| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.24 |
| Score | 0% | 65% |
What is \( \frac{3}{9} \) x \( \frac{3}{6} \)?
| \(\frac{1}{6}\) | |
| \(\frac{1}{18}\) | |
| 1 | |
| 1\(\frac{1}{2}\) |
To multiply fractions, multiply the numerators together and then multiply the denominators together:
\( \frac{3}{9} \) x \( \frac{3}{6} \) = \( \frac{3 x 3}{9 x 6} \) = \( \frac{9}{54} \) = \(\frac{1}{6}\)
A machine in a factory has an error rate of 7 parts per 100. The machine normally runs 24 hours a day and produces 9 parts per hour. Yesterday the machine was shut down for 6 hours for maintenance.
How many error-free parts did the machine produce yesterday?
| 150.7 | |
| 186.2 | |
| 103 | |
| 126.5 |
The hourly error rate for this machine is the error rate in parts per 100 multiplied by the number of parts produced per hour:
\( \frac{7}{100} \) x 9 = \( \frac{7 \times 9}{100} \) = \( \frac{63}{100} \) = 0.63 errors per hour
So, in an average hour, the machine will produce 9 - 0.63 = 8.37 error free parts.
The machine ran for 24 - 6 = 18 hours yesterday so you would expect that 18 x 8.37 = 150.7 error free parts were produced yesterday.
What is \( \sqrt{\frac{36}{4}} \)?
| 3 | |
| \(\frac{2}{7}\) | |
| 1 | |
| 1\(\frac{1}{8}\) |
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:
\( \sqrt{\frac{36}{4}} \)
\( \frac{\sqrt{36}}{\sqrt{4}} \)
\( \frac{\sqrt{6^2}}{\sqrt{2^2}} \)
\( \frac{6}{2} \)
3
How many 1 gallon cans worth of fuel would you need to pour into an empty 4 gallon tank to fill it exactly halfway?
| 3 | |
| 2 | |
| 2 | |
| 4 |
To fill a 4 gallon tank exactly halfway you'll need 2 gallons of fuel. Each fuel can holds 1 gallons so:
cans = \( \frac{2 \text{ gallons}}{1 \text{ gallons}} \) = 2
What is (c3)2?
| c5 | |
| c6 | |
| 2c3 | |
| c-1 |
To raise a term with an exponent to another exponent, retain the base and multiply the exponents:
(c3)2