| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.39 |
| Score | 0% | 68% |
What is \( \frac{4}{9} \) ÷ \( \frac{1}{6} \)?
| \(\frac{1}{6}\) | |
| \(\frac{1}{14}\) | |
| \(\frac{1}{18}\) | |
| 2\(\frac{2}{3}\) |
To divide fractions, invert the second fraction and then multiply:
\( \frac{4}{9} \) ÷ \( \frac{1}{6} \) = \( \frac{4}{9} \) x \( \frac{6}{1} \)
To multiply fractions, multiply the numerators together and then multiply the denominators together:
\( \frac{4}{9} \) x \( \frac{6}{1} \) = \( \frac{4 x 6}{9 x 1} \) = \( \frac{24}{9} \) = 2\(\frac{2}{3}\)
What is \( \frac{4}{7} \) x \( \frac{4}{7} \)?
| \(\frac{16}{49}\) | |
| \(\frac{1}{12}\) | |
| \(\frac{1}{14}\) | |
| \(\frac{1}{6}\) |
To multiply fractions, multiply the numerators together and then multiply the denominators together:
\( \frac{4}{7} \) x \( \frac{4}{7} \) = \( \frac{4 x 4}{7 x 7} \) = \( \frac{16}{49} \) = \(\frac{16}{49}\)
What is \( \frac{8}{4} \) - \( \frac{5}{12} \)?
| 2 \( \frac{3}{10} \) | |
| 2 \( \frac{1}{12} \) | |
| 1\(\frac{7}{12}\) | |
| 2 \( \frac{9}{14} \) |
To subtract these fractions, first find the lowest common multiple of their denominators. The first few multiples of 4 are [4, 8, 12, 16, 20, 24, 28, 32, 36, 40] and the first few multiples of 12 are [12, 24, 36, 48, 60, 72, 84, 96]. The first few multiples they share are [12, 24, 36, 48, 60] making 12 the smallest multiple 4 and 12 share.
Next, convert the fractions so each denominator equals the lowest common multiple:
\( \frac{8 x 3}{4 x 3} \) - \( \frac{5 x 1}{12 x 1} \)
\( \frac{24}{12} \) - \( \frac{5}{12} \)
Now, because the fractions share a common denominator, you can subtract them:
\( \frac{24 - 5}{12} \) = \( \frac{19}{12} \) = 1\(\frac{7}{12}\)
What is \( \frac{6}{2} \) + \( \frac{2}{6} \)?
| 1 \( \frac{9}{6} \) | |
| 1 \( \frac{7}{6} \) | |
| 3\(\frac{1}{3}\) | |
| 2 \( \frac{8}{6} \) |
To add these fractions, first find the lowest common multiple of their denominators. The first few multiples of 2 are [2, 4, 6, 8, 10, 12, 14, 16, 18, 20] and the first few multiples of 6 are [6, 12, 18, 24, 30, 36, 42, 48, 54, 60]. The first few multiples they share are [6, 12, 18, 24, 30] making 6 the smallest multiple 2 and 6 share.
Next, convert the fractions so each denominator equals the lowest common multiple:
\( \frac{6 x 3}{2 x 3} \) + \( \frac{2 x 1}{6 x 1} \)
\( \frac{18}{6} \) + \( \frac{2}{6} \)
Now, because the fractions share a common denominator, you can add them:
\( \frac{18 + 2}{6} \) = \( \frac{20}{6} \) = 3\(\frac{1}{3}\)
Simplify \( \frac{40}{68} \).
| \( \frac{5}{13} \) | |
| \( \frac{8}{17} \) | |
| \( \frac{10}{17} \) | |
| \( \frac{4}{11} \) |
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 68 are [1, 2, 4, 17, 34, 68]. They share 3 factors [1, 2, 4] making 4 their greatest common factor (GCF).
Next, divide both numerator and denominator by the GCF:
\( \frac{40}{68} \) = \( \frac{\frac{40}{4}}{\frac{68}{4}} \) = \( \frac{10}{17} \)