| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.79 |
| Score | 0% | 56% |
What is \( \frac{9}{2} \) + \( \frac{8}{6} \)?
| 2 \( \frac{4}{12} \) | |
| 5\(\frac{5}{6}\) | |
| \( \frac{1}{6} \) | |
| 2 \( \frac{7}{14} \) |
To add 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 6 are [6, 12, 18, 24, 30, 36, 42, 48, 54, 60]. The first few multiples they share are [6, 12, 18, 24, 30] making 6 the smallest multiple 2 and 6 share.
Next, convert the fractions so each denominator equals the lowest common multiple:
\( \frac{9 x 3}{2 x 3} \) + \( \frac{8 x 1}{6 x 1} \)
\( \frac{27}{6} \) + \( \frac{8}{6} \)
Now, because the fractions share a common denominator, you can add them:
\( \frac{27 + 8}{6} \) = \( \frac{35}{6} \) = 5\(\frac{5}{6}\)
Christine scored 83% on her final exam. If each question was worth 2 points and there were 60 possible points on the exam, how many questions did Christine answer correctly?
| 29 | |
| 25 | |
| 37 | |
| 26 |
Christine scored 83% on the test meaning she earned 83% of the possible points on the test. There were 60 possible points on the test so she earned 60 x 0.83 = 50 points. Each question is worth 2 points so she got \( \frac{50}{2} \) = 25 questions right.
If a mayor is elected with 61% of the votes cast and 62% of a town's 21,000 voters cast a vote, how many votes did the mayor receive?
| 10,546 | |
| 7,031 | |
| 11,067 | |
| 7,942 |
If 62% of the town's 21,000 voters cast ballots the number of votes cast is:
(\( \frac{62}{100} \)) x 21,000 = \( \frac{1,302,000}{100} \) = 13,020
The mayor got 61% of the votes cast which is:
(\( \frac{61}{100} \)) x 13,020 = \( \frac{794,220}{100} \) = 7,942 votes.
What is \( \frac{2}{9} \) ÷ \( \frac{1}{7} \)?
| 1\(\frac{5}{9}\) | |
| \(\frac{2}{81}\) | |
| \(\frac{1}{8}\) | |
| \(\frac{3}{32}\) |
To divide fractions, invert the second fraction and then multiply:
\( \frac{2}{9} \) ÷ \( \frac{1}{7} \) = \( \frac{2}{9} \) x \( \frac{7}{1} \)
To multiply fractions, multiply the numerators together and then multiply the denominators together:
\( \frac{2}{9} \) x \( \frac{7}{1} \) = \( \frac{2 x 7}{9 x 1} \) = \( \frac{14}{9} \) = 1\(\frac{5}{9}\)
On 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 15 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?
| 15 | |
| 27 | |
| 25 | |
| 23 |
guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 15 x \( \frac{60}{100} \) = \( \frac{60 x 15}{100} \) = \( \frac{900}{100} \) = 9 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 = \( \frac{9}{\frac{40}{100}} \) = 9 x \( \frac{100}{40} \) = \( \frac{9 x 100}{40} \) = \( \frac{900}{40} \) = 23 shots
to make the same number of shots as the guard and thus score the same number of points.