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5-1. Objective: Solving proportions. An equation in which two ratios are equal is called a proportion . A ratio is the comparison of two numbers written as a fraction. A proportion can be written using colon notation like this . a:b::c:d.

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5-1
• Objective: Solving proportions
• A ratio is the comparison of two numbers written as a fraction.
• A proportion can be written using colon notation like this

a:b::c:d

• Or as the more recognizable (and useable) equivalence of two fractions.
Proportions
• To set up a proportion think part/whole

part

part

______

_____

=

whole

whole

If you can travel 120 miles on 6 gallons of gas, how far can you drive on 8 gallons of gas?

(8)gas

(6)gas

______

______

x=160

6x=960

=

(x) miles

120miles

RATIOS & PROPORTIONS

Are the following proportions?

Write the ones that are proportions on your slates.

RATIOS & PROPORTIONS

Find the missing numbers to make the following proportions.

10 10

9 9

5-2
• Objective: Solve proportions involving scale drawings and models

SCALE DRAWINGS

• A scale drawing is a drawing of an object with dimensions proportional to those of the actual object. To find lengths from scale drawings, set up and solve proportions.
SCALE DRAWINGS USING PROPORTIONS

EXAMPLE#1: ¼ in = 5 ft is a scale for a rock band’s concert stage.

A. The scale length of the drum stand is 1 in. What is the actual length of the drum stand?

Cross multiply.

Divide by .25

.25 .25

SCALE DRAWINGS USING PROPORTIONS

Given a scale of .5 in = 4 ft, find the actual length for each scale length given.

.5 .5

.5 .5

5-3
• Objective: Solve problems by using the percent equations
PERCENTS & DECIMALS
• Percent (%) means per hundred.
• To change a decimal to a percent
• Multiply the decimal by 100
• Write a percent sign after it

Multiply the decimal by 100(move the decimal point 2 places to the right)

Write a percent sign after it

To change a percent to a decimal

• Divide the percent by 100
• Omit the percent sign
• Divide the percent by 100 (move decimal 2 places to the left)
• Omit the percent sign
PERCENTS AND DECIMALS

Convert the following decimals to percents:

E. 0.445

44.5%

A. 0.15

15%

1.5%

F. 0.1111

11.11%

B. 0.015

0.5%

62.5%

G. 0.005

C. 0.625

104.2%

H. 1.042

D. 0.9

90%

PERCENTS AND DECIMALS

Convert the following percents to decimals:

E. 1.5%

0.015

A. 23.45%

0.2345

0.25

F. 35%

0.35

B. 25%

0.00005

0.125

G. 0.005%

C. 12.5%

3.1

H. 310%

D. 45%

0.45

The percent equation

P

r

=

100

B

Percent

r (percentage)

=

100

Base

Figuring out what goes where?
• Remember is/of
• “is” will always be “P”
• “of” will always be “B”

What number is 15% of 10

What percent of 60 is 3

3

r

P

r

=

=

100

100

60

10