| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.07 |
| Score | 0% | 61% |
\({b + c \over a} = {b \over a} + {c \over a}\) defines which of the following?
commutative property for division |
|
commutative property for multiplication |
|
distributive property for division |
|
distributive property for multiplication |
The distributive property for division helps in solving expressions like \({b + c \over a}\). It specifies that the result of dividing a fraction with multiple terms in the numerator and one term in the denominator can be obtained by dividing each term individually and then totaling the results: \({b + c \over a} = {b \over a} + {c \over a}\). For example, \({a^3 + 6a^2 \over a^2} = {a^3 \over a^2} + {6a^2 \over a^2} = a + 6\).
What is the distance in miles of a trip that takes 8 hours at an average speed of 25 miles per hour?
| 120 miles | |
| 200 miles | |
| 280 miles | |
| 560 miles |
Average speed in miles per hour is the number of miles traveled divided by the number of hours:
speed = \( \frac{\text{distance}}{\text{time}} \)Solving for distance:
distance = \( \text{speed} \times \text{time} \)
distance = \( 25mph \times 8h \)
200 miles
What is \( \frac{7}{3} \) + \( \frac{9}{7} \)?
| 3\(\frac{13}{21}\) | |
| \( \frac{6}{14} \) | |
| 1 \( \frac{2}{7} \) | |
| 2 \( \frac{6}{21} \) |
To add these fractions, first find the lowest common multiple of their denominators. The first few multiples of 3 are [3, 6, 9, 12, 15, 18, 21, 24, 27, 30] 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 [21, 42, 63, 84] making 21 the smallest multiple 3 and 7 share.
Next, convert the fractions so each denominator equals the lowest common multiple:
\( \frac{7 x 7}{3 x 7} \) + \( \frac{9 x 3}{7 x 3} \)
\( \frac{49}{21} \) + \( \frac{27}{21} \)
Now, because the fractions share a common denominator, you can add them:
\( \frac{49 + 27}{21} \) = \( \frac{76}{21} \) = 3\(\frac{13}{21}\)
Simplify \( \sqrt{12} \)
| 8\( \sqrt{6} \) | |
| 2\( \sqrt{3} \) | |
| 2\( \sqrt{6} \) | |
| 8\( \sqrt{3} \) |
To simplify a radical, factor out the perfect squares:
\( \sqrt{12} \)
\( \sqrt{4 \times 3} \)
\( \sqrt{2^2 \times 3} \)
2\( \sqrt{3} \)
On average, the center for a basketball team hits 25% of his shots while a guard on the same team hits 45% 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?
| 36 | |
| 20 | |
| 38 | |
| 18 |
guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 20 x \( \frac{45}{100} \) = \( \frac{45 x 20}{100} \) = \( \frac{900}{100} \) = 9 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 = \( \frac{9}{\frac{25}{100}} \) = 9 x \( \frac{100}{25} \) = \( \frac{9 x 100}{25} \) = \( \frac{900}{25} \) = 36 shots
to make the same number of shots as the guard and thus score the same number of points.