| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.36 |
| Score | 0% | 67% |
What is \( \frac{2}{7} \) ÷ \( \frac{4}{8} \)?
| \(\frac{4}{7}\) | |
| \(\frac{1}{27}\) | |
| \(\frac{1}{18}\) | |
| 4 |
To divide fractions, invert the second fraction and then multiply:
\( \frac{2}{7} \) ÷ \( \frac{4}{8} \) = \( \frac{2}{7} \) x \( \frac{8}{4} \)
To multiply fractions, multiply the numerators together and then multiply the denominators together:
\( \frac{2}{7} \) x \( \frac{8}{4} \) = \( \frac{2 x 8}{7 x 4} \) = \( \frac{16}{28} \) = \(\frac{4}{7}\)
Convert x-3 to remove the negative exponent.
| \( \frac{1}{x^{-3}} \) | |
| \( \frac{3}{x} \) | |
| \( \frac{1}{x^3} \) | |
| \( \frac{-1}{-3x^{3}} \) |
To convert a negative exponent to a positive exponent, calculate the positive exponent then take the reciprocal.
The total water usage for a city is 35,000 gallons each day. Of that total, 24% is for personal use and 42% is for industrial use. How many more gallons of water each day is consumed for industrial use over personal use?
| 6,300 | |
| 6,900 | |
| 7,800 | |
| 7,200 |
42% of the water consumption is industrial use and 24% is personal use so (42% - 24%) = 18% more water is used for industrial purposes. 35,000 gallons are consumed daily so industry consumes \( \frac{18}{100} \) x 35,000 gallons = 6,300 gallons.
What is \( \frac{24\sqrt{14}}{8\sqrt{7}} \)?
| \(\frac{1}{2}\) \( \sqrt{\frac{1}{3}} \) | |
| \(\frac{1}{3}\) \( \sqrt{2} \) | |
| 3 \( \sqrt{2} \) | |
| \(\frac{1}{2}\) \( \sqrt{3} \) |
To divide terms with radicals, divide the coefficients and radicands separately:
\( \frac{24\sqrt{14}}{8\sqrt{7}} \)
\( \frac{24}{8} \) \( \sqrt{\frac{14}{7}} \)
3 \( \sqrt{2} \)
What is \( \sqrt{\frac{16}{81}} \)?
| 3\(\frac{1}{2}\) | |
| \(\frac{4}{9}\) | |
| \(\frac{6}{7}\) | |
| 1\(\frac{1}{2}\) |
To take the square root of a fraction, break the fraction into two separate roots then calculate the square root of the numerator and denominator separately:
\( \sqrt{\frac{16}{81}} \)
\( \frac{\sqrt{16}}{\sqrt{81}} \)
\( \frac{\sqrt{4^2}}{\sqrt{9^2}} \)
\(\frac{4}{9}\)