| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.25 |
| Score | 0% | 65% |
On average, the center for a basketball team hits 30% of his shots while a guard on the same team hits 50% 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?
| 17 | |
| 18 | |
| 19 | |
| 23 |
guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 15 x \( \frac{50}{100} \) = \( \frac{50 x 15}{100} \) = \( \frac{750}{100} \) = 7 shots
The center makes 30% 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 = \( \frac{7}{\frac{30}{100}} \) = 7 x \( \frac{100}{30} \) = \( \frac{7 x 100}{30} \) = \( \frac{700}{30} \) = 23 shots
to make the same number of shots as the guard and thus score the same number of points.
This property states taht the order of addition or multiplication does not mater. For example, 2 + 5 and 5 + 2 are equivalent.
distributive |
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PEDMAS |
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associative |
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commutative |
The commutative property states that, when adding or multiplying numbers, the order in which they're added or multiplied does not matter. For example, 3 + 4 and 4 + 3 give the same result, as do 3 x 4 and 4 x 3.
What is \( \frac{3}{8} \) ÷ \( \frac{3}{7} \)?
| \(\frac{7}{8}\) | |
| \(\frac{1}{7}\) | |
| \(\frac{2}{45}\) | |
| \(\frac{1}{8}\) |
To divide fractions, invert the second fraction and then multiply:
\( \frac{3}{8} \) ÷ \( \frac{3}{7} \) = \( \frac{3}{8} \) x \( \frac{7}{3} \)
To multiply fractions, multiply the numerators together and then multiply the denominators together:
\( \frac{3}{8} \) x \( \frac{7}{3} \) = \( \frac{3 x 7}{8 x 3} \) = \( \frac{21}{24} \) = \(\frac{7}{8}\)
Which of the following is an improper fraction?
\({7 \over 5} \) |
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\({a \over 5} \) |
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\(1 {2 \over 5} \) |
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\({2 \over 5} \) |
A rational number (or fraction) is represented as a ratio between two integers, a and b, and has the form \({a \over b}\) where a is the numerator and b is the denominator. An improper fraction (\({5 \over 3} \)) has a numerator with a greater absolute value than the denominator and can be converted into a mixed number (\(1 {2 \over 3} \)) which has a whole number part and a fractional part.
How many 7-passenger vans will it take to drive all 83 members of the football team to an away game?
| 9 vans | |
| 11 vans | |
| 5 vans | |
| 12 vans |
Calculate the number of vans needed by dividing the number of people that need transported by the capacity of one van:
vans = \( \frac{83}{7} \) = 11\(\frac{6}{7}\)
So, it will take 11 full vans and one partially full van to transport the entire team making a total of 12 vans.