Inverse Property of Multiplication - worksheet
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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

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Sep 07, 2012
inverse property of addition and multiplication
by: Staff


Answer:
Part I

The 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 31

The "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 =10

Because of the additive inverse, you know that
2 + the additive inverse of 2 will equal 0.
You can add the additive inverse of 2 to
both 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 =10

Because 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



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