| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.12 |
| Score | 0% | 62% |
Convert c-3 to remove the negative exponent.
| \( \frac{-1}{c^{-3}} \) | |
| \( \frac{1}{c^3} \) | |
| \( \frac{3}{c} \) | |
| \( \frac{-3}{-c} \) |
To convert a negative exponent to a positive exponent, calculate the positive exponent then take the reciprocal.
What is \( \frac{6}{6} \) + \( \frac{5}{10} \)?
| 1 \( \frac{1}{30} \) | |
| 1 \( \frac{9}{18} \) | |
| 1\(\frac{1}{2}\) | |
| 1 \( \frac{7}{16} \) |
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 10 are [10, 20, 30, 40, 50, 60, 70, 80, 90]. The first few multiples they share are [30, 60, 90] making 30 the smallest multiple 6 and 10 share.
Next, convert the fractions so each denominator equals the lowest common multiple:
\( \frac{6 x 5}{6 x 5} \) + \( \frac{5 x 3}{10 x 3} \)
\( \frac{30}{30} \) + \( \frac{15}{30} \)
Now, because the fractions share a common denominator, you can add them:
\( \frac{30 + 15}{30} \) = \( \frac{45}{30} \) = 1\(\frac{1}{2}\)
Convert 806,000 to scientific notation.
| 8.06 x 10-4 | |
| 8.06 x 10-5 | |
| 8.06 x 106 | |
| 8.06 x 105 |
A number in scientific notation has the format 0.000 x 10exponent. To convert to scientific notation, move the decimal point to the right or the left until the number is a decimal between 1 and 10. The exponent of the 10 is the number of places you moved the decimal point and is positive if you moved the decimal point to the left and negative if you moved it to the right:
806,000 in scientific notation is 8.06 x 105
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?
| 1 | |
| 2 | |
| 4 | |
| 8 |
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.
What is \( \frac{2}{7} \) ÷ \( \frac{2}{8} \)?
| \(\frac{3}{20}\) | |
| \(\frac{4}{35}\) | |
| \(\frac{1}{14}\) | |
| 1\(\frac{1}{7}\) |
To divide fractions, invert the second fraction and then multiply:
\( \frac{2}{7} \) ÷ \( \frac{2}{8} \) = \( \frac{2}{7} \) x \( \frac{8}{2} \)
To multiply fractions, multiply the numerators together and then multiply the denominators together:
\( \frac{2}{7} \) x \( \frac{8}{2} \) = \( \frac{2 x 8}{7 x 2} \) = \( \frac{16}{14} \) = 1\(\frac{1}{7}\)