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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.
commutative |
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associative |
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distributive |
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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.
What is \( \frac{-5c^8}{7c^2} \)?
| -1\(\frac{2}{5}\)c10 | |
| -1\(\frac{2}{5}\)c-6 | |
| -\(\frac{5}{7}\)c10 | |
| -\(\frac{5}{7}\)c6 |
To divide terms with exponents, the base of both exponents must be the same. In this case they are so divide the coefficients and subtract the exponents:
\( \frac{-5c^8}{7c^2} \)
\( \frac{-5}{7} \) c(8 - 2)
-\(\frac{5}{7}\)c6
What is (y5)2?
| 2y5 | |
| y-3 | |
| y3 | |
| y10 |
To raise a term with an exponent to another exponent, retain the base and multiply the exponents:
(y5)2A bread recipe calls for 3\(\frac{1}{2}\) cups of flour. If you only have \(\frac{7}{8}\) cup, how much more flour is needed?
| 1\(\frac{3}{4}\) cups | |
| 2\(\frac{5}{8}\) cups | |
| 1\(\frac{1}{4}\) cups | |
| 2\(\frac{1}{8}\) cups |
The amount of flour you need is (3\(\frac{1}{2}\) - \(\frac{7}{8}\)) cups. Rewrite the quantities so they share a common denominator and subtract:
(\( \frac{28}{8} \) - \( \frac{7}{8} \)) cups
\( \frac{21}{8} \) cups
2\(\frac{5}{8}\) cups
Simplify \( \frac{20}{44} \).
| \( \frac{5}{13} \) | |
| \( \frac{1}{3} \) | |
| \( \frac{9}{17} \) | |
| \( \frac{5}{11} \) |
To simplify this fraction, first find the greatest common factor between them. The factors of 20 are [1, 2, 4, 5, 10, 20] and the factors of 44 are [1, 2, 4, 11, 22, 44]. They share 3 factors [1, 2, 4] making 4 their greatest common factor (GCF).
Next, divide both numerator and denominator by the GCF:
\( \frac{20}{44} \) = \( \frac{\frac{20}{4}}{\frac{44}{4}} \) = \( \frac{5}{11} \)