| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.18 |
| Score | 0% | 64% |
What is \( \frac{5}{6} \) + \( \frac{2}{14} \)?
| \( \frac{3}{42} \) | |
| 1 \( \frac{3}{8} \) | |
| \(\frac{41}{42}\) | |
| 2 \( \frac{9}{42} \) |
To add these fractions, first find the lowest common multiple of their denominators. The first few multiples of 6 are [6, 12, 18, 24, 30, 36, 42, 48, 54, 60] and the first few multiples of 14 are [14, 28, 42, 56, 70, 84, 98]. The first few multiples they share are [42, 84] making 42 the smallest multiple 6 and 14 share.
Next, convert the fractions so each denominator equals the lowest common multiple:
\( \frac{5 x 7}{6 x 7} \) + \( \frac{2 x 3}{14 x 3} \)
\( \frac{35}{42} \) + \( \frac{6}{42} \)
Now, because the fractions share a common denominator, you can add them:
\( \frac{35 + 6}{42} \) = \( \frac{41}{42} \) = \(\frac{41}{42}\)
What is \( \frac{24\sqrt{56}}{8\sqrt{8}} \)?
| \(\frac{1}{7}\) \( \sqrt{3} \) | |
| \(\frac{1}{3}\) \( \sqrt{\frac{1}{7}} \) | |
| 3 \( \sqrt{7} \) | |
| 7 \( \sqrt{\frac{1}{3}} \) |
To divide terms with radicals, divide the coefficients and radicands separately:
\( \frac{24\sqrt{56}}{8\sqrt{8}} \)
\( \frac{24}{8} \) \( \sqrt{\frac{56}{8}} \)
3 \( \sqrt{7} \)
Which of the following is an improper fraction?
\({2 \over 5} \) |
|
\({7 \over 5} \) |
|
\(1 {2 \over 5} \) |
|
\({a \over 5} \) |
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.
Convert 1,945,000 to scientific notation.
| 1.945 x 106 | |
| 1.945 x 10-6 | |
| 1.945 x 10-5 | |
| 0.195 x 107 |
A number in scientific notation has the format 0.000 x 10exponent. To convert to scientific notation, move the decimal point to the right or the left until the number is a decimal between 1 and 10. The exponent of the 10 is the number of places you moved the decimal point and is positive if you moved the decimal point to the left and negative if you moved it to the right:
1,945,000 in scientific notation is 1.945 x 106
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?
| 9 | |
| 8 | |
| 6 | |
| 14 |
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.