| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.79 |
| Score | 0% | 56% |
\({b + c \over a} = {b \over a} + {c \over a}\) defines which of the following?
commutative property for multiplication |
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distributive property for multiplication |
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distributive property for division |
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commutative property for division |
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, \({a^3 + 6a^2 \over a^2} = {a^3 \over a^2} + {6a^2 \over a^2} = a + 6\).
If \(\left|a\right| = 7\), which of the following best describes a?
a = 7 |
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a = -7 |
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a = 7 or a = -7 |
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none of these is correct |
The absolute value is the positive magnitude of a particular number or variable and is indicated by two vertical lines: \(\left|-5\right| = 5\). In the case of a variable absolute value (\(\left|a\right| = 5\)) the value of a can be either positive or negative (a = -5 or a = 5).
What is 3\( \sqrt{3} \) x 9\( \sqrt{4} \)?
| 27\( \sqrt{3} \) | |
| 54\( \sqrt{3} \) | |
| 27\( \sqrt{4} \) | |
| 12\( \sqrt{4} \) |
To multiply terms with radicals, multiply the coefficients and radicands separately:
3\( \sqrt{3} \) x 9\( \sqrt{4} \)
(3 x 9)\( \sqrt{3 \times 4} \)
27\( \sqrt{12} \)
Now we need to simplify the radical:
27\( \sqrt{12} \)
27\( \sqrt{3 \times 4} \)
27\( \sqrt{3 \times 2^2} \)
(27)(2)\( \sqrt{3} \)
54\( \sqrt{3} \)
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 5 complete crews out on jobs?
| 8 | |
| 16 | |
| 17 | |
| 1 |
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. 5 crews are needed for the busy season which, at 4 workers per crew, means that the roofing company will need 5 x 4 = 20 total workers to staff the crews during the busy season. The company already employs 12 workers so they need to add 20 - 12 = 8 new staff for the busy season.
What is \( \frac{8}{4} \) + \( \frac{5}{12} \)?
| 2\(\frac{5}{12}\) | |
| 1 \( \frac{6}{12} \) | |
| 1 \( \frac{1}{9} \) | |
| 1 \( \frac{2}{12} \) |
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 12 are [12, 24, 36, 48, 60, 72, 84, 96]. The first few multiples they share are [12, 24, 36, 48, 60] making 12 the smallest multiple 4 and 12 share.
Next, convert the fractions so each denominator equals the lowest common multiple:
\( \frac{8 x 3}{4 x 3} \) + \( \frac{5 x 1}{12 x 1} \)
\( \frac{24}{12} \) + \( \frac{5}{12} \)
Now, because the fractions share a common denominator, you can add them:
\( \frac{24 + 5}{12} \) = \( \frac{29}{12} \) = 2\(\frac{5}{12}\)