# Inverse Property of Multiplication - worksheet

by Robert
(Getzville,NY)

inverse property of addition and multiplication

The additive inverse of any number is the same number with the opposite sign.

The multiplicative inverse of any number is the reciprocal of that number.

Worksheet problems.

i don't understand it at all

### Comments for Inverse Property of Multiplication - worksheet

 Sep 07, 2012 inverse property of addition and multiplication by: Staff Answer:Part IThe numbers on your worksheet are blurry and almost impossible for us to read accurately.However, I have included some information below which should help you answer the questions.There are two important concepts related to the mathematics of an “inverse”: 1) the Inverse Operation, and 2) the inverse Property.A third concept (the most important concept) is really a question: Why learn about the Inverse Operation and Inverse Property? 1) the Inverse Operation     • An Inverse Operation is a mathematical procedure in reverse. It is a procedure that reverses the effect of another mathematical procedure.       Addition and Subtraction        The Inverse Operation of addition is subtraction. The Inverse Operation of subtraction is addition.       For example:` Addition Subtraction (Inverse Operation) 22 31 + 9 - 9 ----- ----- 31 22 The "Inverse Operation" of subtraction reversed the addition, and returned the number 22. 22 is the number you started with. This means that the original operation of addition (22 + 9 = 31) was completed correctly. If it had not been completed correctly, the inverse operation would not have returned the number 22 (the original starting point). Subtraction Addition (Inverse Operation) 31 22 - 9 + 9 ----- ----- 22 31The "Inverse Operation" of addition reversed the subtraction, and returned the number 31. 31 is the number you started with. This means that the original operation of subtraction (31 - 9 = 22) was completed correctly. If it had not been completed correctly, the inverse operation would not have returned the number 31 (the original starting point).`-----------------------------

 Sep 07, 2012 inverse property of addition and multiplication by: Staff -----------------------------Part II       Multiplication and Division        The Inverse Operation of multiplication is division. The Inverse Operation of division is multiplication.        For example:` Multiply Divide (Inverse Operation) 6 12 x 2 ÷ 2 ----- ----- 12 = 6 The "Inverse Operation" of division reversed the multiplication, and returned the number 6. 6 is the number you started with. This means that the original operation of multiplication (6 x 2 = 12) was completed correctly. If it had not been completed correctly, the inverse operation would not have returned the number 6 (the original starting point). Divide Multiply (Inverse Operation) 12 6 ÷ 2 x 2 ----- ----- = 6 12 The "Inverse Operation" of multiplication reversed the division, and returned the number 12. 12 is the number you started with. This means that the original operation of division (12 ÷ 2 = 6) was completed correctly. If it had not been completed correctly, the inverse operation would not have returned the number 22 (the original starting point).`       Square Root and Squaring       The Inverse Operation of a square root is a square (an exponent of 2). The Inverse Operation of a square is a square root.        For example:` Square Square Root (Inverse Operation) √25 5² ----- ----- = 5 = 25 Square Square Root (Inverse Operation) 5² √25 ----- ----- = 25 = 5 `-----------------------------

 Sep 07, 2012 inverse property of addition and multiplication by: Staff -----------------------------Part III       Logarithm and Anti-Log        The Inverse Operation of a logarithm is the anti-log. The Inverse Operation of an anti-log is a logarithm.        For example:` logarithm Anti-Log (Inverse Operation) Log₁₀(100) Anti-Log(2) ----- ----- = 2 = 100 Anti-Log logarithm (Inverse Operation)Anti-Log(2) Log₁₀(100) ----- ----- = 100 = 2 `And so on . . . This idea can also be extended to functions.       Function and Inverse Function       The Inverse of a function is called the Inverse Function. An inverse function reverses what a function has done.       For example:` function inverse function (Inverse Operation) f(x)=x+3 f⁻¹(x)=x-3 e.g.: when x = 5 when x = 8 f(x)=5+3 f⁻¹(x)=8-3 =8 =5 The "Inverse Operation" of f⁻¹(x)=x-3 reversed the operation of f(x)=x+3. x = 5 when used in the function f(x)=x+3. x = 8 when used in the function f⁻¹(x)=x-3. The inverse function f⁻¹returned the number of 5. 5 is the number you started with. `2) the Inverse Property     • An Inverse Property is another number . It is NOT A PROCEDURE (such as addition, or subtraction).       additive inverse       The additive inverse of a number is the same number with the opposite sign. When a number and its additive inverse are added to one another, the result is always 0 (zero). 0 (zero) is called the identity element for addition.       For example:` 25 number+ (-25) additive inverse ---- 0 identity element for addition (-25) number+ (+25) additive inverse ---- 0 identity element for addition x variable+ (-x) additive inverse ---- 0 identity element for addition (-x) variable+ (+x) additive inverse ---- 0 identity element for addition`-----------------------------

 Sep 07, 2012 inverse property of addition and multiplication by: Staff -----------------------------Part IV       multiplicative inverse       The multiplicative inverse of a number is the reciprocal of same number. When a number and its multiplicative inverse are multiplied together, the result is always 1 (one). 1 (one) is called the identity element of multiplication.       For example:` 25 number 1/25 multiplicative inverse 25 * (1/25) = 25/25 =1 (identity element of multiplication) x variable 1/x multiplicative inverse (x ≠ 0) x * (1/x) = x/x =1 (identity element of multiplication)`3) Why learn about the Inverse Operation and Inverse Property?     • Inverse Operations and Inverse Properties allow us to simplify equations.        For example:` Solve for x in the equation: x + 2 =10Because of the additive inverse, you know that 2 + the additive inverse of 2 will equal 0. You can add the additive inverse of 2 toboth sides of the equation to determine the value of x. x + 2 = 10 x + 2 + (additive inverse of 2) = 10 + (additive inverse of 2) x + 0 = 10 + (additive inverse of 2) x = 10 + (additive inverse of 2) or x + 2 = 10 x + 2 + (-2) = 10 + (-2) x + 0 = 8 x = 8 Solve for x in the equation: 2x =10Because of the multiplicative inverse, you know that 2 multiplied by its multiplicative inverse will equal 1. You can multiply both sides of the equation by the multiplicative inverse of 2 to determine the value of x. 2x * (multiplicative inverse of 2) = 10 * (multiplicative inverse of 2) 1x = 10 * (multiplicative inverse of 2) x = 10 * (multiplicative inverse of 2)or 2x * (1/2) = 10 * (1/2) x * (2/2) = (10/2) x * (1) = (10/2) x = 5`Thanks for writing. Staff www.solving-math-problems.com