| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.20 |
| Score | 0% | 64% |
What is \( \frac{2}{7} \) x \( \frac{4}{9} \)?
| \(\frac{8}{45}\) | |
| \(\frac{3}{20}\) | |
| \(\frac{1}{36}\) | |
| \(\frac{8}{63}\) |
To multiply fractions, multiply the numerators together and then multiply the denominators together:
\( \frac{2}{7} \) x \( \frac{4}{9} \) = \( \frac{2 x 4}{7 x 9} \) = \( \frac{8}{63} \) = \(\frac{8}{63}\)
Ezra loaned Betty $1,000 at an annual interest rate of 2%. If no payments are made, what is the total amount owed at the end of the first year?
| $1,010 | |
| $1,030 | |
| $1,070 | |
| $1,020 |
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 $1,000
i = 0.02 x $1,000
No payments were made so the total amount due is the original amount + the accumulated interest:
total = $1,000 + $20What is \( \frac{8}{3} \) + \( \frac{9}{5} \)?
| 2 \( \frac{4}{15} \) | |
| \( \frac{8}{15} \) | |
| 1 \( \frac{9}{12} \) | |
| 4\(\frac{7}{15}\) |
To add these fractions, first find the lowest common multiple of their denominators. The first few multiples of 3 are [3, 6, 9, 12, 15, 18, 21, 24, 27, 30] and the first few multiples of 5 are [5, 10, 15, 20, 25, 30, 35, 40, 45, 50]. The first few multiples they share are [15, 30, 45, 60, 75] making 15 the smallest multiple 3 and 5 share.
Next, convert the fractions so each denominator equals the lowest common multiple:
\( \frac{8 x 5}{3 x 5} \) + \( \frac{9 x 3}{5 x 3} \)
\( \frac{40}{15} \) + \( \frac{27}{15} \)
Now, because the fractions share a common denominator, you can add them:
\( \frac{40 + 27}{15} \) = \( \frac{67}{15} \) = 4\(\frac{7}{15}\)
On average, the center for a basketball team hits 35% of his shots while a guard on the same team hits 55% of his shots. If the guard takes 30 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?
| 44 | |
| 46 | |
| 27 | |
| 34 |
guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 30 x \( \frac{55}{100} \) = \( \frac{55 x 30}{100} \) = \( \frac{1650}{100} \) = 16 shots
The center makes 35% 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 = \( \frac{16}{\frac{35}{100}} \) = 16 x \( \frac{100}{35} \) = \( \frac{16 x 100}{35} \) = \( \frac{1600}{35} \) = 46 shots
to make the same number of shots as the guard and thus score the same number of points.
What is the least common multiple of 6 and 12?
| 12 | |
| 24 | |
| 71 | |
| 46 |
The first few multiples of 6 are [6, 12, 18, 24, 30, 36, 42, 48, 54, 60] 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 6 and 12 have in common.