Proficiency Exam
Exercise \(\PageIndex{1}\)
Compare 4 cassette tapes to 7 dollars.
- Answer
-
\(\dfrac{\text{4 cassette tapes}}{\text{7 dollars}}\)
Exercise \(\PageIndex{2}\)
What do we call a comparison, by division, of two unlike denominate numbers?
- Answer
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Rate
For problems 3 and 4, express each ratio or rate as a fraction.
Exercise \(\PageIndex{3}\)
11 to 9
- Answer
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\(\dfrac{11}{9}\)
Exercise \(\PageIndex{4}\)
5 televisions to 2 radios
- Answer
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\(\dfrac{\text{5 televisions}}{\text{2 radios}}\)
For problems 5 and 6, write each ratio or rate in the form "\(a\) to \(b\)".
Exercise \(\PageIndex{5}\)
\(\dfrac{\text{8 maps}}{\text{3 people}}\)
- Answer
-
8 maps to 3 people
Exercise \(\PageIndex{6}\)
\(\dfrac{\text{2 psychologists}}{\text{75 people}}\)
- Answer
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two psychologists to seventy-five people
For problems 7-9, solve each proportion.
Exercise \(\PageIndex{7}\)
\(\dfrac{8}{x} = \dfrac{48}{90}\)
- Answer
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15
Exercise \(\PageIndex{8}\)
\(\dfrac{x}{7} = \dfrac{4}{28}\)
- Answer
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1
Exercise \(\PageIndex{9}\)
\(\dfrac{\text{3 computers}}{\text{8 students}} = \dfrac{\text{24 computers}}{\text{x students}}\)
- Answer
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64
Exercise \(\PageIndex{10}\)
On a map, 4 inches represents 50 miles. How many miles does 3 inches represent?
- Answer
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\(37\dfrac{1}{2}\)
Exercise \(\PageIndex{11}\)
An acid solution is composed of 6 milliliters of acid to 10 milliliters of water. How many milliliters of acid are there in an acid solution that is composed of 3 milliliters of water?
- Answer
-
1.8
Exercise \(\PageIndex{12}\)
The odds that a particular event will occur are 9 to 7. If the event occurs 27 times, how many times would you predict it will it not occur?
- Answer
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21
For problems 13 and 14, convert each decimal to a percent.
Exercise \(\PageIndex{13}\)
0.82
- Answer
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82%
Exercise \(\PageIndex{14}\)
\(3.\overline{7}\)
- Answer
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\(377 \dfrac{7}{9}\)%
For problems 15 and 16, convert each percent to a decimal.
Exercise \(\PageIndex{15}\)
2.813%
- Answer
-
0.02813
Exercise \(\PageIndex{16}\)
0.006%
- Answer
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0.00006
For problems 17-19, convert each fraction to a percent.
Exercise \(\PageIndex{17}\)
\(\dfrac{42}{5}\)
- Answer
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840%
Exercise \(\PageIndex{18}\)
\(\dfrac{1}{8}\)
- Answer
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12.5%
Exercise \(\PageIndex{19}\)
\(\dfrac{800}{80}\)
- Answer
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1,000%
For problems 20 and 21, convert each percent to a fraction.
Exercise \(\PageIndex{20}\)
15%
- Answer
-
\(\dfrac{3}{20}\)
Exercise \(\PageIndex{21}\)
\(\dfrac{4}{27}\)%
- Answer
-
\(\dfrac{4}{2,700}\) or \(\dfrac{1}{675}\)
For problems 22-25, find each indicated quantity.
Exercise \(\PageIndex{22}\)
What is 18% of 26?
- Answer
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4.68
Exercise \(\PageIndex{23}\)
0.618 is what percent of 0.3?
- Answer
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206
Exercise \(\PageIndex{24}\)
0.1 is 1.1% of what number?
- Answer
-
\(9.\overline{09}\)
Exercise \(\PageIndex{25}\)
A salesperson makes a monthly salary of $1,000.00. He also gets a commission of 12% of his total monthly sales. If, in a particular month, he sells $5,500.00 worth of merchandise, what is his income that month?
- Answer
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$1,660