| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.45 |
| Score | 0% | 69% |
| 3.5 | |
| 1.6 | |
| 0.6 | |
| 1 |
1
Simplify \( \frac{32}{64} \).
| \( \frac{5}{9} \) | |
| \( \frac{2}{3} \) | |
| \( \frac{4}{7} \) | |
| \( \frac{1}{2} \) |
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 64 are [1, 2, 4, 8, 16, 32, 64]. They share 6 factors [1, 2, 4, 8, 16, 32] making 32 their greatest common factor (GCF).
Next, divide both numerator and denominator by the GCF:
\( \frac{32}{64} \) = \( \frac{\frac{32}{32}}{\frac{64}{32}} \) = \( \frac{1}{2} \)
Convert x-5 to remove the negative exponent.
| \( \frac{-5}{-x} \) | |
| \( \frac{-5}{x} \) | |
| \( \frac{1}{x^5} \) | |
| \( \frac{1}{x^{-5}} \) |
To convert a negative exponent to a positive exponent, calculate the positive exponent then take the reciprocal.
What is the greatest common factor of 36 and 48?
| 12 | |
| 19 | |
| 32 | |
| 15 |
The factors of 36 are [1, 2, 3, 4, 6, 9, 12, 18, 36] and the factors of 48 are [1, 2, 3, 4, 6, 8, 12, 16, 24, 48]. They share 6 factors [1, 2, 3, 4, 6, 12] making 12 the greatest factor 36 and 48 have in common.
What is \( \frac{2}{5} \) ÷ \( \frac{1}{6} \)?
| \(\frac{4}{45}\) | |
| \(\frac{1}{14}\) | |
| 2\(\frac{2}{5}\) | |
| \(\frac{3}{56}\) |
To divide fractions, invert the second fraction and then multiply:
\( \frac{2}{5} \) ÷ \( \frac{1}{6} \) = \( \frac{2}{5} \) x \( \frac{6}{1} \)
To multiply fractions, multiply the numerators together and then multiply the denominators together:
\( \frac{2}{5} \) x \( \frac{6}{1} \) = \( \frac{2 x 6}{5 x 1} \) = \( \frac{12}{5} \) = 2\(\frac{2}{5}\)