| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.54 |
| Score | 0% | 71% |
What is \( \frac{10\sqrt{15}}{2\sqrt{5}} \)?
| \(\frac{1}{3}\) \( \sqrt{5} \) | |
| \(\frac{1}{5}\) \( \sqrt{3} \) | |
| 5 \( \sqrt{3} \) | |
| \(\frac{1}{3}\) \( \sqrt{\frac{1}{5}} \) |
To divide terms with radicals, divide the coefficients and radicands separately:
\( \frac{10\sqrt{15}}{2\sqrt{5}} \)
\( \frac{10}{2} \) \( \sqrt{\frac{15}{5}} \)
5 \( \sqrt{3} \)
Simplify \( \frac{36}{60} \).
| \( \frac{5}{9} \) | |
| \( \frac{3}{5} \) | |
| \( \frac{8}{13} \) | |
| \( \frac{5}{8} \) |
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 60 are [1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60]. They share 6 factors [1, 2, 3, 4, 6, 12] making 12 their greatest common factor (GCF).
Next, divide both numerator and denominator by the GCF:
\( \frac{36}{60} \) = \( \frac{\frac{36}{12}}{\frac{60}{12}} \) = \( \frac{3}{5} \)
A menswear store is having a sale: "Buy one shirt at full price and get another shirt for 45% off." If Frank buys two shirts, each with a regular price of $30, how much money will he save?
| $1.50 | |
| $13.50 | |
| $6.00 | |
| $10.50 |
By buying two shirts, Frank will save $30 x \( \frac{45}{100} \) = \( \frac{$30 x 45}{100} \) = \( \frac{$1350}{100} \) = $13.50 on the second shirt.
What is \( \frac{1}{7} \) x \( \frac{2}{6} \)?
| \(\frac{2}{21}\) | |
| \(\frac{1}{14}\) | |
| \(\frac{1}{3}\) | |
| \(\frac{1}{21}\) |
To multiply fractions, multiply the numerators together and then multiply the denominators together:
\( \frac{1}{7} \) x \( \frac{2}{6} \) = \( \frac{1 x 2}{7 x 6} \) = \( \frac{2}{42} \) = \(\frac{1}{21}\)
A bread recipe calls for 3 cups of flour. If you only have 1\(\frac{3}{4}\) cups, how much more flour is needed?
| 2\(\frac{1}{4}\) cups | |
| 1\(\frac{1}{4}\) cups | |
| \(\frac{3}{4}\) cups | |
| 1\(\frac{7}{8}\) cups |
The amount of flour you need is (3 - 1\(\frac{3}{4}\)) cups. Rewrite the quantities so they share a common denominator and subtract:
(\( \frac{24}{8} \) - \( \frac{14}{8} \)) cups
\( \frac{10}{8} \) cups
1\(\frac{1}{4}\) cups