| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.39 |
| Score | 0% | 68% |
The __________ is the smallest positive integer that is a multiple of two or more integers.
absolute value |
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greatest common factor |
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least common factor |
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least common multiple |
The least common multiple (LCM) is the smallest positive integer that is a multiple of two or more integers.
How many hours does it take a car to travel 315 miles at an average speed of 35 miles per hour?
| 2 hours | |
| 6 hours | |
| 9 hours | |
| 1 hour |
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 = \( \frac{315mi}{35mph} \)
9 hours
In a class of 24 students, 10 are taking German and 7 are taking Spanish. Of the students studying German or Spanish, 4 are taking both courses. How many students are not enrolled in either course?
| 11 | |
| 18 | |
| 19 | |
| 17 |
The number of students taking German or Spanish is 10 + 7 = 17. Of that group of 17, 4 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 17 - 4 = 13 who are taking at least one language. 24 - 13 = 11 students who are not taking either language.
Convert x-5 to remove the negative exponent.
| \( \frac{1}{x^{-5}} \) | |
| \( \frac{1}{x^5} \) | |
| \( \frac{5}{x} \) | |
| \( \frac{-5}{-x} \) |
To convert a negative exponent to a positive exponent, calculate the positive exponent then take the reciprocal.
What is \( \frac{2}{6} \) ÷ \( \frac{2}{8} \)?
| \(\frac{2}{45}\) | |
| \(\frac{1}{54}\) | |
| 8 | |
| 1\(\frac{1}{3}\) |
To divide fractions, invert the second fraction and then multiply:
\( \frac{2}{6} \) ÷ \( \frac{2}{8} \) = \( \frac{2}{6} \) x \( \frac{8}{2} \)
To multiply fractions, multiply the numerators together and then multiply the denominators together:
\( \frac{2}{6} \) x \( \frac{8}{2} \) = \( \frac{2 x 8}{6 x 2} \) = \( \frac{16}{12} \) = 1\(\frac{1}{3}\)