| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.65 |
| Score | 0% | 73% |
Simplify \( \frac{36}{76} \).
| \( \frac{9}{19} \) | |
| \( \frac{1}{3} \) | |
| \( \frac{2}{5} \) | |
| \( \frac{5}{13} \) |
To simplify this fraction, first find the greatest common factor between them. The factors of 36 are [1, 2, 3, 4, 6, 9, 12, 18, 36] and the factors of 76 are [1, 2, 4, 19, 38, 76]. They share 3 factors [1, 2, 4] making 4 their greatest common factor (GCF).
Next, divide both numerator and denominator by the GCF:
\( \frac{36}{76} \) = \( \frac{\frac{36}{4}}{\frac{76}{4}} \) = \( \frac{9}{19} \)
4! = ?
5 x 4 x 3 x 2 x 1 |
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4 x 3 |
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3 x 2 x 1 |
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4 x 3 x 2 x 1 |
A factorial has the form n! and is the product of the integer (n) and all the positive integers below it. For example, 5! = 5 x 4 x 3 x 2 x 1 = 120.
If \( \left|y + 3\right| \) - 5 = 6, which of these is a possible value for y?
| -14 | |
| -11 | |
| -7 | |
| 16 |
First, solve for \( \left|y + 3\right| \):
\( \left|y + 3\right| \) - 5 = 6
\( \left|y + 3\right| \) = 6 + 5
\( \left|y + 3\right| \) = 11
The value inside the absolute value brackets can be either positive or negative so (y + 3) must equal + 11 or -11 for \( \left|y + 3\right| \) to equal 11:
| y + 3 = 11 y = 11 - 3 y = 8 | y + 3 = -11 y = -11 - 3 y = -14 |
So, y = -14 or y = 8.
17 members of a bridal party need transported to a wedding reception but there are only 4 4-passenger taxis available to take them. How many will need to find other transportation?
| 5 | |
| 7 | |
| 1 | |
| 4 |
There are 4 4-passenger taxis available so that's 4 x 4 = 16 total seats. There are 17 people needing transportation leaving 17 - 16 = 1 who will have to find other transportation.
The __________ is the greatest factor that divides two integers.
least common multiple |
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greatest common factor |
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absolute value |
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greatest common multiple |
The greatest common factor (GCF) is the greatest factor that divides two integers.