The Distributive Property
Multiplication is distributive over addition and subtraction.
If a, b, and c are represented by real numbers, then a + ( b + c ) = ( a + b ) + c a ( b + c ) = ( ab) * (ac) Example: Is this statement true or false? 5 ( 3 + 7 ) = ( 5 * 3 ) + ( 5 * 7 ) Since 5 ( 3 + 7 ) 5 * 10 50 And ( 5 * 3 ) + ( 5 * 7 ) 15 + 35 50 Therefore this equation is true by the distributive property Let's look at another example:
Is this statement true or false: 5 ( 3 * 4 ) = ( 5 * 3 ) * ( 5 * 4 ) First half of the equation: 5 ( 3 * 4 ) 3 * 4 = 12 5 * 12 = 60 Second half of the equation: First half of the second half of the equation: ( 5 * 3 ) ( 5 * 4 ) 15 * 20 300 60 does not equal 300 Therefore the statement is false You cannot distribute over multiplication. You can only distribute over addition and subtraction. |
Example:
Is the following statement true or false? 5 ( 4 - 2 ) = ( 5 * 4 ) - ( 5 * 2 ) First equation: ( 4 - 2 ) 2 5 * 2 10 Second equation: ( 5 * 4 ) - ( 5 * 2 ) ( 5 * 4 ) 20 First half of the second equation ( 5 * 2 ) 10 Second half of the second equation 20 - 10 10 This statement is true by the distributive property. Classwork:State whether the statement is true or false.
Name the property that states that the statement is true. 1) 2 + 3 = 3 + 2 2) 5 + 4 = 4 + 5 3) ( 2 + 3 ) + 4 = 2 + ( 3 + 4 ) 4) ( 1 + 6 ) + 4 = 1 + ( 6 + 4 ) 5) 5 - 3 = 3 - 5 6) 4 - 7 = 7 - 4 7) ( a + b ) + c = a + ( b + c ) 8) ( r + s ) + t = r + ( s + t ) 9) a / b = b / a 10) x / y = y / x 11) ax = xa 12) pn = np 13) 2 + ( - 5 ) = ( - 5 ) + 2 14) ( - 8 ) + 5 = 5 + ( - 8 ) 15) ( 3 * 4 ) * 5 = 3 * ( 4 * 5 ) 16) ( 2 * 4 ) * 6 = 2 * ( 4 * 6 ) 17) 3 ( 4 + 5 ) = ( 3 * 4 ) + ( 3 * 5 ) 18) 4 ( 2 + 3 ) = ( 4 * 2 ) + ( 4 * 3 ) 19) 3 ( 4 * 5 ) = ( 3 * 4 ) ( 3 * 5 ) 20) 4 ( 2 * 3 ) = ( 4 * 2 ) ( 4 * 3 ) 21) - 3 + 0 = -3 22) 5 + 0 = 5 23) 4 + - 4 = 0 24) 2 + -2 = 0 25) a ( x + y ) = ax + ay 26) 5 ( 3 - 2 ) = ( 5 * 3 ) - ( 5 * 2 ) 27) 9 * 0 = 0 28) 4 * 0 = 4 29) 3 + ( 5 + 7 ) = ( 3 + 5 ) + 7 30) 2 * ( 5 * 7 ) = 2 * ( 7 * 5 ) 31) 3 * ( 5 + 7 ) = 3 * ( 7 + 5 ) 32) 2 ( 6 + 8 ) = 2 ( 8 + 6 ) Once you have completed these problems, turn to page 39 in the Beginning Algebra textbook and complete the problems for Set 2. |