| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.70 |
| Score | 0% | 74% |
Simplify \( \frac{40}{60} \).
| \( \frac{3}{10} \) | |
| \( \frac{2}{3} \) | |
| \( \frac{9}{20} \) | |
| \( \frac{10}{13} \) |
To simplify this fraction, first find the greatest common factor between them. The factors of 40 are [1, 2, 4, 5, 8, 10, 20, 40] and the factors of 60 are [1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60]. They share 6 factors [1, 2, 4, 5, 10, 20] making 20 their greatest common factor (GCF).
Next, divide both numerator and denominator by the GCF:
\( \frac{40}{60} \) = \( \frac{\frac{40}{20}}{\frac{60}{20}} \) = \( \frac{2}{3} \)
In a class of 36 students, 11 are taking German and 14 are taking Spanish. Of the students studying German or Spanish, 2 are taking both courses. How many students are not enrolled in either course?
| 32 | |
| 11 | |
| 13 | |
| 20 |
The number of students taking German or Spanish is 11 + 14 = 25. Of that group of 25, 2 are taking both languages so they've been counted twice (once in the German group and once in the Spanish group). Subtracting them out leaves 25 - 2 = 23 who are taking at least one language. 36 - 23 = 13 students who are not taking either language.
4! = ?
3 x 2 x 1 |
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4 x 3 |
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5 x 4 x 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.
Which of the following is not an integer?
\({1 \over 2}\) |
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-1 |
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0 |
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1 |
An integer is any whole number, including zero. An integer can be either positive or negative. Examples include -77, -1, 0, 55, 119.
The __________ is the greatest factor that divides two integers.
greatest common factor |
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absolute value |
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greatest common multiple |
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least common multiple |
The greatest common factor (GCF) is the greatest factor that divides two integers.