| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.40 |
| Score | 0% | 68% |
| 3.2 | |
| 0.9 | |
| 1 | |
| 1.0 |
1
Simplify \( \frac{24}{60} \).
| \( \frac{2}{3} \) | |
| \( \frac{10}{11} \) | |
| \( \frac{10}{13} \) | |
| \( \frac{2}{5} \) |
To simplify this fraction, first find the greatest common factor between them. The factors of 24 are [1, 2, 3, 4, 6, 8, 12, 24] 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:
\( \frac{24}{60} \) = \( \frac{\frac{24}{12}}{\frac{60}{12}} \) = \( \frac{2}{5} \)
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?
| 17\(\frac{1}{2}\)% | |
| 15% | |
| 37\(\frac{1}{2}\)% | |
| 27\(\frac{1}{2}\)% |
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\(\frac{1}{2}\)%
What is \( \frac{25\sqrt{8}}{5\sqrt{2}} \)?
| 4 \( \sqrt{5} \) | |
| 4 \( \sqrt{\frac{1}{5}} \) | |
| 5 \( \sqrt{4} \) | |
| 5 \( \sqrt{\frac{1}{4}} \) |
To divide terms with radicals, divide the coefficients and radicands separately:
\( \frac{25\sqrt{8}}{5\sqrt{2}} \)
\( \frac{25}{5} \) \( \sqrt{\frac{8}{2}} \)
5 \( \sqrt{4} \)
Which of the following is a mixed number?
\({a \over 5} \) |
|
\(1 {2 \over 5} \) |
|
\({5 \over 7} \) |
|
\({7 \over 5} \) |
A rational number (or fraction) is represented as a ratio between two integers, a and b, and has the form \({a \over b}\) where a is the numerator and b is the denominator. An improper fraction (\({5 \over 3} \)) has a numerator with a greater absolute value than the denominator and can be converted into a mixed number (\(1 {2 \over 3} \)) which has a whole number part and a fractional part.