| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.10 |
| Score | 0% | 62% |
A factor is a positive __________ that divides evenly into a given number.
mixed number |
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integer |
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improper fraction |
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fraction |
A factor is a positive integer that divides evenly into a given number. For example, the factors of 8 are 1, 2, 4, and 8.
A bread recipe calls for 3\(\frac{1}{8}\) cups of flour. If you only have \(\frac{7}{8}\) cup, how much more flour is needed?
| 2\(\frac{3}{4}\) cups | |
| 2\(\frac{1}{4}\) cups | |
| 2 cups | |
| 1\(\frac{7}{8}\) cups |
The amount of flour you need is (3\(\frac{1}{8}\) - \(\frac{7}{8}\)) cups. Rewrite the quantities so they share a common denominator and subtract:
(\( \frac{25}{8} \) - \( \frac{7}{8} \)) cups
\( \frac{18}{8} \) cups
2\(\frac{1}{4}\) cups
If all of a roofing company's 6 workers are required to staff 2 roofing crews, how many workers need to be added during the busy season in order to send 4 complete crews out on jobs?
| 1 | |
| 6 | |
| 17 | |
| 14 |
In order to find how many additional workers are needed to staff the extra crews you first need to calculate how many workers are on a crew. There are 6 workers at the company now and that's enough to staff 2 crews so there are \( \frac{6}{2} \) = 3 workers on a crew. 4 crews are needed for the busy season which, at 3 workers per crew, means that the roofing company will need 4 x 3 = 12 total workers to staff the crews during the busy season. The company already employs 6 workers so they need to add 12 - 6 = 6 new staff for the busy season.
In a class of 22 students, 12 are taking German and 6 are taking Spanish. Of the students studying German or Spanish, 2 are taking both courses. How many students are not enrolled in either course?
| 18 | |
| 15 | |
| 22 | |
| 6 |
The number of students taking German or Spanish is 12 + 6 = 18. Of that group of 18, 2 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 18 - 2 = 16 who are taking at least one language. 22 - 16 = 6 students who are not taking either language.
A machine in a factory has an error rate of 3 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?
| 147.2 | |
| 139.5 | |
| 157.1 | |
| 138.3 |
The hourly error rate for this machine is the error rate in parts per 100 multiplied by the number of parts produced per hour:
\( \frac{3}{100} \) x 9 = \( \frac{3 \times 9}{100} \) = \( \frac{27}{100} \) = 0.27 errors per hour
So, in an average hour, the machine will produce 9 - 0.27 = 8.73 error free parts.
The machine ran for 24 - 6 = 18 hours yesterday so you would expect that 18 x 8.73 = 157.1 error free parts were produced yesterday.