| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.01 |
| Score | 0% | 60% |
Simplify \( \frac{28}{76} \).
| \( \frac{7}{19} \) | |
| \( \frac{4}{11} \) | |
| \( \frac{7}{20} \) | |
| \( \frac{4}{13} \) |
To simplify this fraction, first find the greatest common factor between them. The factors of 28 are [1, 2, 4, 7, 14, 28] and the factors of 76 are [1, 2, 4, 19, 38, 76]. They share 3 factors [1, 2, 4] making 4 their greatest common factor (GCF).
Next, divide both numerator and denominator by the GCF:
\( \frac{28}{76} \) = \( \frac{\frac{28}{4}}{\frac{76}{4}} \) = \( \frac{7}{19} \)
Convert b-4 to remove the negative exponent.
| \( \frac{-4}{b} \) | |
| \( \frac{4}{b} \) | |
| \( \frac{-1}{-4b^{4}} \) | |
| \( \frac{1}{b^4} \) |
To convert a negative exponent to a positive exponent, calculate the positive exponent then take the reciprocal.
What is \( \frac{4}{4} \) - \( \frac{3}{6} \)?
| \( \frac{5}{13} \) | |
| \(\frac{1}{2}\) | |
| 1 \( \frac{9}{15} \) | |
| 2 \( \frac{2}{12} \) |
To subtract these fractions, first find the lowest common multiple of their denominators. The first few multiples of 4 are [4, 8, 12, 16, 20, 24, 28, 32, 36, 40] 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 [12, 24, 36, 48, 60] making 12 the smallest multiple 4 and 6 share.
Next, convert the fractions so each denominator equals the lowest common multiple:
\( \frac{4 x 3}{4 x 3} \) - \( \frac{3 x 2}{6 x 2} \)
\( \frac{12}{12} \) - \( \frac{6}{12} \)
Now, because the fractions share a common denominator, you can subtract them:
\( \frac{12 - 6}{12} \) = \( \frac{6}{12} \) = \(\frac{1}{2}\)
On average, the center for a basketball team hits 25% of his shots while a guard on the same team hits 40% 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?
| 57 | |
| 24 | |
| 48 | |
| 26 |
guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 30 x \( \frac{40}{100} \) = \( \frac{40 x 30}{100} \) = \( \frac{1200}{100} \) = 12 shots
The center makes 25% 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 = \( \frac{12}{\frac{25}{100}} \) = 12 x \( \frac{100}{25} \) = \( \frac{12 x 100}{25} \) = \( \frac{1200}{25} \) = 48 shots
to make the same number of shots as the guard and thus score the same number of points.
If a mayor is elected with 52% of the votes cast and 64% of a town's 43,000 voters cast a vote, how many votes did the mayor receive?
| 21,741 | |
| 22,016 | |
| 14,310 | |
| 19,814 |
If 64% of the town's 43,000 voters cast ballots the number of votes cast is:
(\( \frac{64}{100} \)) x 43,000 = \( \frac{2,752,000}{100} \) = 27,520
The mayor got 52% of the votes cast which is:
(\( \frac{52}{100} \)) x 27,520 = \( \frac{1,431,040}{100} \) = 14,310 votes.