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Percents: Problems with Solutions
By Catalin David
Problem 1
Express [tex]\frac{2}{5}[/tex] as a percent.
Solution:
Percent derives from the Latin words "per centum",
which means "on 100", which is why to express a fraction to a percent,
the denominator has to be 100.
If it's possible, we amplify the fraction to have the denominator be 100.
In this case, we amplify the fraction by 20
and we get [tex]\frac{40}{100}[/tex] which means 40%.
Problem 2
Express [tex]\frac{1}{4}[/tex] as a percent.
Solution:
Percent derives from the Latin words "per centum",
which mean "on 100"
which is why to express a fraction as a percent,
the denominator has to be 100.
If it's possible, we amplify the fraction to have the denominator be 100.
In this case, we amplify the fraction by 25
and we get [tex]\frac{25}{100}[/tex] which means 25%
Problem 3
Express [tex]\frac {7}{10}[/tex] as a percent.
Solution:
Percent derives from the Latin words "per centum",
which mean "on 100",
which is why to express a fraction as a percent,
the denominator has to be 100.
If it's possible, we amplify the fraction to have the denominator be 100.
In this case, we amplify the fraction by 10
and we get [tex]\frac{70}{100}[/tex] which means 70%.
Problem 4
Express 0.15 as a percent.
Solution:
[tex]0.15 = \frac {15}{100}= 15\% [/tex]
Problem 5
Express 0.236 as a percent.
Solution:
[tex]0.236 = \frac{236}{1000}=\frac{23.6}{100}=23.6\% [/tex]
Problem 6
Express 2.7 as a percent.
Solution:
[tex] 2.7 = \frac{27}{10} = \frac{270}{100}= 270\% [/tex]
Problem 7
Express [tex]\frac{5}{8}[/tex] as a percentage.
Solution:
In this case we cannot amplify the fraction to obtain the denominator 100.
We will transform it into a decimal number and then into a percentage.
[tex]\frac{5}{8} = 0.625 = \frac{625}{1000} = \frac{62.5}{100} = 62.5\% [/tex]
Problem 8
Express [tex]\frac{9}{16}[/tex] as a percent.
Solution:
In this case we cannot amplify the fraction to obtain the denominator 100.
We will transform it into a decimal number and then into a percent.
[tex]\frac{9}{16} = 0.5625 = \frac{5625}{10000}= \frac{56.25}{100} = 56.25\%[/tex]
Problem 9
Express one half as a percent.
Solution:
One half is [tex]\frac{1}{2} = \frac{50}{100} = 50\%[/tex]
Problem 10
Express three quarters as a percent.
Solution:
3 quarters is [tex]\frac{3}{4} = \frac{75}{100} = 75\%[/tex]
Problem 11
What percentage of the circle in the drawing is occupied by the red zone?
Solution:
The circle is divided in 4 equal parts.
The red zone occupies [tex]\frac{3}{4}[/tex] of the circle, which means 75%.
Problem 12
What percentage of the rectangle in the drawing is occupied by the blue zone?
Solution:
The blue zone occupies [tex]\frac{2}{5}[/tex] of the rectangle. [tex]\frac{2}{5} = 40\%[/tex]
Problem 13
Mary sliced a pizza into 10 equal pieces and ate two.
John ate 15% of a pizza of the same size.
Who ate more?
Solution:
Mary ate [tex]\frac{2}{10} = \frac{20}{100} = 20\%[/tex] of the pizza. John ate 15%. So Mary ate more(20% > 15%).
Problem 14
Compare: 40%
>
=
<
52%
Solution:
[tex]40\% = \frac{40}{100}[/tex]
[tex]52\% = \frac {52}{100} [/tex]
[tex]\frac{40}{100} < \frac{52}{100}[/tex]
[tex]40\% < 52\%[/tex]
Problem 15
40% of 200 =
Solution:
[tex]40\% \text{ of } 200 = \frac{40}{100}\cdot 200 = 40 \cdot 2 = 80[/tex]
Problem 16
25% of 240 =
Solution:
25% of 240 = [tex]\frac{25}{100} \cdot 240 = \frac{1}{4} \cdot 240 = 60[/tex]
Problem 17
If 20% of a number is 8, then the number is
Solution:
20% × a = 8
5 × 20% × a = 5 × 8
100% × a = 40
100% = 1
So a = 40
Problem 18
If 45% of a number is 36, then the number is
Solution:
Let "a" be the number we seek. We get
45% × a = 36
2 × 45% × a = 2 × 36 = 72
90% × a = 72
10% × a = 72 : 9 = 8
100% × a = 8 × 10 = 80
a = 80
Problem 19
If 24% of a number is 96, then the number is
Solution:
Let "a" be the number we seek.
[tex]\frac{24}{100} \cdot a = 96[/tex]
[tex]a = 96 \div \frac{24}{100}=96 \cdot \frac{100}{24} = 4 \cdot {100} = 400[/tex]
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