| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.77 |
| Score | 0% | 55% |
What is \( \frac{8}{4} \) + \( \frac{2}{10} \)?
| \( \frac{4}{13} \) | |
| \( \frac{9}{16} \) | |
| 2\(\frac{1}{5}\) | |
| 2 \( \frac{1}{6} \) |
To add 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 10 are [10, 20, 30, 40, 50, 60, 70, 80, 90]. The first few multiples they share are [20, 40, 60, 80] making 20 the smallest multiple 4 and 10 share.
Next, convert the fractions so each denominator equals the lowest common multiple:
\( \frac{8 x 5}{4 x 5} \) + \( \frac{2 x 2}{10 x 2} \)
\( \frac{40}{20} \) + \( \frac{4}{20} \)
Now, because the fractions share a common denominator, you can add them:
\( \frac{40 + 4}{20} \) = \( \frac{44}{20} \) = 2\(\frac{1}{5}\)
If all of a roofing company's 12 workers are required to staff 3 roofing crews, how many workers need to be added during the busy season in order to send 8 complete crews out on jobs?
| 7 | |
| 20 | |
| 18 | |
| 9 |
In order to find how many additional workers are needed to staff the extra crews you first need to calculate how many workers are on a crew. There are 12 workers at the company now and that's enough to staff 3 crews so there are \( \frac{12}{3} \) = 4 workers on a crew. 8 crews are needed for the busy season which, at 4 workers per crew, means that the roofing company will need 8 x 4 = 32 total workers to staff the crews during the busy season. The company already employs 12 workers so they need to add 32 - 12 = 20 new staff for the busy season.
A machine in a factory has an error rate of 6 parts per 100. The machine normally runs 24 hours a day and produces 7 parts per hour. Yesterday the machine was shut down for 6 hours for maintenance.
How many error-free parts did the machine produce yesterday?
| 132.5 | |
| 129.6 | |
| 118.4 | |
| 184 |
The hourly error rate for this machine is the error rate in parts per 100 multiplied by the number of parts produced per hour:
\( \frac{6}{100} \) x 7 = \( \frac{6 \times 7}{100} \) = \( \frac{42}{100} \) = 0.42 errors per hour
So, in an average hour, the machine will produce 7 - 0.42 = 6.58 error free parts.
The machine ran for 24 - 6 = 18 hours yesterday so you would expect that 18 x 6.58 = 118.4 error free parts were produced yesterday.
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?
| 75 | |
| 72 | |
| 49 | |
| 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.
A menswear store is having a sale: "Buy one shirt at full price and get another shirt for 20% off." If Roger buys two shirts, each with a regular price of $22, how much money will he save?
| $9.90 | |
| $4.40 | |
| $2.20 | |
| $5.50 |
By buying two shirts, Roger will save $22 x \( \frac{20}{100} \) = \( \frac{$22 x 20}{100} \) = \( \frac{$440}{100} \) = $4.40 on the second shirt.