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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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