Identify The Properties Of Addition And Multiplication Worksheets [PDF]: Algebra 1 Math

How Will This Worksheet on "Identify the Properties of Addition and Multiplication" Benefit Your Students' Learning?

Commutative Property:
Addition: You can add numbers in any order.
Multiplication: You can multiply numbers in any order.

Associative Property:
Addition: You can group numbers in any way when adding.
Multiplication: You can group numbers in any way when multiplying.

Identity Property:
Addition: Adding zero to a number gives you the same number.
Multiplication: Multiplying a number by one gives you the same number.

Inverse Property:
Addition: Every number has an opposite (negative) that adds to zero.
Multiplication: Every non-zero number has a reciprocal (fraction) that multiplies to one.

Distributive Property:
Multiplication distributes over addition
Recognizing and understanding these properties helps in solving math problems efficiently

Solved Example

Q. Which property of multiplication is shown?

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k \cdot (m + n) = k \cdot m + k \cdot n

Solution:

Identify Property of Multiplication: Identify the property of multiplication demonstrated by the equation $k \cdot (m + n) = k \cdot m + k \cdot n$ . $\newline$ In this equation, a single number $k$ is being multiplied by the sum of two numbers $m$ and $n$ . The result is the same as when $k$ is multiplied by each of $m$ and $n$ separately, and then those products are added together. This is a classic example of the distributive property of multiplication over addition.
Match with Correct Choice: Match the property identified in Step $1$ with the correct choice from the given options. $\newline$ The distributive property allows us to multiply a number by a sum by distributing the multiplication over each addend and then adding the results. This matches choice $(B)$ distributive from the given options.