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6.5 Expressions
Test Review
| Term | Definition |
|---|---|
| Base | Big Number, the number you are multiplying |
| Exponent | The small number, the number of times you are multiplying (repeated multiplication) |
| Exponential form (write with an exponent) | write using base and exponent ex. 5 x 5 x 5 x 5 = 5^4 |
| Expanded form (write using multiplication) | Write out the base exponent number of times. Ex. 3^5 = 3 x 3 x 3 x 3 x 3 |
| Standard form (solve) | Calculate the answer Ex. 2^5 = 2 x 2 x 2 x 2 x 2 = 32 |
| Order of operations | The order in which all problems should be solved P (parentheses) E (exponents) MD (multiplication OR division left to right in problem) AS (addition OR subtraction left to right in problem) |
| Power of 0 | Anything raised to the power of zero is 1. Ex. 1^0 = 1, 2^0=1, ... |
| Power of 1 | Anything raised to the power of 1 is itself. Ex. 1^1 = 1, 2^1=2, ... |
| Base of 1 | The base of 1 raised to any power is 1, because it is 1 multiplied by itself, which is always 1. Ex. 1^1=1, 1^2=1, ... |
| Distributive | a(b+c)=ab+ac 2 ( 3 + 4) = 2(3) + 2(4) multiply a sum by multiplying EACH addend separately and then add the products. |
| Associative | (a+b)+c=a+(b+c) 2 + ( 3 + 4 ) = (2 + 3 ) + 4 Grouping |
| Commutative | a+b=b+a ab=ba Order |
| Identity Property of Addition | a + 0 = a If you add zero to a number, the sum is the same as that number. |
| Identity Property of Multiplication | a x 1 = a If you multiply a number by one, the product is the same as that number. |
| Evaluate an Expression | Substitute a number for each variable in an algebraic expression and simplify (find the value) Ex. 2x if x = 3 2(3) = 6 |
| Sum | addition Ex. the sum of a number and 8 n + 8 |
| Less than, subtracted from | subtraction *order is switched* Ex. 6 less than a number n - 6 |
| Product | Multiplication Ex. The product of a number and 6 6n |
| Half (multiplication) | x 1/2 |
| Twice | x 2 |
| Double | x 2 |
| Triple | x 3 |
| Quotient | Division Ex. The quotient of a number and 10 n/10 |
| Half (division) | divided by 2 |
| Squared | to the 2nd power |
| Cubed | to the 3rd power |
| Multiplied by itself | exponent |
| Other possible addition words | more, older, together, increased, total, all together, plus, combine, in all, both |
| Other possible subtraction words | spends, younger, take away, difference, are left, remain, change, decreased by, fewer, HOW MANY more |
| Other possible division words | divided by, parts, split, shared, separated, cut up, HOW MANY times, per*, each* |
| Other possible multiplication words | times, by, of, per*, each* |
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