| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.17 |
| Score | 0% | 63% |
Convert b-3 to remove the negative exponent.
| \( \frac{-3}{b} \) | |
| \( \frac{1}{b^3} \) | |
| \( \frac{-1}{-3b^{3}} \) | |
| \( \frac{-1}{-3b} \) |
To convert a negative exponent to a positive exponent, calculate the positive exponent then take the reciprocal.
What is \( \frac{2}{5} \) ÷ \( \frac{1}{5} \)?
| 10 | |
| \(\frac{8}{63}\) | |
| 2 | |
| \(\frac{2}{25}\) |
To divide fractions, invert the second fraction and then multiply:
\( \frac{2}{5} \) ÷ \( \frac{1}{5} \) = \( \frac{2}{5} \) x \( \frac{5}{1} \)
To multiply fractions, multiply the numerators together and then multiply the denominators together:
\( \frac{2}{5} \) x \( \frac{5}{1} \) = \( \frac{2 x 5}{5 x 1} \) = \( \frac{10}{5} \) = 2
The __________ is the smallest positive integer that is a multiple of two or more integers.
greatest common factor |
|
absolute value |
|
least common multiple |
|
least common factor |
The least common multiple (LCM) is the smallest positive integer that is a multiple of two or more integers.
In a class of 33 students, 13 are taking German and 13 are taking Spanish. Of the students studying German or Spanish, 8 are taking both courses. How many students are not enrolled in either course?
| 15 | |
| 13 | |
| 26 | |
| 12 |
The number of students taking German or Spanish is 13 + 13 = 26. Of that group of 26, 8 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 26 - 8 = 18 who are taking at least one language. 33 - 18 = 15 students who are not taking either language.
If \( \left|a + 5\right| \) + 7 = 0, which of these is a possible value for a?
| 3 | |
| -11 | |
| 2 | |
| -23 |
First, solve for \( \left|a + 5\right| \):
\( \left|a + 5\right| \) + 7 = 0
\( \left|a + 5\right| \) = 0 - 7
\( \left|a + 5\right| \) = -7
The value inside the absolute value brackets can be either positive or negative so (a + 5) must equal - 7 or --7 for \( \left|a + 5\right| \) to equal -7:
| a + 5 = -7 a = -7 - 5 a = -12 | a + 5 = 7 a = 7 - 5 a = 2 |
So, a = 2 or a = -12.