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32 Cards in this Set
- Front
- Back
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Commutative |
Changing the order of the term / numbers will not change the result, |
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Commutative Property of Addition |
a + b = b + a 3 + 4 = 4 + 3 = 7 |
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Commutative Property of Multiplication |
ab = ba (3)(4) = (4)(3) = 12 |
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Associative |
Changing the grouping of the term/numbers will not change the result (without changing the order) |
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Associative Property of Addition |
(a + b) + c = a + (b + c) (1 + 2) + 3 = 1 + (2 + 3) = 6 |
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Associative Property of Mutiplication |
(ab)c = a(bc) (2 x 3) x 4 = 2 x (3 x 4) = 24 |
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Identify |
Zero and One preserve identities under addition and multiplication respectively. |
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Identity Property of Addition |
a + 0 = a 4 + 0 = 4 |
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Identity Property of Multiplication |
a (1) = a -3 (1) = -3 |
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Inverse Property |
For each real number, there is a unique -a and 1/a for additive or multiplicative inverse |
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inverse Property of Addition |
a + (-a) = 0 4 + (-4) = 0 |
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Inverse Property of Multiplication |
a ( 1/a) = 1 3(1/3) = 1 (Reciprocal) |
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Distributive Property |
Multiplication distributes across addition (and subtraction) |
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Distribution |
a(b + c) = ab + ac 5(x + 3) = (5x) + (5)(3) = 5x + 15 |
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Undistributive Property |
Multiplication undistributes across addition (and subtraction) |
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Undistribution |
ab + ac = a(b + c) 3x + 15 = 3(x + 5) |
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Symmetric Property of Equality |
An equation may be written in the opposite order |
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Symmetric Property of Equality |
c = a + b is the same as a + b = c 9 = 2x + 5 is the same as 2x + 5 = 9 |
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Transitive Property of Equality |
Two quantities that are equal to the same thing are equal to each other |
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Transitive Property of Equality |
If a = b and c = b then a = c (8)(2) = 16 and (4)(4) = 16 then (8)(2) = (4)(4) |
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Addition Property of Equality |
The same number/term can be added to both sides of an equation |
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Addition Property of Equality |
a + b = c + b 3x - 2 + 2 = 4 + 2 |
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Subtraction Property of Equality |
The same number/term can be added to both sides of an equation |
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Subtraction Property of Equality |
a - b = c - b 2x + 3 - 3 = 7 - 3 |
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Multiplication Property of Equality |
The same number/term can be multiplies to both sides of an equation |
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Multiplication Property of Equality |
ab = cb (2) (x/2) - (6)(2) |
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Division Property of Equality |
Both sides of an equation can be divided by the same number |
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Division Property of Equality |
a/b = c/b 4x/4 = 8/4 |
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Addition/Subtraction Property of Inequality |
the same number can be added/subtracted to both sides of an equation |
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Addition/Subtraction Property of Inequality |
a + b < c + b or a - b < c - b 5 + 1 < 7 + 1 or 5 - 1 < 7 - 1 |
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Multiplication/Division Property of Inequality (*inequality sign flips direction if the number is negative) |
The same number can be mutiplied/divided to both sides of an equation |
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Multiplication/Division Property of Inequality(*inequality sign flips direction if the number is negative) |
ab > cb or a/b > c/b (4)(2) > (6)(2) or 4/2 > 6/2 |
