PROPERTIES OF REAL NUMBERS

COMMUTATIVE PROPERTY OF ADDITION What it means We can add numbers in any order Numeric Example Algebraic Example = a + b =b + a

COMMUTATIVE PROPERTY OF MULTIPLICATION What it is We can multiply numbers in any order Numeric Example Algebraic Example 6 x 5 5 x 6 = a x b = b x a ab = ba

ASSOCIATIVE PROPERTY OF ADDITION What it is When adding, we can group numbers in any way and still get the same answer Numeric Example Algebraic Example 4 + (5 + 6) (4 + 5) + 6 = (a + b) + c = a + (b + c)

ASSOCIATIVE PROPERTY OF MULTIPLICATION What it is When multiplying, we can group numbers in any order and still get the same answer Numeric Example Algebraic Example 4 x (5 x 6)(4 x 5) x 6 = (a x b) x c =a x (b x c) (ab)c = a(bc)

IDENTITY PROPERTY OF ADDITION What it is Zero added to any number is the number itself Numeric Example Algebraic Example = a + 0 = a

IDENTITY PROPERTY OF MULTIPLICATION What it is Any number multiplied by 1 is the number itself Numeric Example Algebraic Example 44 x 1 = a x 1 = a

INVERSE PROPERTY OF MULTIPLICATION What it is Any number multiplied by its multiplicative inverse is1 Numeric Example Algebraic Example 1 4 x a x 1 = a1a = (a) 1a1a = 1

DISTRIBUTIVE PROPERTY What it is Numeric Example Algebraic Example (4 x 5) + (4 x 6) 4 x (5 + 6) = a x (b + c) = (a x b) + (a x c) a(b + c) = ab + ac

DISTRIBUTIVE PROPERTY 4(a + 5) =4a (2a - 3) = 6a - 9 2(x + 3) =2x + 6 4( 6y - 4) =24y- 16

DISTRIBUTIVE PROPERTY 5(x + 7y -2 ) = 5x + 35y 6(3a – 4b +1) = 18a - 24b 3( 2u – 5v - 4) = 6u - 15v