| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.18 |
| Score | 0% | 64% |
The __________ is the smallest positive integer that is a multiple of two or more integers.
greatest common factor |
|
least common factor |
|
least common multiple |
|
absolute value |
The least common multiple (LCM) is the smallest positive integer that is a multiple of two or more integers.
If \(\left|a\right| = 7\), which of the following best describes a?
a = 7 |
|
a = -7 |
|
a = 7 or a = -7 |
|
none of these is correct |
The absolute value is the positive magnitude of a particular number or variable and is indicated by two vertical lines: \(\left|-5\right| = 5\). In the case of a variable absolute value (\(\left|a\right| = 5\)) the value of a can be either positive or negative (a = -5 or a = 5).
Solve for \( \frac{2!}{3!} \)
| \( \frac{1}{42} \) | |
| \( \frac{1}{3} \) | |
| \( \frac{1}{8} \) | |
| 336 |
A factorial is the product of an integer and all the positive integers below it. To solve a fraction featuring factorials, expand the factorials and cancel out like numbers:
\( \frac{2!}{3!} \)
\( \frac{2 \times 1}{3 \times 2 \times 1} \)
\( \frac{1}{3} \)
\( \frac{1}{3} \)
A circular logo is enlarged to fit the lid of a jar. The new diameter is 50% larger than the original. By what percentage has the area of the logo increased?
| 27\(\frac{1}{2}\)% | |
| 37\(\frac{1}{2}\)% | |
| 20% | |
| 25% |
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 50% the radius (and, consequently, the total area) increases by \( \frac{50\text{%}}{2} \) = 25%
What is the greatest common factor of 28 and 72?
| 28 | |
| 11 | |
| 4 | |
| 26 |
The factors of 28 are [1, 2, 4, 7, 14, 28] and the factors of 72 are [1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72]. They share 3 factors [1, 2, 4] making 4 the greatest factor 28 and 72 have in common.