| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.43 |
| Score | 0% | 69% |
What is \( \frac{6}{9} \) + \( \frac{4}{15} \)?
| 1 \( \frac{8}{45} \) | |
| \(\frac{14}{15}\) | |
| \( \frac{5}{45} \) | |
| 1 \( \frac{8}{15} \) |
To add these fractions, first find the lowest common multiple of their denominators. The first few multiples of 9 are [9, 18, 27, 36, 45, 54, 63, 72, 81, 90] and the first few multiples of 15 are [15, 30, 45, 60, 75, 90]. The first few multiples they share are [45, 90] making 45 the smallest multiple 9 and 15 share.
Next, convert the fractions so each denominator equals the lowest common multiple:
\( \frac{6 x 5}{9 x 5} \) + \( \frac{4 x 3}{15 x 3} \)
\( \frac{30}{45} \) + \( \frac{12}{45} \)
Now, because the fractions share a common denominator, you can add them:
\( \frac{30 + 12}{45} \) = \( \frac{42}{45} \) = \(\frac{14}{15}\)
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 6 complete crews out on jobs?
| 14 | |
| 6 | |
| 8 | |
| 7 |
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. 6 crews are needed for the busy season which, at 3 workers per crew, means that the roofing company will need 6 x 3 = 18 total workers to staff the crews during the busy season. The company already employs 12 workers so they need to add 18 - 12 = 6 new staff for the busy season.
What is the distance in miles of a trip that takes 8 hours at an average speed of 70 miles per hour?
| 390 miles | |
| 560 miles | |
| 400 miles | |
| 360 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 = \( 70mph \times 8h \)
560 miles
Which of the following is an improper fraction?
\({7 \over 5} \) |
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\({2 \over 5} \) |
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\(1 {2 \over 5} \) |
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\({a \over 5} \) |
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.
a(b + c) = ab + ac defines which of the following?
commutative property for multiplication |
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distributive property for multiplication |
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commutative property for division |
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distributive property for division |
The distributive property for multiplication helps in solving expressions like a(b + c). It specifies that the result of multiplying one number by the sum or difference of two numbers can be obtained by multiplying each number individually and then totaling the results: a(b + c) = ab + ac. For example, 4(10-5) = (4 x 10) - (4 x 5) = 40 - 20 = 20.