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Algebra Properties
| Property | Definition |
|---|---|
| Order of opperations | 1. Parentheses, 2. Powers from left to right, 3. Multiplication or division from left to right, 4. Addition or subtraction from left to right. |
| Square of Square Root Property | For any nonnegative numbers, the square root of n, times the square root of n, is equal to n |
| Pythagorean Theorem | In a right triangle with legs of lengths a and b and hypotinuse of length c, a^2 + b^2=c^2 |
| Area Model for Multiplication | The area A of a rectangle with length L and width W in LW |
| Commutative Property of Multiplication | For any real numbers a and b, ab=ba |
| Area Model for multiplication (discrete form) | The number of elements in a rectangular array with rows r and c columns is rc |
| Associative Property of Multiplication | For any real numbers a, b, and c, (ab)c = a(bc) |
| Multiplication Identity Property of 1 | For any real number a, a x 1 = 1 x a = a |
| Property of reciprocals | suppose a doesn't equal 0, the reciprocal or a is 1/a. That is a x 1/a = 1/a x a = 1 |
| Reciprocal of a Fraction Property | suppose a and b do not equal 0, the reciprocal of a/b is b/a |
| Multiplication Property of 0 | For any real number a, a x 0 = 0 x a = 0 |
| Multiplying Fractions Property | For all real numbers a, b, c, and d, with b and d not 0, a/b x c/d = ac/bd |
| Equal fractions Property | If b does not equal 0 and k does not equal 0, then ak/bk = a/b |
| Rate Factor Model for Multiplication | When a rate r is multiplied by another quantity x, the product in rx. So the unit of rx is the product of the units for r and x |
| Multiplication Property of -1 | For any real number a, a x -1 = -1 x a = -a |
| Rules for multiplying positive and negative numbers | If two numbers have the same sign, their product is positive, If two numbers have different signs, their product is negative |
| Properties of Multiplication of Positive and Negative Numbers | !. The product of an odd number of a negative number is negative. 2. the product of an even number of negative numbers is positive |
| Multiplication Property of Equality | For all real numbers a, b, and c, if a =b, then ca=cb |
| Multiplication Property of Inequality ( part 1) | If x < y and a is positive, then ax < ay |
| Multipliation Property of Inequality (part 2) | If x < y and a is negative, then ax > ay |
| Putting-Together Model for Addition | If a quantity x is put together with a quantity y with the same units, and there is no overlap, then the result is the quantity x + y |
| Slide Model for Addition | If a slide x is followed by a slide y, the result is the slide x + y |
| Commutative Property of Addition | For any real numbers a and b, a + b + b + a |
| Associative Property of Addition | For any real numbers a, b, and c, ( a + b) + c = a + ( b + c) |
| Additive Identity Property | For any real number a, a + 0 = 0 + a = 0 |
| Property of Opposites | For any real number a, a + -a = -a + a = 0 |
| Opposites of Opposites (op-op) Property | For any real number a, -(-a) = a |
| Addition Property of Equality | For all real numbers a, b, and c, if a = b, then a + c = b + c |
| ax+b=c property | (order of opp) ax+b=c, ax+b+-b=c+-b,a * 1/a * x = (c +-b) * 1/a = x |
| distrubutive property: adding or subtracting like terms forms | for any real numbers a, b, and c, ac+bc=(a+b)c and ac-bc = (a - b)c |
| The distrubutive property: removing parentheses | for all real numbers a, b, and c, c(a+b) =ca +cb and c(a - b) =ca - cb |
| Distrubutive property:adding fractions | for all real numbers a, b, and c, with c not equal to 0, a/c +b/c = a+b/c |
| addition property of inequality | for all real numbers a, b, and c, if a<b, then a+c<b+c |
Created by:
sally