Pre-Algebra : Operations and Properties
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Example Questions
Example Question #361 : Operations
Fill in the blank using 
The term 
So, we can rewrite the orignal problem as
and we can easily see that
Example Question #362 : Operations
Compare the following using
The absolute value of a number is the distance that number is from zero on a number. Because it is a distance, the absolute value can never be negative. So,
can be written as
Therefore, it's easy to solve.
Example Question #363 : Operations
Simplify the following expression:
Simplify the following expression:
Let's begin by focusing on the inside of the absolute value signs:
However, because we are within the absolute value signs, we need to change the negative sign to a positive one.
Anytime you have something within the absolute value sign, you need to make it positive.
Our answer is 6.
Example Question #362 : Operations
Simplify the following:
None of the above
It is important to be careful of where the negative sign is when simplifying.
When simplifying you should end up with:
Example Question #363 : Operations
Solve for x in the following equation:
The absolute value is defined as the distance that number is from zero on the number line. Because it is a distance, the absolute value cannot be negative. So, in the equation
we look at the absolute value.
because -9 is 9 units from zero. Now, we can solve for x.
Example Question #366 : Operations
Compare the following using
Absolute values are defined as the distance the number is from zero on a number line. Because it is a distance, the absolute value cannot be negative. So,
because -9 is 9 units from zero on a number line. So,
can easily be solved as
Example Question #364 : Operations
The symbol | | around each real number signifies absolute value. Absolute value is the true magnitude of a real number, without looking at the positive or negative sign attached to it. To rewrite this problem when solving, remove all absolute value symbols as well as signs.
Example Question #368 : Operations
Solve the following:
The absolute value of a number is defined as the position or distance of the number from zero on the number. Because it is a distance, the value cannot be negative. So,
and
so
Example Question #365 : Operations
If 
Substitute 5 for 
Remember that the absolute value of a number is its distance from zero on a number line. Distance is always positive; therefore, you can rewrite the expression.
Subtracting a positive number from a negative number is the same as adding a negative number.
Solve.
Example Question #1 : Identities And Properties
What property can be applied to the following expression?
Commutative of Multiplication
Additive Identity
Additive Inverse
Associative of Addition
Commutative of Addition
Commutative of Addition
The rule for Commutative Property of Addition is
Expression given in the question is:
Hence the property is Commutative of Addition.
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