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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.
PEDMAS |
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distributive |
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associative |
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commutative |
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.
What is 8x2 x x2?
| 9x2 | |
| 9x4 | |
| 8x4 | |
| 8x0 |
To multiply terms with exponents, the base of both exponents must be the same. In this case they are so multiply the coefficients and add the exponents:
8x2 x x2
(8 x 1)x(2 + 2)
8x4
A triathlon course includes a 300m swim, a 50.8km bike ride, and a 7.8km run. What is the total length of the race course?
| 50.5km | |
| 58.9km | |
| 63.4km | |
| 40.8km |
To add these distances, they must share the same unit so first you need to first convert the swim distance from meters (m) to kilometers (km) before adding it to the bike and run distances which are already in km. To convert 300 meters to kilometers, divide the distance by 1000 to get 0.3km then add the remaining distances:
total distance = swim + bike + run
total distance = 0.3km + 50.8km + 7.8km
total distance = 58.9km
What is (c5)2?
| 2c5 | |
| c-3 | |
| c3 | |
| c10 |
To raise a term with an exponent to another exponent, retain the base and multiply the exponents:
(c5)2What is \( \frac{4}{7} \) ÷ \( \frac{4}{5} \)?
| \(\frac{5}{7}\) | |
| \(\frac{3}{49}\) | |
| \(\frac{1}{24}\) | |
| 2\(\frac{6}{7}\) |
To divide fractions, invert the second fraction and then multiply:
\( \frac{4}{7} \) ÷ \( \frac{4}{5} \) = \( \frac{4}{7} \) x \( \frac{5}{4} \)
To multiply fractions, multiply the numerators together and then multiply the denominators together:
\( \frac{4}{7} \) x \( \frac{5}{4} \) = \( \frac{4 x 5}{7 x 4} \) = \( \frac{20}{28} \) = \(\frac{5}{7}\)