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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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commutative |
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associative |
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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.
A bread recipe calls for 3\(\frac{5}{8}\) cups of flour. If you only have \(\frac{1}{8}\) cup, how much more flour is needed?
| 2 cups | |
| 2\(\frac{1}{4}\) cups | |
| 2\(\frac{5}{8}\) cups | |
| 3\(\frac{1}{2}\) cups |
The amount of flour you need is (3\(\frac{5}{8}\) - \(\frac{1}{8}\)) cups. Rewrite the quantities so they share a common denominator and subtract:
(\( \frac{29}{8} \) - \( \frac{1}{8} \)) cups
\( \frac{28}{8} \) cups
3\(\frac{1}{2}\) cups
What is -8c4 - 6c4?
| 14c4 | |
| -14c-4 | |
| -14c4 | |
| 14c-4 |
To add or subtract terms with exponents, both the base and the exponent must be the same. In this case they are so subtract the coefficients and retain the base and exponent:
-8c4 - 6c4
(-8 - 6)c4
-14c4
If \( \left|b + 3\right| \) - 5 = -7, which of these is a possible value for b?
| 7 | |
| -5 | |
| -17 | |
| -2 |
First, solve for \( \left|b + 3\right| \):
\( \left|b + 3\right| \) - 5 = -7
\( \left|b + 3\right| \) = -7 + 5
\( \left|b + 3\right| \) = -2
The value inside the absolute value brackets can be either positive or negative so (b + 3) must equal - 2 or --2 for \( \left|b + 3\right| \) to equal -2:
| b + 3 = -2 b = -2 - 3 b = -5 | b + 3 = 2 b = 2 - 3 b = -1 |
So, b = -1 or b = -5.
What is the next number in this sequence: 1, 5, 13, 25, 41, __________ ?
| 68 | |
| 61 | |
| 70 | |
| 53 |
The equation for this sequence is:
an = an-1 + 4(n - 1)
where n is the term's order in the sequence, an is the value of the term, and an-1 is the value of the term before an. This makes the next number:
a6 = a5 + 4(6 - 1)
a6 = 41 + 4(5)
a6 = 61