| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.16 |
| Score | 0% | 63% |
What is \( \frac{1}{7} \) x \( \frac{1}{9} \)?
| \(\frac{3}{40}\) | |
| \(\frac{1}{63}\) | |
| \(\frac{1}{9}\) | |
| \(\frac{4}{21}\) |
To multiply fractions, multiply the numerators together and then multiply the denominators together:
\( \frac{1}{7} \) x \( \frac{1}{9} \) = \( \frac{1 x 1}{7 x 9} \) = \( \frac{1}{63} \) = \(\frac{1}{63}\)
If the ratio of home fans to visiting fans in a crowd is 3:1 and all 42,000 seats in a stadium are filled, how many home fans are in attendance?
| 37,500 | |
| 31,500 | |
| 32,667 | |
| 32,800 |
A ratio of 3:1 means that there are 3 home fans for every one visiting fan. So, of every 4 fans, 3 are home fans and \( \frac{3}{4} \) of every fan in the stadium is a home fan:
42,000 fans x \( \frac{3}{4} \) = \( \frac{126000}{4} \) = 31,500 fans.
What is the greatest common factor of 52 and 36?
| 4 | |
| 2 | |
| 29 | |
| 5 |
The factors of 52 are [1, 2, 4, 13, 26, 52] and the factors of 36 are [1, 2, 3, 4, 6, 9, 12, 18, 36]. They share 3 factors [1, 2, 4] making 4 the greatest factor 52 and 36 have in common.
What is \( \frac{-1c^8}{3c^2} \)?
| -\(\frac{1}{3}\)c6 | |
| -3c-6 | |
| -3c10 | |
| -3c6 |
To divide terms with exponents, the base of both exponents must be the same. In this case they are so divide the coefficients and subtract the exponents:
\( \frac{-c^8}{3c^2} \)
\( \frac{-1}{3} \) c(8 - 2)
-\(\frac{1}{3}\)c6
If all of a roofing company's 10 workers are required to staff 5 roofing crews, how many workers need to be added during the busy season in order to send 7 complete crews out on jobs?
| 6 | |
| 13 | |
| 4 | |
| 3 |
In order to find how many additional workers are needed to staff the extra crews you first need to calculate how many workers are on a crew. There are 10 workers at the company now and that's enough to staff 5 crews so there are \( \frac{10}{5} \) = 2 workers on a crew. 7 crews are needed for the busy season which, at 2 workers per crew, means that the roofing company will need 7 x 2 = 14 total workers to staff the crews during the busy season. The company already employs 10 workers so they need to add 14 - 10 = 4 new staff for the busy season.