Identities and Properties - Pre-Algebra

The identity property of addition states that there is a number 0, called the additive identity, that can be added to any number to yield that number as the sum. Of the four statements,

demonstrates this property.

By the additive identity property, zero added to a number yields that second number as the sum. This is shown by the statement

.

Pre-algebra brings with it many different properties for memorization, and it is easy to forget one or mix two of them up. But maybe we can jog our memory by looking closely at the name of the property. The first word in the additive identity property is "additive". This tells us very quickly that the property involves addition. That means we can already eliminate any answer choices that don't involve adding, which in our case is the choice .

With four choices left, we look at the next word in the name, "identity". The identity of something is what the thing is. In order for a spy to avoid being caught, he/she might change their idenity. They might take a different name, wear a wig, fake an accent, or dress differently. If the value of a number changes, its identity changes. In math, the only number I can add to any number without changing its value is 0. Therefore, we call 0 the additive identity because adding it preserves the identity of a number. This fact--namely that adding 0 to a number results in the same number--is what we call the Additive Identity Property.

If we look once more at our answer choices, the only one involving the addition of 0 to a number is the choice . This is the correct answer.

The additive identity property states that adding zero to any value will leave the value unchanged. The equations that will best describe this scenario is:

Zero is the additive identity.

The above two equations are the only possible correct answers.

The inverse property of addition states that for every real number, a number exists, called the additive inverse, such that the number and its inverse have sum 0. Of the statements given, only

demonstrates this property, so it is the correct choice.

The additive inverse of is . This means that when is added to the result is zero.

can be written as .

Since zero is the only number that is neither positive nor negative the answer is .

The rule for Additive Inverse Property is .

Using this rule if ,

So the additive inverse is .

The question asks us what number added with 30 will equal zero. Write the mathematical equation that represents this scenario.

Subtract 30 from both sides.

The additive inverse property is when two numbers added together equal zero. So,

displays that property.

The associative property of addition states:

When considering only addition and subtraction, the order of operations does not matter.

The associative property of addition states that to add three numbers, any two can be added first, followed by adding the sum to the third. Of the statements given, only

demonstrates this property, so it is the correct choice.

The Associative Property of Addition says that when we add more than two numbers the grouping of the addends does not change the sum.

Working left to right use the distributive property by multiplying the 4 to each term in parentheses.

Now, use the associative property to group like terms. Note that cannot be combined because they are not like terms.

Like terms can be combined with addition or subtraction.

The rule for Associative Property of Addition is

Expression given in the question is:

Hence the property is Associative of Addition.

The rule for Associative Property of Addition is

Using this rule, the expression can be written as

The associative property of addition states that you can group, or "associate," additive terms in any order and still get the same answer. Here does just that: whether you add first and then add , or add first and then , as long as you add those three terms you'll get the same answer.

The rule for Associative Property of Multiplication is

Using this rule, we can determine that for the given expression ,

is the distributive property. Multiply each term in the parenthesis by the outside term.

is the Commutative property of Multiplication. The order of two like terms being multiplied does not change the product.

is the Multiplicative Identity property. Anything multiplied by 1 does not change.

is Associative property of Multiplication. The grouping of terms does not change their product as long as all terms remain in the equation. Try the green equation without the variables to see for yourself.

The property states that changing the order of multiplying any two numbers will not change the final answer.

Looking at the answer choices:

The answer is the best choice.

The associative property of multiplication states that you can multiply numbers together in any order, and the answer will not change. Therefore,

displays the associative property of multiplication since the two sides are equal no matter which set of parentheses you solve first.