2014-11-29
Unit 5: Percent, Ratio, and Rate
Math 8
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Math-8-5-1
Unit 5: Key Words
Percent increase
Percent decrease
Discount
Two-term ratio
Three-term ratio
Part-to-whole ratio
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2
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Part-to-part ratio
Equivalent ratios
Proportion
Rate
Unit rate
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5.1 Relating Fractions, Decimals,
and Percents
Focus: Given a fraction, decimal, or percent, calculate the
other two forms.
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Investigate, pg. 234
The grade 8 students at two schools in Edmonton
were surveyed about which singer/band is their
favourite.

Musical Artist
# of students in
School A
# of students in
School B
One Direction
48
18
Justin Bieber
30
24
Katy Perry
39
3
2 Chainz
33
15
How many students were surveyed in each school?
Which school had the greatest percent of One
Direction fans? 2 Chainz fans?
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Math-8-5-1
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Hundred Chart
We can use a hundred
chart to represent one
whole, or 100%
Each small square
represents 1%.
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Hundred Chart
We can describe the
shaded part of the
hundred chart in three
ways:
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6
As a percent: 8.5%
As a decimal: 0.085
8.5
17
As a fraction: 100 or 200
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Hundred Chart
We can also use a hundred
chart to represent one 1%.
Each small square represents
1
of 1%, which we can write
100
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
1
as 100% or 0.01%.
1
5
To represent of 1%, shade

1
in 5 of the chart, or 20
squares. This is equal to
0.2% or 0.002.
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Converting Decimals to Percents
To change a decimal to
a percent, multiply by
100.
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Multiplying by 100
means moving the
decimal two places to
the right.
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Example: Write 0.75 as
a percent.
0.75 x 100 = 75%
Example: Write 0.05 as
a percent.
0.05 x 100 = 5%
Example: Write 5.2 as
a percent.
5.2 x 100 = 520%
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Converting Percents to Decimals
To change a percent to
a decimal, divide by
100.
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

Dividing by 100 means
moving the decimal two
places to the left.
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Example: Write 0.75%
as a decimal.
0.75% ÷ 100 = 0.007 5
Example: Write 58% as
a decimal.
58% ÷ 100 = 0.58
Example: Write 5.2% as
a decimal.
5.2% ÷ 100 = 0.052
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Converting Decimals to Fractions
To change a decimal to a
fraction, use a place value chart
to write in all of the values in
your decimal.
The place value of the last digit
is your denominator.
The digits behind the decimal
become your new numerator.
Any digits in front of the
decimal are whole numbers
(make a mixed number).
Simplify, if possible.
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



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Example: Write 0.23 as a
fraction.
23
=
Ones
.
Tenths
Hundredths
0
.
2
3
10
100
Thousandths
Ten
Thousandths
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Converting Decimals to Fractions
(continued)
To change a decimal to a
fraction, use a place value chart
to write in all of the values in
your decimal.
The place value of the last digit
is your denominator.
The digits behind the decimal
become your new numerator.
Any digits in front of the
decimal are whole numbers
(make a mixed number).
Simplify, if possible.
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
Ones
.
Tenths
1
.
2

Example: Write 1.2 as a
fraction.
2
=1
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=1
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10
1
5
Hundredths
11
Thousandths
Ten
Thousandths
Math-8-5-1
Converting (Whole Number) Percents to
Fractions

To change a percent to
a fraction, write the
percent as a fraction
over the denominator of
100. Then, simplify the
fraction, if possible.
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Percent literally means
“per 100” or “out of
100”.
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Example: Write 58% as
a fraction.

58
100

29
50
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Converting (Decimal) Percents to Fractions





To change a percent to a fraction, first
change the percent to a decimal.
Then, use a place value chart to write
in all of the values in your decimal.
The place value of the last digit is your
denominator.
The digits behind the decimal become
your new numerator. Any digits in front
of the decimal are whole numbers
(make a mixed number).
Simplify, if possible.

Example: Write 0.75% as a
fraction.
0.75% ÷ 100 = 0.007 5

=

= 400

75
10 000
3
Ones
.
Tenths
Hundredths
Thousandths
Ten
Thousandths
0
.
0
0
7
5
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Converting (Decimal) Percents to Fractions
(continued)





To change a percent to a fraction, first
change the percent to a decimal.
Then, use a place value chart to write
in all of the values in your decimal.
The place value of the last digit is your
denominator.
The digits behind the decimal become
your new numerator. Any digits in front
of the decimal are whole numbers
(make a mixed number).
Simplify, if possible.
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
Example: Write 5.2% as a fraction.

5.2% ÷ 100 = 0.052

=

= 250
52
1 000
13
Ones
.
Tenths
Hundredths
Thousandths
0
.
0
5
2
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Converting Fractions to Decimals

To change a fraction to a
decimal, divide the
numerator by the
denominator.
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3
Example: Write 4 as a
decimal.
3
= 3 ÷ 4 = 0.75
4
13
Example: Write 24 as a
decimal.
13
= 13 ÷ 24 = 0.541 6
24
2
Example: Write 3 as a
decimal.
2
= 2 ÷ 3 = 0.6
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Math-8-5-1
Converting Fractions to Percents

To change a
fraction to a
percent, first divide
the numerator by
the denominator,
and then multiply
by 100.
16
3
4

Example: Write as a percent.

3
4

0.75 x 100% = 75%

Example: Write 24 as a percent.
= 3 ÷ 4 = 0.75
13
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13
24
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0.541 6 x 100% = 54.16%
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Example: Write 3 as a percent.
= 13 ÷ 24 = 0.541 6
2
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2
3
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0.6 x 100% ≈ 66.6%
= 2 ÷ 3 = 0.6
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Textbook Practice Questions
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Pg. 239 – 241
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# 6-9, 12-14, 16, 19
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