| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.63 |
| Score | 0% | 73% |
Which of the following is a mixed number?
\(1 {2 \over 5} \) |
|
\({a \over 5} \) |
|
\({5 \over 7} \) |
|
\({7 \over 5} \) |
A rational number (or fraction) is represented as a ratio between two integers, a and b, and has the form \({a \over b}\) where a is the numerator and b is the denominator. An improper fraction (\({5 \over 3} \)) has a numerator with a greater absolute value than the denominator and can be converted into a mixed number (\(1 {2 \over 3} \)) which has a whole number part and a fractional part.
A machine in a factory has an error rate of 5 parts per 100. The machine normally runs 24 hours a day and produces 5 parts per hour. Yesterday the machine was shut down for 5 hours for maintenance.
How many error-free parts did the machine produce yesterday?
| 90.3 | |
| 84.6 | |
| 119.7 | |
| 169.2 |
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 5 = \( \frac{5 \times 5}{100} \) = \( \frac{25}{100} \) = 0.25 errors per hour
So, in an average hour, the machine will produce 5 - 0.25 = 4.75 error free parts.
The machine ran for 24 - 5 = 19 hours yesterday so you would expect that 19 x 4.75 = 90.3 error free parts were produced yesterday.
How many hours does it take a car to travel 630 miles at an average speed of 70 miles per hour?
| 9 hours | |
| 7 hours | |
| 3 hours | |
| 2 hours |
Average speed in miles per hour is the number of miles traveled divided by the number of hours:
speed = \( \frac{\text{distance}}{\text{time}} \)Solving for time:
time = \( \frac{\text{distance}}{\text{speed}} \)
time = \( \frac{630mi}{70mph} \)
9 hours
How many 14-passenger vans will it take to drive all 85 members of the football team to an away game?
| 7 vans | |
| 6 vans | |
| 8 vans | |
| 5 vans |
Calculate the number of vans needed by dividing the number of people that need transported by the capacity of one van:
vans = \( \frac{85}{14} \) = 6\(\frac{1}{14}\)
So, it will take 6 full vans and one partially full van to transport the entire team making a total of 7 vans.
In a class of 23 students, 7 are taking German and 12 are taking Spanish. Of the students studying German or Spanish, 3 are taking both courses. How many students are not enrolled in either course?
| 15 | |
| 10 | |
| 20 | |
| 7 |
The number of students taking German or Spanish is 7 + 12 = 19. Of that group of 19, 3 are taking both languages so they've been counted twice (once in the German group and once in the Spanish group). Subtracting them out leaves 19 - 3 = 16 who are taking at least one language. 23 - 16 = 7 students who are not taking either language.