| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.39 |
| Score | 0% | 68% |
What is \( \frac{5}{2} \) - \( \frac{8}{4} \)?
| \( \frac{1}{4} \) | |
| 1 \( \frac{9}{4} \) | |
| 2 \( \frac{5}{4} \) | |
| \(\frac{1}{2}\) |
To subtract these fractions, first find the lowest common multiple of their denominators. The first few multiples of 2 are [2, 4, 6, 8, 10, 12, 14, 16, 18, 20] and the first few multiples of 4 are [4, 8, 12, 16, 20, 24, 28, 32, 36, 40]. The first few multiples they share are [4, 8, 12, 16, 20] making 4 the smallest multiple 2 and 4 share.
Next, convert the fractions so each denominator equals the lowest common multiple:
\( \frac{5 x 2}{2 x 2} \) - \( \frac{8 x 1}{4 x 1} \)
\( \frac{10}{4} \) - \( \frac{8}{4} \)
Now, because the fractions share a common denominator, you can subtract them:
\( \frac{10 - 8}{4} \) = \( \frac{2}{4} \) = \(\frac{1}{2}\)
How many hours does it take a car to travel 180 miles at an average speed of 30 miles per hour?
| 7 hours | |
| 4 hours | |
| 8 hours | |
| 6 hours |
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 = \( \frac{180mi}{30mph} \)
6 hours
Monty loaned Christine $1,300 at an annual interest rate of 1%. If no payments are made, what is the total amount owed at the end of the first year?
| $1,417 | |
| $1,391 | |
| $1,378 | |
| $1,313 |
The yearly interest charged on this loan is the annual interest rate multiplied by the amount borrowed:
interest = annual interest rate x loan amount
i = (\( \frac{6}{100} \)) x $1,300
i = 0.01 x $1,300
No payments were made so the total amount due is the original amount + the accumulated interest:
total = $1,300 + $13On average, the center for a basketball team hits 40% of his shots while a guard on the same team hits 60% of his shots. If the guard takes 25 shots during a game, how many shots will the center have to take to score as many points as the guard assuming each shot is worth the same number of points?
| 27 | |
| 38 | |
| 33 | |
| 36 |
guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 25 x \( \frac{60}{100} \) = \( \frac{60 x 25}{100} \) = \( \frac{1500}{100} \) = 15 shots
The center makes 40% of his shots so he'll have to take:
shots made = shots taken x \( \frac{\text{% made}}{100} \)
shots taken = \( \frac{\text{shots taken}}{\frac{\text{% made}}{100}} \)
to make as many shots as the guard. Plugging in values for the center gives us:
center shots taken = \( \frac{15}{\frac{40}{100}} \) = 15 x \( \frac{100}{40} \) = \( \frac{15 x 100}{40} \) = \( \frac{1500}{40} \) = 38 shots
to make the same number of shots as the guard and thus score the same number of points.
What is the greatest common factor of 24 and 60?
| 19 | |
| 18 | |
| 12 | |
| 2 |
The factors of 24 are [1, 2, 3, 4, 6, 8, 12, 24] and the factors of 60 are [1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60]. They share 6 factors [1, 2, 3, 4, 6, 12] making 12 the greatest factor 24 and 60 have in common.