Comparing and Scaling
Ratios, Percents, Fractions,
Scaling and Differences
Example
The class has 12
girls and 15 boys.
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Ratios
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Can be written 3 ways:


12:15
12/15
Compare part-to-part:
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
12 to 15
Boys to girls is 15 to 12 (reduced = 5 to 4)
Or part-to-whole

boys to class is 15 to 27 (reduced = 5 to 9)
Differences
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Compare how much more or less one
quantity is than another.
Found by subtracting.
Example: 15 boys – 12 girls = 3

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There are 3 more boys than girls.
The boys outnumber the girls by 3.
There is a difference of 3 between boys
and girls.
Scaling


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The number multiplied by one quantity
to get another quantity.
The scale factor is found by dividing.
Example: Jane is 6 feet tall and Tom is
3 feet tall. How many times taller is
Jane than Tom?

6÷3=2
Jane is 2 times taller than
Tom.
Fractions


Compares part-to-whole.
Example 1: What fraction of the class is
boys?


15/27 (15 is the part of the class that is boys,
27 is the whole class).
Example 2: What fraction of the class
are girls?

12/27 (12 is the part of the class that are girls,
27 is the whole class).
Percents
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

Means “out of 100.”
30% = 30/100
72% = 72/100
To find a percent:



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1. Write the fraction.
2. Divide the numerator by the denominator.
3. Multiply by 100.
Example: What percent of the class are boys?

15/27 = 15 ÷ 27 = 0.5555 x 100 = 55.6%
Examples



25 chocolate cookies
20 vanilla cookies.
1. What is the ratio of chocolate cookies
to vanilla cookies?


25 to 20 which reduces to 5 to 4
2. How many more cookies are
chocolate than vanilla?

25 - 20 = 5 more cookies are chocolate
Examples

3. What fraction of the cookies are
vanilla?


4. What percent of the cookies are
chocolate?


20/45 which reduces to 4/9
25/45 = 25 ÷ 45 = 0.5555 x 100 = 55.6%
5. How many times more chocolate
cookies are there than vanilla cookies?

25 ÷ 20 = 1.25 times
Practice
Hamburger
Hot Dog
Pizza
Boys
25
15
60
Girls
26
19
55
1. What is the ratio of boys who like pizza to girls who like pizza?
60 to 55
2. Girls who like hot dogs outnumber boys who like hot dogs by how
many?
19-15 = 4
3. What fraction of the students like hamburgers?
51/200
4. What percent of the students like pizza?
115/200 = 115 ÷ 200 = 0.575 x 100 = 57.5%
5. How many times more boys like pizza than girls?
60 ÷ 55 = 1.09