| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.19 |
| Score | 0% | 64% |
What is \( \frac{2}{6} \) ÷ \( \frac{4}{7} \)?
| \(\frac{7}{12}\) | |
| 2\(\frac{1}{3}\) | |
| \(\frac{1}{15}\) | |
| \(\frac{1}{36}\) |
To divide fractions, invert the second fraction and then multiply:
\( \frac{2}{6} \) ÷ \( \frac{4}{7} \) = \( \frac{2}{6} \) x \( \frac{7}{4} \)
To multiply fractions, multiply the numerators together and then multiply the denominators together:
\( \frac{2}{6} \) x \( \frac{7}{4} \) = \( \frac{2 x 7}{6 x 4} \) = \( \frac{14}{24} \) = \(\frac{7}{12}\)
If a rectangle is twice as long as it is wide and has a perimeter of 42 meters, what is the area of the rectangle?
| 98 m2 | |
| 32 m2 | |
| 18 m2 | |
| 2 m2 |
The area of a rectangle is width (w) x height (h). In this problem we know that the rectangle is twice as long as it is wide so h = 2w. The perimeter of a rectangle is 2w + 2h and we know that the perimeter of this rectangle is 42 meters so the equation becomes: 2w + 2h = 42.
Putting these two equations together and solving for width (w):
2w + 2h = 42
w + h = \( \frac{42}{2} \)
w + h = 21
w = 21 - h
From the question we know that h = 2w so substituting 2w for h gives us:
w = 21 - 2w
3w = 21
w = \( \frac{21}{3} \)
w = 7
Since h = 2w that makes h = (2 x 7) = 14 and the area = h x w = 7 x 14 = 98 m2
A machine in a factory has an error rate of 5 parts per 100. The machine normally runs 24 hours a day and produces 6 parts per hour. Yesterday the machine was shut down for 2 hours for maintenance.
How many error-free parts did the machine produce yesterday?
| 125.4 | |
| 142.3 | |
| 71.3 | |
| 159.6 |
The hourly error rate for this machine is the error rate in parts per 100 multiplied by the number of parts produced per hour:
\( \frac{5}{100} \) x 6 = \( \frac{5 \times 6}{100} \) = \( \frac{30}{100} \) = 0.3 errors per hour
So, in an average hour, the machine will produce 6 - 0.3 = 5.7 error free parts.
The machine ran for 24 - 2 = 22 hours yesterday so you would expect that 22 x 5.7 = 125.4 error free parts were produced yesterday.
If a car travels 180 miles in 4 hours, what is the average speed?
| 40 mph | |
| 45 mph | |
| 65 mph | |
| 20 mph |
Average speed in miles per hour is the number of miles traveled divided by the number of hours:
speed = \( \frac{\text{distance}}{\text{time}} \)A triathlon course includes a 100m swim, a 20.9km bike ride, and a 3.4km run. What is the total length of the race course?
| 62.9km | |
| 24.4km | |
| 31.4km | |
| 54.3km |
To add these distances, they must share the same unit so first you need to first convert the swim distance from meters (m) to kilometers (km) before adding it to the bike and run distances which are already in km. To convert 100 meters to kilometers, divide the distance by 1000 to get 0.1km then add the remaining distances:
total distance = swim + bike + run
total distance = 0.1km + 20.9km + 3.4km
total distance = 24.4km