| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.33 |
| Score | 0% | 67% |
What is the greatest common factor of 80 and 64?
| 10 | |
| 57 | |
| 17 | |
| 16 |
The factors of 80 are [1, 2, 4, 5, 8, 10, 16, 20, 40, 80] and the factors of 64 are [1, 2, 4, 8, 16, 32, 64]. They share 5 factors [1, 2, 4, 8, 16] making 16 the greatest factor 80 and 64 have in common.
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 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?
| 30 | |
| 75 | |
| 55 | |
| 45 |
guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 30 x \( \frac{60}{100} \) = \( \frac{60 x 30}{100} \) = \( \frac{1800}{100} \) = 18 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 = \( \frac{18}{\frac{40}{100}} \) = 18 x \( \frac{100}{40} \) = \( \frac{18 x 100}{40} \) = \( \frac{1800}{40} \) = 45 shots
to make the same number of shots as the guard and thus score the same number of points.
Simplify \( \frac{36}{60} \).
| \( \frac{3}{5} \) | |
| \( \frac{4}{17} \) | |
| \( \frac{4}{19} \) | |
| \( \frac{7}{12} \) |
To simplify this fraction, first find the greatest common factor between them. The factors of 36 are [1, 2, 3, 4, 6, 9, 12, 18, 36] 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 their greatest common factor (GCF).
Next, divide both numerator and denominator by the GCF:
\( \frac{36}{60} \) = \( \frac{\frac{36}{12}}{\frac{60}{12}} \) = \( \frac{3}{5} \)
What is -9x2 x 7x4?
| -63x-2 | |
| -2x2 | |
| -63x6 | |
| -2x4 |
To multiply terms with exponents, the base of both exponents must be the same. In this case they are so multiply the coefficients and add the exponents:
-9x2 x 7x4
(-9 x 7)x(2 + 4)
-63x6
What is \( \frac{6}{5} \) + \( \frac{2}{9} \)?
| 1\(\frac{19}{45}\) | |
| \( \frac{4}{45} \) | |
| \( \frac{5}{9} \) | |
| 1 \( \frac{6}{12} \) |
To add 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 9 are [9, 18, 27, 36, 45, 54, 63, 72, 81, 90]. The first few multiples they share are [45, 90] making 45 the smallest multiple 5 and 9 share.
Next, convert the fractions so each denominator equals the lowest common multiple:
\( \frac{6 x 9}{5 x 9} \) + \( \frac{2 x 5}{9 x 5} \)
\( \frac{54}{45} \) + \( \frac{10}{45} \)
Now, because the fractions share a common denominator, you can add them:
\( \frac{54 + 10}{45} \) = \( \frac{64}{45} \) = 1\(\frac{19}{45}\)