| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.08 |
| Score | 0% | 62% |
What is \( \frac{3}{5} \) - \( \frac{6}{7} \)?
| 2 \( \frac{1}{35} \) | |
| 2 \( \frac{6}{14} \) | |
| -\(\frac{9}{35}\) | |
| 1 \( \frac{7}{15} \) |
To subtract these fractions, first find the lowest common multiple of their denominators. The first few multiples of 5 are [5, 10, 15, 20, 25, 30, 35, 40, 45, 50] and the first few multiples of 7 are [7, 14, 21, 28, 35, 42, 49, 56, 63, 70]. The first few multiples they share are [35, 70] making 35 the smallest multiple 5 and 7 share.
Next, convert the fractions so each denominator equals the lowest common multiple:
\( \frac{3 x 7}{5 x 7} \) - \( \frac{6 x 5}{7 x 5} \)
\( \frac{21}{35} \) - \( \frac{30}{35} \)
Now, because the fractions share a common denominator, you can subtract them:
\( \frac{21 - 30}{35} \) = \( \frac{-9}{35} \) = -\(\frac{9}{35}\)
On average, the center for a basketball team hits 35% of his shots while a guard on the same team hits 50% of his shots. If the guard takes 20 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 | |
| 29 | |
| 19 | |
| 45 |
guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 20 x \( \frac{50}{100} \) = \( \frac{50 x 20}{100} \) = \( \frac{1000}{100} \) = 10 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 = \( \frac{10}{\frac{35}{100}} \) = 10 x \( \frac{100}{35} \) = \( \frac{10 x 100}{35} \) = \( \frac{1000}{35} \) = 29 shots
to make the same number of shots as the guard and thus score the same number of points.
What is \( \frac{-9a^7}{1a^3} \)?
| -9a4 | |
| -\(\frac{1}{9}\)a-4 | |
| -\(\frac{1}{9}\)a4 | |
| -\(\frac{1}{9}\)a10 |
To divide terms with exponents, the base of both exponents must be the same. In this case they are so divide the coefficients and subtract the exponents:
\( \frac{-9a^7}{a^3} \)
\( \frac{-9}{1} \) a(7 - 3)
-9a4
Damon loaned Jennifer $1,500 at an annual interest rate of 6%. If no payments are made, what is the total amount owed at the end of the first year?
| $1,590 | |
| $1,620 | |
| $1,545 | |
| $1,515 |
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 $1,500
i = 0.06 x $1,500
No payments were made so the total amount due is the original amount + the accumulated interest:
total = $1,500 + $90What is \( \frac{4}{5} \) x \( \frac{1}{8} \)?
| \(\frac{1}{2}\) | |
| \(\frac{1}{10}\) | |
| \(\frac{1}{21}\) | |
| \(\frac{4}{21}\) |
To multiply fractions, multiply the numerators together and then multiply the denominators together:
\( \frac{4}{5} \) x \( \frac{1}{8} \) = \( \frac{4 x 1}{5 x 8} \) = \( \frac{4}{40} \) = \(\frac{1}{10}\)