travel 224 miles in 4 hours.
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Write a proportion for each problem. Then solve.
Example 9 A mechanic charged 92 for 4 hours of
work. At this rate, how much will be charged for
6 hours?
Example 10 Mr. Green used 3 gallons of paint to
cover 1,350 sq ft. At this rate, how much paint
will be needed to cover 1,800 sq. ft.?
Example 11 The ratio of football players to
cheerleaders in the NFL is 48 to 6. If there are
1,440 football players, how many cheerleaders are
there?
Example 12 Sue, the speed reader, can read 12
pages in 4.5 minutes. At that rate, how many
pages will she read in 60 minutes?
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Example 9 The mechanic will charge 138 for 6
hours of work.
Example 10 Mr. Green will need 4 gallons of
paint.
Example 11 There are 180 cheerleaders.
Example 12 Sue will read 160 pages.
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Example 9 A mechanic charged 92 for 4 hours of
work. At this rate, how much will be charged for
6 hours?
Write a word ratio.
Sentence.
The mechanic will charge 138 for 6 hours of work.
Do the arithmetic work off to the side or make a
separate column for this work!
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Example 10 Mr. Green used 3 gallons of paint to
cover 1,350 sq ft. At this rate, how much paint
will be needed to cover 1,800 sq. ft.?
Write word ratio.
Mr. Green will need 4 gallons of paint.
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Example 11 The ratio of football players to
cheerleaders in the NFL is 48 to 6. If there are
1,440 football players, how many cheerleaders are
there?
Write word ratio.
There are 180 cheerleaders.
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Example 12 Sue, the speed reader, can read 12
pages in 4.5 minutes. At that rate, how many
pages will she read in 60 minutes?
Sue will read 160 pages.
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Homework
2-A11 Pages 109-110 9-33,41-48.