| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.62 |
| Score | 0% | 72% |
Convert a-2 to remove the negative exponent.
| \( \frac{-1}{a^{-2}} \) | |
| \( \frac{-1}{-2a^{2}} \) | |
| \( \frac{1}{a^2} \) | |
| \( \frac{1}{a^{-2}} \) |
To convert a negative exponent to a positive exponent, calculate the positive exponent then take the reciprocal.
What is \( \frac{5}{9} \) + \( \frac{4}{15} \)?
| 1 \( \frac{9}{15} \) | |
| \(\frac{37}{45}\) | |
| \( \frac{9}{45} \) | |
| 1 \( \frac{4}{45} \) |
To add 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:
\( \frac{5 x 5}{9 x 5} \) + \( \frac{4 x 3}{15 x 3} \)
\( \frac{25}{45} \) + \( \frac{12}{45} \)
Now, because the fractions share a common denominator, you can add them:
\( \frac{25 + 12}{45} \) = \( \frac{37}{45} \) = \(\frac{37}{45}\)
If a car travels 540 miles in 9 hours, what is the average speed?
| 35 mph | |
| 50 mph | |
| 65 mph | |
| 60 mph |
Average speed in miles per hour is the number of miles traveled divided by the number of hours:
speed = \( \frac{\text{distance}}{\text{time}} \)A factor is a positive __________ that divides evenly into a given number.
fraction |
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integer |
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mixed number |
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improper 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.
What is the least common multiple of 4 and 12?
| 17 | |
| 35 | |
| 12 | |
| 22 |
The first few multiples of 4 are [4, 8, 12, 16, 20, 24, 28, 32, 36, 40] and the first few multiples of 12 are [12, 24, 36, 48, 60, 72, 84, 96]. The first few multiples they share are [12, 24, 36, 48, 60] making 12 the smallest multiple 4 and 12 have in common.