| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.42 |
| Score | 0% | 68% |
| 6.3 | |
| 1 | |
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| 0.6 |
1
The __________ is the greatest factor that divides two integers.
greatest common multiple |
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absolute value |
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greatest common factor |
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least common multiple |
The greatest common factor (GCF) is the greatest factor that divides two integers.
What is \( \frac{42\sqrt{18}}{6\sqrt{9}} \)?
| \(\frac{1}{7}\) \( \sqrt{\frac{1}{2}} \) | |
| 2 \( \sqrt{7} \) | |
| \(\frac{1}{2}\) \( \sqrt{7} \) | |
| 7 \( \sqrt{2} \) |
To divide terms with radicals, divide the coefficients and radicands separately:
\( \frac{42\sqrt{18}}{6\sqrt{9}} \)
\( \frac{42}{6} \) \( \sqrt{\frac{18}{9}} \)
7 \( \sqrt{2} \)
What is \( \frac{2}{9} \) x \( \frac{1}{7} \)?
| \(\frac{2}{7}\) | |
| \(\frac{2}{63}\) | |
| \(\frac{2}{9}\) | |
| \(\frac{1}{18}\) |
To multiply fractions, multiply the numerators together and then multiply the denominators together:
\( \frac{2}{9} \) x \( \frac{1}{7} \) = \( \frac{2 x 1}{9 x 7} \) = \( \frac{2}{63} \) = \(\frac{2}{63}\)
Simplify \( \frac{32}{60} \).
| \( \frac{8}{15} \) | |
| \( \frac{5}{12} \) | |
| \( \frac{7}{17} \) | |
| \( \frac{8}{11} \) |
To simplify this fraction, first find the greatest common factor between them. The factors of 32 are [1, 2, 4, 8, 16, 32] and the factors of 60 are [1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60]. They share 3 factors [1, 2, 4] making 4 their greatest common factor (GCF).
Next, divide both numerator and denominator by the GCF:
\( \frac{32}{60} \) = \( \frac{\frac{32}{4}}{\frac{60}{4}} \) = \( \frac{8}{15} \)