| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.00 |
| Score | 0% | 60% |
Simplify \( \frac{36}{76} \).
| \( \frac{5}{8} \) | |
| \( \frac{7}{12} \) | |
| \( \frac{9}{19} \) | |
| \( \frac{5}{14} \) |
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 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:
\( \frac{36}{76} \) = \( \frac{\frac{36}{4}}{\frac{76}{4}} \) = \( \frac{9}{19} \)
Which of these numbers is a factor of 36?
| 7 | |
| 2 | |
| 31 | |
| 18 |
The factors of a number are all positive integers that divide evenly into the number. The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36.
A machine in a factory has an error rate of 5 parts per 100. The machine normally runs 24 hours a day and produces 10 parts per hour. Yesterday the machine was shut down for 5 hours for maintenance.
How many error-free parts did the machine produce yesterday?
| 104.9 | |
| 180.5 | |
| 190 | |
| 140.8 |
The hourly error rate for this machine is the error rate in parts per 100 multiplied by the number of parts produced per hour:
\( \frac{5}{100} \) x 10 = \( \frac{5 \times 10}{100} \) = \( \frac{50}{100} \) = 0.5 errors per hour
So, in an average hour, the machine will produce 10 - 0.5 = 9.5 error free parts.
The machine ran for 24 - 5 = 19 hours yesterday so you would expect that 19 x 9.5 = 180.5 error free parts were produced yesterday.
This property states taht the order of addition or multiplication does not mater. For example, 2 + 5 and 5 + 2 are equivalent.
distributive |
|
associative |
|
PEDMAS |
|
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.
On average, the center for a basketball team hits 45% of his shots while a guard on the same team hits 60% of his shots. If the guard takes 25 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?
| 29 | |
| 45 | |
| 41 | |
| 33 |
guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 25 x \( \frac{60}{100} \) = \( \frac{60 x 25}{100} \) = \( \frac{1500}{100} \) = 15 shots
The center makes 45% 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 = \( \frac{15}{\frac{45}{100}} \) = 15 x \( \frac{100}{45} \) = \( \frac{15 x 100}{45} \) = \( \frac{1500}{45} \) = 33 shots
to make the same number of shots as the guard and thus score the same number of points.