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This property states taht the order of addition or multiplication does not mater. For example, 2 + 5 and 5 + 2 are equivalent.
distributive |
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PEDMAS |
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commutative |
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associative |
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 car travels 250 miles in 5 hours, what is the average speed?
| 75 mph | |
| 45 mph | |
| 50 mph | |
| 40 mph |
Average speed in miles per hour is the number of miles traveled divided by the number of hours:
speed = \( \frac{\text{distance}}{\text{time}} \)Which of these numbers is a factor of 20?
| 12 | |
| 2 | |
| 5 | |
| 13 |
The factors of a number are all positive integers that divide evenly into the number. The factors of 20 are 1, 2, 4, 5, 10, 20.
What is 4\( \sqrt{5} \) x 6\( \sqrt{5} \)?
| 10\( \sqrt{25} \) | |
| 120 | |
| 24\( \sqrt{10} \) | |
| 10\( \sqrt{5} \) |
To multiply terms with radicals, multiply the coefficients and radicands separately:
4\( \sqrt{5} \) x 6\( \sqrt{5} \)
(4 x 6)\( \sqrt{5 \times 5} \)
24\( \sqrt{25} \)
Now we need to simplify the radical:
24\( \sqrt{25} \)
24\( \sqrt{5^2} \)
(24)(5)
120
Simplify \( \sqrt{20} \)
| 2\( \sqrt{5} \) | |
| 5\( \sqrt{5} \) | |
| 5\( \sqrt{10} \) | |
| 9\( \sqrt{5} \) |
To simplify a radical, factor out the perfect squares:
\( \sqrt{20} \)
\( \sqrt{4 \times 5} \)
\( \sqrt{2^2 \times 5} \)
2\( \sqrt{5} \)