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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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slide1
5-1
  • Objective: Solving proportions
slide2

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

  • Or as the more recognizable (and useable) equivalence of two fractions.
proportions
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
RATIOS & PROPORTIONS

Are the following proportions?

Write the ones that are proportions on your slates.

ratios proportions5
RATIOS & PROPORTIONS

Find the missing numbers to make the following proportions.

10 10

9 9

slide6
5-2
  • Objective: Solve proportions involving scale drawings and models
slide7

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
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 proportions10
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

slide11
5-3
  • Objective: Solve problems by using the percent equations
percents decimals
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

slide13

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
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 decimals15
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
The percent equation

P

r

=

100

B

Percent

r (percentage)

=

100

Base

figuring out what goes where
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