| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.13 |
| Score | 0% | 63% |
Convert y-5 to remove the negative exponent.
| \( \frac{-5}{y} \) | |
| \( \frac{1}{y^5} \) | |
| \( \frac{5}{y} \) | |
| \( \frac{-1}{-5y} \) |
To convert a negative exponent to a positive exponent, calculate the positive exponent then take the reciprocal.
| 1 | |
| 1.2 | |
| 6.3 | |
| 0.8 |
1
Simplify \( \frac{28}{48} \).
| \( \frac{9}{20} \) | |
| \( \frac{7}{15} \) | |
| \( \frac{6}{11} \) | |
| \( \frac{7}{12} \) |
To simplify this fraction, first find the greatest common factor between them. The factors of 28 are [1, 2, 4, 7, 14, 28] and the factors of 48 are [1, 2, 3, 4, 6, 8, 12, 16, 24, 48]. They share 3 factors [1, 2, 4] making 4 their greatest common factor (GCF).
Next, divide both numerator and denominator by the GCF:
\( \frac{28}{48} \) = \( \frac{\frac{28}{4}}{\frac{48}{4}} \) = \( \frac{7}{12} \)
If all of a roofing company's 6 workers are required to staff 2 roofing crews, how many workers need to be added during the busy season in order to send 4 complete crews out on jobs?
| 11 | |
| 16 | |
| 6 | |
| 17 |
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 6 workers at the company now and that's enough to staff 2 crews so there are \( \frac{6}{2} \) = 3 workers on a crew. 4 crews are needed for the busy season which, at 3 workers per crew, means that the roofing company will need 4 x 3 = 12 total workers to staff the crews during the busy season. The company already employs 6 workers so they need to add 12 - 6 = 6 new staff for the busy season.
What is \( \frac{5}{2} \) + \( \frac{3}{6} \)?
| 1 \( \frac{4}{6} \) | |
| 1 \( \frac{3}{6} \) | |
| 2 \( \frac{1}{6} \) | |
| 3 |
To add these fractions, first find the lowest common multiple of their denominators. The first few multiples of 2 are [2, 4, 6, 8, 10, 12, 14, 16, 18, 20] and the first few multiples of 6 are [6, 12, 18, 24, 30, 36, 42, 48, 54, 60]. The first few multiples they share are [6, 12, 18, 24, 30] making 6 the smallest multiple 2 and 6 share.
Next, convert the fractions so each denominator equals the lowest common multiple:
\( \frac{5 x 3}{2 x 3} \) + \( \frac{3 x 1}{6 x 1} \)
\( \frac{15}{6} \) + \( \frac{3}{6} \)
Now, because the fractions share a common denominator, you can add them:
\( \frac{15 + 3}{6} \) = \( \frac{18}{6} \) = 3