| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.20 |
| Score | 0% | 64% |
A factor is a positive __________ that divides evenly into a given number.
improper fraction |
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integer |
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fraction |
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mixed number |
A factor is a positive integer that divides evenly into a given number. For example, the factors of 8 are 1, 2, 4, and 8.
If the ratio of home fans to visiting fans in a crowd is 5:1 and all 38,000 seats in a stadium are filled, how many home fans are in attendance?
| 31,667 | |
| 25,600 | |
| 26,667 | |
| 37,500 |
A ratio of 5:1 means that there are 5 home fans for every one visiting fan. So, of every 6 fans, 5 are home fans and \( \frac{5}{6} \) of every fan in the stadium is a home fan:
38,000 fans x \( \frac{5}{6} \) = \( \frac{190000}{6} \) = 31,667 fans.
The total water usage for a city is 30,000 gallons each day. Of that total, 15% is for personal use and 36% is for industrial use. How many more gallons of water each day is consumed for industrial use over personal use?
| 3,200 | |
| 500 | |
| 11,600 | |
| 6,300 |
36% of the water consumption is industrial use and 15% is personal use so (36% - 15%) = 21% more water is used for industrial purposes. 30,000 gallons are consumed daily so industry consumes \( \frac{21}{100} \) x 30,000 gallons = 6,300 gallons.
Simplify \( \frac{16}{48} \).
| \( \frac{7}{12} \) | |
| \( \frac{1}{3} \) | |
| \( \frac{8}{19} \) | |
| \( \frac{10}{19} \) |
To simplify this fraction, first find the greatest common factor between them. The factors of 16 are [1, 2, 4, 8, 16] and the factors of 48 are [1, 2, 3, 4, 6, 8, 12, 16, 24, 48]. They share 5 factors [1, 2, 4, 8, 16] making 16 their greatest common factor (GCF).
Next, divide both numerator and denominator by the GCF:
\( \frac{16}{48} \) = \( \frac{\frac{16}{16}}{\frac{48}{16}} \) = \( \frac{1}{3} \)
Solve 4 + (4 + 3) ÷ 2 x 2 - 32
| 2\(\frac{1}{2}\) | |
| 2 | |
| \(\frac{3}{5}\) | |
| \(\frac{7}{9}\) |
Use PEMDAS (Parentheses, Exponents, Multipy/Divide, Add/Subtract):
4 + (4 + 3) ÷ 2 x 2 - 32
P: 4 + (7) ÷ 2 x 2 - 32
E: 4 + 7 ÷ 2 x 2 - 9
MD: 4 + \( \frac{7}{2} \) x 2 - 9
MD: 4 + \( \frac{14}{2} \) - 9
AS: \( \frac{8}{2} \) + \( \frac{14}{2} \) - 9
AS: \( \frac{22}{2} \) - 9
AS: \( \frac{22 - 18}{2} \)
\( \frac{4}{2} \)
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