| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.14 |
| Score | 0% | 63% |
The __________ is the smallest positive integer that is a multiple of two or more integers.
absolute value |
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least common multiple |
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greatest common factor |
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least common factor |
The least common multiple (LCM) is the smallest positive integer that is a multiple of two or more integers.
If a rectangle is twice as long as it is wide and has a perimeter of 24 meters, what is the area of the rectangle?
| 32 m2 | |
| 72 m2 | |
| 8 m2 | |
| 18 m2 |
The area of a rectangle is width (w) x height (h). In this problem we know that the rectangle is twice as long as it is wide so h = 2w. The perimeter of a rectangle is 2w + 2h and we know that the perimeter of this rectangle is 24 meters so the equation becomes: 2w + 2h = 24.
Putting these two equations together and solving for width (w):
2w + 2h = 24
w + h = \( \frac{24}{2} \)
w + h = 12
w = 12 - h
From the question we know that h = 2w so substituting 2w for h gives us:
w = 12 - 2w
3w = 12
w = \( \frac{12}{3} \)
w = 4
Since h = 2w that makes h = (2 x 4) = 8 and the area = h x w = 4 x 8 = 32 m2
Simplify \( \frac{24}{80} \).
| \( \frac{3}{10} \) | |
| \( \frac{3}{4} \) | |
| \( \frac{7}{17} \) | |
| \( \frac{6}{17} \) |
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 80 are [1, 2, 4, 5, 8, 10, 16, 20, 40, 80]. They share 4 factors [1, 2, 4, 8] making 8 their greatest common factor (GCF).
Next, divide both numerator and denominator by the GCF:
\( \frac{24}{80} \) = \( \frac{\frac{24}{8}}{\frac{80}{8}} \) = \( \frac{3}{10} \)
What is \( \frac{24\sqrt{28}}{8\sqrt{4}} \)?
| 3 \( \sqrt{7} \) | |
| \(\frac{1}{7}\) \( \sqrt{\frac{1}{3}} \) | |
| \(\frac{1}{3}\) \( \sqrt{\frac{1}{7}} \) | |
| 7 \( \sqrt{3} \) |
To divide terms with radicals, divide the coefficients and radicands separately:
\( \frac{24\sqrt{28}}{8\sqrt{4}} \)
\( \frac{24}{8} \) \( \sqrt{\frac{28}{4}} \)
3 \( \sqrt{7} \)
In a class of 25 students, 7 are taking German and 13 are taking Spanish. Of the students studying German or Spanish, 3 are taking both courses. How many students are not enrolled in either course?
| 23 | |
| 8 | |
| 24 | |
| 10 |
The number of students taking German or Spanish is 7 + 13 = 20. Of that group of 20, 3 are taking both languages so they've been counted twice (once in the German group and once in the Spanish group). Subtracting them out leaves 20 - 3 = 17 who are taking at least one language. 25 - 17 = 8 students who are not taking either language.