Integers and Their Properties

Integers and Their Properties

_{Eka Ratna Anjanuarti Latifah, S.Pd., Gr}

A. The Associative and Commutative Properties

The associative and commutative properties are laws that just can be applied to addition and multiplication.

It means, not applied for subtractions and divisions.

The associative property states that you can regroup numbers and you will get the same answer and the commutative property states that you can move numbers around and still arrive at the same answer.

Example:

The Commutative Properties
1) $3+4=4+3$  
2) $5\times7=7\times5$  

The Associative Properties
1) $(2+3)+4=2+(3+4)$  
2) $6\times(7\times3)=(6\times7)\times3$  

B. Inverse Operations

The words "SUBTRACT IS AN INVERSE OF ADD" and "DIVIDE IS AN INVERSE OF MULTIPLE" means that if you multiple and divide at the same time with same value number, it doesn't change at all.

Example:
1) $2+5-5=2$  
2) $12\times6\div6=12$  

C. Identity Properties for Additions

For additions and subtractions the identity properties is 0 (zero)
Because every number that add or subtract by 0 is remain the same value

Example:
1) $2+0=2$  
2) $-5-0=-5$  

D. Identity Properties for Multiplications

For multiplications and divisions the identity properties is 1 (one)
Because every number that multiple or divide by 1 is remain the same value

Example:
1) $3\times1=3$  
2) $(-7)\div1=-7$  

Multiple Choice

The suitable numbers to fill in the blank $\left(12+13\right)\times3=\left(...\times...\right)+\left(...\times...\right)$ is...

•  $\left(12\times13\right)+\left(12\times13\right)$ 

•  $\left(12\times3\right)+\left(13\times3\right)$ 

•  $\left(12\times3\right)+\left(12\times3\right)$  

•  $\left(13\times3\right)+\left(13\times3\right)$  

Multiple Choice

The result of $\left(11-6\right)\times12$ is...

• 60

• 72

• 126

• 132