Inverse Property

Standard

There is an inverse property of addition and multiplication.  Lets look at the inverse property of addition first.

Definition of Additive Inverse:  When a number and its additive inverse (same number with opposite sign) are added together, the result is always 0. 

Examples:  35 + (-35) = 0                                  -44 + 44 = 0

Definition of Multiplicative Inverse:  When a number and its multiplicative inverse (reciprocal) are multiplied together, the result is always 1.

Examples:  25 * 1/25 = 25/1 * 1/25 = 25/25 or 1         

-66 *  1/-66 =  -66/1 *  1/-66  =  -66/-66  or  1

When will we use this information?  When solving equations.

Use the additive inverse property and solve for x.     x + 6 = 10

To eliminate the +6, the additive inverse property of (-6) can be used.  Add the additive inverse to each side of the equation.

                                                           x + 6 = 10

                                                                -6        -6

                                                           X + 0  =  4

                                                                    X = 4

Use the Multiplicative Inverse property and solve for x.  3x = 9

To eliminate the +3, the multiplicative inverse property of 1/3 can be used.  Multiply each side of the equation by the multiplicative inverse.

                                                     3 x = 9

                   1/3 * 3x = 1/3 * 9     =     1/3 * (3/1)x = 1/3 * 9/1 =    (3/3)x = 9/3   =    1x = 3  or   x = 3

 

 

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One response »

  1. Donna,

    This is a great way to explain to students. The examples clearly provide simple easy to understand models and you have used very kid friendly language. I could use something like this as a good reference for my students.

    Pat

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