| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.20 |
| Score | 0% | 64% |
What is \( \frac{3}{5} \) ÷ \( \frac{2}{9} \)?
| \(\frac{1}{35}\) | |
| 13\(\frac{1}{2}\) | |
| \(\frac{4}{63}\) | |
| 2\(\frac{7}{10}\) |
To divide fractions, invert the second fraction and then multiply:
\( \frac{3}{5} \) ÷ \( \frac{2}{9} \) = \( \frac{3}{5} \) x \( \frac{9}{2} \)
To multiply fractions, multiply the numerators together and then multiply the denominators together:
\( \frac{3}{5} \) x \( \frac{9}{2} \) = \( \frac{3 x 9}{5 x 2} \) = \( \frac{27}{10} \) = 2\(\frac{7}{10}\)
Simplify \( \frac{28}{48} \).
| \( \frac{8}{15} \) | |
| \( \frac{7}{12} \) | |
| \( \frac{2}{7} \) | |
| \( \frac{10}{11} \) |
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:
\( \frac{28}{48} \) = \( \frac{\frac{28}{4}}{\frac{48}{4}} \) = \( \frac{7}{12} \)
The total water usage for a city is 30,000 gallons each day. Of that total, 30% is for personal use and 51% is for industrial use. How many more gallons of water each day is consumed for industrial use over personal use?
| 6,300 | |
| 14,000 | |
| 8,400 | |
| 2,100 |
51% of the water consumption is industrial use and 30% is personal use so (51% - 30%) = 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.
If all of a roofing company's 8 workers are required to staff 4 roofing crews, how many workers need to be added during the busy season in order to send 8 complete crews out on jobs?
| 10 | |
| 18 | |
| 12 | |
| 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 8 workers at the company now and that's enough to staff 4 crews so there are \( \frac{8}{4} \) = 2 workers on a crew. 8 crews are needed for the busy season which, at 2 workers per crew, means that the roofing company will need 8 x 2 = 16 total workers to staff the crews during the busy season. The company already employs 8 workers so they need to add 16 - 8 = 8 new staff for the busy season.
What is \( \frac{1a^8}{5a^4} \)?
| 5a12 | |
| \(\frac{1}{5}\)a32 | |
| \(\frac{1}{5}\)a2 | |
| \(\frac{1}{5}\)a4 |
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:
\( \frac{a^8}{5a^4} \)
\( \frac{1}{5} \) a(8 - 4)
\(\frac{1}{5}\)a4