| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.87 |
| Score | 0% | 57% |
What is \( \frac{8a^8}{9a^3} \)?
| 1\(\frac{1}{8}\)a5 | |
| \(\frac{8}{9}\)a11 | |
| \(\frac{8}{9}\)a5 | |
| \(\frac{8}{9}\)a-5 |
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:
\( \frac{8a^8}{9a^3} \)
\( \frac{8}{9} \) a(8 - 3)
\(\frac{8}{9}\)a5
On average, the center for a basketball team hits 50% of his shots while a guard on the same team hits 70% of his shots. If the guard takes 25 shots during a game, how many shots will the center have to take to score as many points as the guard assuming each shot is worth the same number of points?
| 34 | |
| 40 | |
| 46 | |
| 39 |
guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 25 x \( \frac{70}{100} \) = \( \frac{70 x 25}{100} \) = \( \frac{1750}{100} \) = 17 shots
The center makes 50% of his shots so he'll have to take:
shots made = shots taken x \( \frac{\text{% made}}{100} \)
shots taken = \( \frac{\text{shots taken}}{\frac{\text{% made}}{100}} \)
to make as many shots as the guard. Plugging in values for the center gives us:
center shots taken = \( \frac{17}{\frac{50}{100}} \) = 17 x \( \frac{100}{50} \) = \( \frac{17 x 100}{50} \) = \( \frac{1700}{50} \) = 34 shots
to make the same number of shots as the guard and thus score the same number of points.
What is \( \frac{3}{5} \) ÷ \( \frac{2}{8} \)?
| \(\frac{3}{10}\) | |
| \(\frac{1}{5}\) | |
| 2\(\frac{2}{5}\) | |
| \(\frac{3}{64}\) |
To divide fractions, invert the second fraction and then multiply:
\( \frac{3}{5} \) ÷ \( \frac{2}{8} \) = \( \frac{3}{5} \) x \( \frac{8}{2} \)
To multiply fractions, multiply the numerators together and then multiply the denominators together:
\( \frac{3}{5} \) x \( \frac{8}{2} \) = \( \frac{3 x 8}{5 x 2} \) = \( \frac{24}{10} \) = 2\(\frac{2}{5}\)
What is \( \frac{8}{6} \) + \( \frac{9}{12} \)?
| 1 \( \frac{3}{8} \) | |
| \( \frac{6}{12} \) | |
| 2\(\frac{1}{12}\) | |
| 1 \( \frac{2}{12} \) |
To add these fractions, first find the lowest common multiple of their denominators. The first few multiples of 6 are [6, 12, 18, 24, 30, 36, 42, 48, 54, 60] and the first few multiples of 12 are [12, 24, 36, 48, 60, 72, 84, 96]. The first few multiples they share are [12, 24, 36, 48, 60] making 12 the smallest multiple 6 and 12 share.
Next, convert the fractions so each denominator equals the lowest common multiple:
\( \frac{8 x 2}{6 x 2} \) + \( \frac{9 x 1}{12 x 1} \)
\( \frac{16}{12} \) + \( \frac{9}{12} \)
Now, because the fractions share a common denominator, you can add them:
\( \frac{16 + 9}{12} \) = \( \frac{25}{12} \) = 2\(\frac{1}{12}\)
If all of a roofing company's 15 workers are required to staff 5 roofing crews, how many workers need to be added during the busy season in order to send 10 complete crews out on jobs?
| 1 | |
| 15 | |
| 3 | |
| 9 |
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 15 workers at the company now and that's enough to staff 5 crews so there are \( \frac{15}{5} \) = 3 workers on a crew. 10 crews are needed for the busy season which, at 3 workers per crew, means that the roofing company will need 10 x 3 = 30 total workers to staff the crews during the busy season. The company already employs 15 workers so they need to add 30 - 15 = 15 new staff for the busy season.