| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.11 |
| Score | 0% | 62% |
What is \( \frac{8}{3} \) + \( \frac{5}{7} \)?
| 3\(\frac{8}{21}\) | |
| 1 \( \frac{2}{21} \) | |
| 1 \( \frac{3}{21} \) | |
| \( \frac{3}{21} \) |
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:
\( \frac{8 x 7}{3 x 7} \) + \( \frac{5 x 3}{7 x 3} \)
\( \frac{56}{21} \) + \( \frac{15}{21} \)
Now, because the fractions share a common denominator, you can add them:
\( \frac{56 + 15}{21} \) = \( \frac{71}{21} \) = 3\(\frac{8}{21}\)
If all of a roofing company's 12 workers are required to staff 4 roofing crews, how many workers need to be added during the busy season in order to send 7 complete crews out on jobs?
| 9 | |
| 18 | |
| 7 | |
| 5 |
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 4 crews so there are \( \frac{12}{4} \) = 3 workers on a crew. 7 crews are needed for the busy season which, at 3 workers per crew, means that the roofing company will need 7 x 3 = 21 total workers to staff the crews during the busy season. The company already employs 12 workers so they need to add 21 - 12 = 9 new staff for the busy season.
How many hours does it take a car to travel 540 miles at an average speed of 60 miles per hour?
| 6 hours | |
| 9 hours | |
| 3 hours | |
| 7 hours |
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 time:
time = \( \frac{\text{distance}}{\text{speed}} \)
time = \( \frac{540mi}{60mph} \)
9 hours
\({b + c \over a} = {b \over a} + {c \over a}\) defines which of the following?
distributive property for division |
|
commutative property for division |
|
commutative property for multiplication |
|
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, \({a^3 + 6a^2 \over a^2} = {a^3 \over a^2} + {6a^2 \over a^2} = a + 6\).
A menswear store is having a sale: "Buy one shirt at full price and get another shirt for 5% off." If Charlie buys two shirts, each with a regular price of $23, how much will he pay for both shirts?
| $31.05 | |
| $1.15 | |
| $21.85 | |
| $44.85 |
By buying two shirts, Charlie will save $23 x \( \frac{5}{100} \) = \( \frac{$23 x 5}{100} \) = \( \frac{$115}{100} \) = $1.15 on the second shirt.
So, his total cost will be
$23.00 + ($23.00 - $1.15)
$23.00 + $21.85
$44.85