| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.10 |
| Score | 0% | 62% |
What is \( \frac{1}{9} \) ÷ \( \frac{1}{8} \)?
| \(\frac{8}{9}\) | |
| \(\frac{2}{15}\) | |
| \(\frac{4}{21}\) | |
| \(\frac{1}{16}\) |
To divide fractions, invert the second fraction and then multiply:
\( \frac{1}{9} \) ÷ \( \frac{1}{8} \) = \( \frac{1}{9} \) x \( \frac{8}{1} \)
To multiply fractions, multiply the numerators together and then multiply the denominators together:
\( \frac{1}{9} \) x \( \frac{8}{1} \) = \( \frac{1 x 8}{9 x 1} \) = \( \frac{8}{9} \) = \(\frac{8}{9}\)
A machine in a factory has an error rate of 2 parts per 100. The machine normally runs 24 hours a day and produces 7 parts per hour. Yesterday the machine was shut down for 9 hours for maintenance.
How many error-free parts did the machine produce yesterday?
| 162.5 | |
| 153.6 | |
| 102.9 | |
| 152 |
The hourly error rate for this machine is the error rate in parts per 100 multiplied by the number of parts produced per hour:
\( \frac{2}{100} \) x 7 = \( \frac{2 \times 7}{100} \) = \( \frac{14}{100} \) = 0.14 errors per hour
So, in an average hour, the machine will produce 7 - 0.14 = 6.86 error free parts.
The machine ran for 24 - 9 = 15 hours yesterday so you would expect that 15 x 6.86 = 102.9 error free parts were produced yesterday.
How many 10-passenger vans will it take to drive all 69 members of the football team to an away game?
| 13 vans | |
| 6 vans | |
| 4 vans | |
| 7 vans |
Calculate the number of vans needed by dividing the number of people that need transported by the capacity of one van:
vans = \( \frac{69}{10} \) = 6\(\frac{9}{10}\)
So, it will take 6 full vans and one partially full van to transport the entire team making a total of 7 vans.
What is \( \frac{4}{2} \) + \( \frac{8}{8} \)?
| 3 | |
| \( \frac{1}{8} \) | |
| 1 \( \frac{9}{13} \) | |
| 2 \( \frac{2}{8} \) |
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 8 are [8, 16, 24, 32, 40, 48, 56, 64, 72, 80]. The first few multiples they share are [8, 16, 24, 32, 40] making 8 the smallest multiple 2 and 8 share.
Next, convert the fractions so each denominator equals the lowest common multiple:
\( \frac{4 x 4}{2 x 4} \) + \( \frac{8 x 1}{8 x 1} \)
\( \frac{16}{8} \) + \( \frac{8}{8} \)
Now, because the fractions share a common denominator, you can add them:
\( \frac{16 + 8}{8} \) = \( \frac{24}{8} \) = 3
Solve 2 + (5 + 4) ÷ 4 x 3 - 42
| -7\(\frac{1}{4}\) | |
| \(\frac{2}{9}\) | |
| 2\(\frac{2}{3}\) | |
| 1 |
Use PEMDAS (Parentheses, Exponents, Multipy/Divide, Add/Subtract):
2 + (5 + 4) ÷ 4 x 3 - 42
P: 2 + (9) ÷ 4 x 3 - 42
E: 2 + 9 ÷ 4 x 3 - 16
MD: 2 + \( \frac{9}{4} \) x 3 - 16
MD: 2 + \( \frac{27}{4} \) - 16
AS: \( \frac{8}{4} \) + \( \frac{27}{4} \) - 16
AS: \( \frac{35}{4} \) - 16
AS: \( \frac{35 - 64}{4} \)
\( \frac{-29}{4} \)
-7\(\frac{1}{4}\)