| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.85 |
| Score | 0% | 57% |
This property states taht the order of addition or multiplication does not mater. For example, 2 + 5 and 5 + 2 are equivalent.
associative |
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distributive |
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commutative |
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PEDMAS |
The commutative property states that, when adding or multiplying numbers, the order in which they're added or multiplied does not matter. For example, 3 + 4 and 4 + 3 give the same result, as do 3 x 4 and 4 x 3.
If a rectangle is twice as long as it is wide and has a perimeter of 6 meters, what is the area of the rectangle?
| 32 m2 | |
| 2 m2 | |
| 162 m2 | |
| 98 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 6 meters so the equation becomes: 2w + 2h = 6.
Putting these two equations together and solving for width (w):
2w + 2h = 6
w + h = \( \frac{6}{2} \)
w + h = 3
w = 3 - h
From the question we know that h = 2w so substituting 2w for h gives us:
w = 3 - 2w
3w = 3
w = \( \frac{3}{3} \)
w = 1
Since h = 2w that makes h = (2 x 1) = 2 and the area = h x w = 1 x 2 = 2 m2
Solve for \( \frac{3!}{5!} \)
| 3024 | |
| 120 | |
| \( \frac{1}{72} \) | |
| \( \frac{1}{20} \) |
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:
\( \frac{3!}{5!} \)
\( \frac{3 \times 2 \times 1}{5 \times 4 \times 3 \times 2 \times 1} \)
\( \frac{1}{5 \times 4} \)
\( \frac{1}{20} \)
If a mayor is elected with 61% of the votes cast and 51% of a town's 26,000 voters cast a vote, how many votes did the mayor receive?
| 11,271 | |
| 10,343 | |
| 8,089 | |
| 11,536 |
If 51% of the town's 26,000 voters cast ballots the number of votes cast is:
(\( \frac{51}{100} \)) x 26,000 = \( \frac{1,326,000}{100} \) = 13,260
The mayor got 61% of the votes cast which is:
(\( \frac{61}{100} \)) x 13,260 = \( \frac{808,860}{100} \) = 8,089 votes.
What is \( \frac{2}{6} \) - \( \frac{4}{14} \)?
| 1 \( \frac{7}{42} \) | |
| 1 \( \frac{9}{16} \) | |
| \( \frac{3}{42} \) | |
| \(\frac{1}{21}\) |
To subtract these fractions, first find the lowest common multiple of their denominators. The first few multiples of 6 are [6, 12, 18, 24, 30, 36, 42, 48, 54, 60] and the first few multiples of 14 are [14, 28, 42, 56, 70, 84, 98]. The first few multiples they share are [42, 84] making 42 the smallest multiple 6 and 14 share.
Next, convert the fractions so each denominator equals the lowest common multiple:
\( \frac{2 x 7}{6 x 7} \) - \( \frac{4 x 3}{14 x 3} \)
\( \frac{14}{42} \) - \( \frac{12}{42} \)
Now, because the fractions share a common denominator, you can subtract them:
\( \frac{14 - 12}{42} \) = \( \frac{2}{42} \) = \(\frac{1}{21}\)