| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.41 |
| Score | 0% | 68% |
If all of a roofing company's 4 workers are required to staff 2 roofing crews, how many workers need to be added during the busy season in order to send 7 complete crews out on jobs?
| 16 | |
| 14 | |
| 18 | |
| 10 |
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 4 workers at the company now and that's enough to staff 2 crews so there are \( \frac{4}{2} \) = 2 workers on a crew. 7 crews are needed for the busy season which, at 2 workers per crew, means that the roofing company will need 7 x 2 = 14 total workers to staff the crews during the busy season. The company already employs 4 workers so they need to add 14 - 4 = 10 new staff for the busy season.
What is \( \frac{2}{9} \) - \( \frac{9}{15} \)?
| 1 \( \frac{8}{11} \) | |
| -\(\frac{17}{45}\) | |
| 2 \( \frac{9}{18} \) | |
| 2 \( \frac{6}{45} \) |
To subtract these fractions, first find the lowest common multiple of their denominators. The first few multiples of 9 are [9, 18, 27, 36, 45, 54, 63, 72, 81, 90] and the first few multiples of 15 are [15, 30, 45, 60, 75, 90]. The first few multiples they share are [45, 90] making 45 the smallest multiple 9 and 15 share.
Next, convert the fractions so each denominator equals the lowest common multiple:
\( \frac{2 x 5}{9 x 5} \) - \( \frac{9 x 3}{15 x 3} \)
\( \frac{10}{45} \) - \( \frac{27}{45} \)
Now, because the fractions share a common denominator, you can subtract them:
\( \frac{10 - 27}{45} \) = \( \frac{-17}{45} \) = -\(\frac{17}{45}\)
In a class of 26 students, 8 are taking German and 12 are taking Spanish. Of the students studying German or Spanish, 5 are taking both courses. How many students are not enrolled in either course?
| 25 | |
| 15 | |
| 20 | |
| 11 |
The number of students taking German or Spanish is 8 + 12 = 20. Of that group of 20, 5 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 20 - 5 = 15 who are taking at least one language. 26 - 15 = 11 students who are not taking either language.
What is the greatest common factor of 52 and 80?
| 4 | |
| 6 | |
| 11 | |
| 35 |
The factors of 52 are [1, 2, 4, 13, 26, 52] and the factors of 80 are [1, 2, 4, 5, 8, 10, 16, 20, 40, 80]. They share 3 factors [1, 2, 4] making 4 the greatest factor 52 and 80 have in common.
Which of the following is a mixed number?
\({a \over 5} \) |
|
\(1 {2 \over 5} \) |
|
\({7 \over 5} \) |
|
\({5 \over 7} \) |
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.