| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.17 |
| Score | 0% | 63% |
The __________ is the greatest factor that divides two integers.
least common multiple |
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absolute value |
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greatest common factor |
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greatest common multiple |
The greatest common factor (GCF) is the greatest factor that divides two integers.
Which of the following is an improper fraction?
\({2 \over 5} \) |
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\({7 \over 5} \) |
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\(1 {2 \over 5} \) |
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\({a \over 5} \) |
A rational number (or fraction) is represented as a ratio between two integers, a and b, and has the form \({a \over b}\) where a is the numerator and b is the denominator. An improper fraction (\({5 \over 3} \)) has a numerator with a greater absolute value than the denominator and can be converted into a mixed number (\(1 {2 \over 3} \)) which has a whole number part and a fractional part.
If the ratio of home fans to visiting fans in a crowd is 2:1 and all 44,000 seats in a stadium are filled, how many home fans are in attendance?
| 25,500 | |
| 25,000 | |
| 39,200 | |
| 29,333 |
A ratio of 2:1 means that there are 2 home fans for every one visiting fan. So, of every 3 fans, 2 are home fans and \( \frac{2}{3} \) of every fan in the stadium is a home fan:
44,000 fans x \( \frac{2}{3} \) = \( \frac{88000}{3} \) = 29,333 fans.
The total water usage for a city is 20,000 gallons each day. Of that total, 13% is for personal use and 40% is for industrial use. How many more gallons of water each day is consumed for industrial use over personal use?
| 13,950 | |
| 1,800 | |
| 5,400 | |
| 2,200 |
40% of the water consumption is industrial use and 13% is personal use so (40% - 13%) = 27% more water is used for industrial purposes. 20,000 gallons are consumed daily so industry consumes \( \frac{27}{100} \) x 20,000 gallons = 5,400 gallons.
What is \( \frac{4}{7} \) ÷ \( \frac{1}{8} \)?
| 4\(\frac{4}{7}\) | |
| \(\frac{9}{49}\) | |
| \(\frac{1}{12}\) | |
| \(\frac{9}{40}\) |
To divide fractions, invert the second fraction and then multiply:
\( \frac{4}{7} \) ÷ \( \frac{1}{8} \) = \( \frac{4}{7} \) x \( \frac{8}{1} \)
To multiply fractions, multiply the numerators together and then multiply the denominators together:
\( \frac{4}{7} \) x \( \frac{8}{1} \) = \( \frac{4 x 8}{7 x 1} \) = \( \frac{32}{7} \) = 4\(\frac{4}{7}\)