The following activity sheets will teach your students how to solve equations using various properties.

There are four basic arithmetic operations, and these include addition, subtraction, multiplication, and division. The properties of operations include commutative, associative, distributive, identity, closure. Closure: When the answers fall into the original set, we call this the closure. If you add two even numbers, the answer is still an even number, the set of even numbers is closed under addition (has to closure). When two odd numbers are added, the answer is not an odd number, the set of odd numbers is not closed under addition (no closure). Commutative: The property of numbers when the order of the sum does not make a difference, i.e., a+b=b+a. This does not work for subtraction and division but only for multiplication and addition. Associative: The change of position of parenthesis does not affect the answer. This does not work for subtraction and division but only for multiplication and addition. Identity: Adding zero (identity) to a number gives the same number as the answer. Any number added to its additive inverse equals zero. For multiplication, the identity is 1. This does not work for the division as dividing a number by zero results in infinity, but only for multiplication, addition, and subtraction. Distributive Property: The property using which we pass the number value outside of the parentheses, using multiplication, to the numbers being added or subtracted inside the parentheses. To apply the distributive property, it must be multiplication outside the parentheses and either addition or subtraction inside the parentheses.

This is a wonderful section for students to review all the properties of operations. In other sections of our site we breakdown each operational property separately, but in this section we mash them altogether. We do spend some time describing the differences that lie between the associative and commutative properties. We also brush of the identity property that basically says anything that is added to zero is itself. Your students will practice applying the associative, commutative, and distributive properties in order to solve various equations. Though all equations have been provided, students should have seen this material before.



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Math Properties Worksheets

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Properties of Operations Lesson

There are three basic number properties (or laws) that apply to arithmetic operations. This lesson will show you each of them.

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Properties Practice

To simplify the given expression, we follow the properties of operations.

Reasons for Arithmetic Worksheet

Which properties of the arithmetic let us reason that these expressions are equal?

Simplifying Practice

Use your knowledge of operations to simplify all of these expressions.

Equal Expressions Drill

Are the two expressions equal, no matter what values x, y and z might get? (Answer with yes or no).

Operator Warm Up

Finish off these problems to give your students a chance at pounding them in.

Properties of the Four Operations Lesson

Are the two expressions equal, no matter the value x has? Name the property if applicable. Give x some test values to try it out.

Lesson and Practice

What special numbers fits into the equations?

Four Operations Worksheet

Are the two expressions equal, no matter value x has? If you answered yes, name the property of the arithmetic that it illustrates.

Show the Skill

What special numbers fits into the equations?

What Applies? Warm Up

Are they equal? If they are, what property of operations applies?

Equal or Not Equal Lesson

An operation is associative if you can group numbers in any way without changing the answer. It doesn't matter how you combine them, the answer will always be the same. Addition and multiplication are both associative.

Distributive Property Lesson and Practice

Write these expressions using the distributive property of multiplication. Find the values.

Both Sides of The Story Worksheet

See if you can get the sides of this to balance out.

Distributive Practice

Write these expressions using the distributive property of multiplication. Find their values.

Four Operations Drill

Take out the parentheses using the distributive property. Solve.

Operations Warm Up

Multiply. Which property is useful here?