| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.31 |
| Score | 0% | 66% |
A factor is a positive __________ that divides evenly into a given number.
mixed number |
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fraction |
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integer |
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improper fraction |
A factor is a positive integer that divides evenly into a given number. For example, the factors of 8 are 1, 2, 4, and 8.
What is \( \frac{3}{8} \) ÷ \( \frac{4}{6} \)?
| \(\frac{2}{63}\) | |
| \(\frac{9}{16}\) | |
| \(\frac{3}{14}\) | |
| \(\frac{1}{14}\) |
To divide fractions, invert the second fraction and then multiply:
\( \frac{3}{8} \) ÷ \( \frac{4}{6} \) = \( \frac{3}{8} \) x \( \frac{6}{4} \)
To multiply fractions, multiply the numerators together and then multiply the denominators together:
\( \frac{3}{8} \) x \( \frac{6}{4} \) = \( \frac{3 x 6}{8 x 4} \) = \( \frac{18}{32} \) = \(\frac{9}{16}\)
Simplify \( \sqrt{125} \)
| 6\( \sqrt{10} \) | |
| 5\( \sqrt{5} \) | |
| 3\( \sqrt{5} \) | |
| 6\( \sqrt{5} \) |
To simplify a radical, factor out the perfect squares:
\( \sqrt{125} \)
\( \sqrt{25 \times 5} \)
\( \sqrt{5^2 \times 5} \)
5\( \sqrt{5} \)
What is \( \frac{6\sqrt{15}}{2\sqrt{3}} \)?
| 5 \( \sqrt{\frac{1}{3}} \) | |
| 3 \( \sqrt{5} \) | |
| 3 \( \sqrt{\frac{1}{5}} \) | |
| \(\frac{1}{5}\) \( \sqrt{3} \) |
To divide terms with radicals, divide the coefficients and radicands separately:
\( \frac{6\sqrt{15}}{2\sqrt{3}} \)
\( \frac{6}{2} \) \( \sqrt{\frac{15}{3}} \)
3 \( \sqrt{5} \)
A circular logo is enlarged to fit the lid of a jar. The new diameter is 75% larger than the original. By what percentage has the area of the logo increased?
| 37\(\frac{1}{2}\)% | |
| 30% | |
| 15% | |
| 32\(\frac{1}{2}\)% |
The area of a circle is given by the formula A = πr2 where r is the radius of the circle. The radius of a circle is its diameter divided by two so A = π(\( \frac{d}{2} \))2. If the diameter of the logo increases by 75% the radius (and, consequently, the total area) increases by \( \frac{75\text{%}}{2} \) = 37\(\frac{1}{2}\)%