Common Core: 6th Grade Math : Apply the Properties of Operations to Generate Equivalent Expressions: CCSS.Math.Content.6.EE.A.3

Study concepts, example questions & explanations for Common Core: 6th Grade Math

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Example Questions

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Example Question #1 : Apply The Properties Of Operations To Generate Equivalent Expressions: Ccss.Math.Content.6.Ee.A.3

Expand:

Possible Answers:

Correct answer:

Explanation:

Distribute the  by multiplying it by each term inside the parentheses. 

 

and

Therefore, 5(2 + y) = 10 + 5y.

 

Example Question #2 : Apply The Properties Of Operations To Generate Equivalent Expressions: Ccss.Math.Content.6.Ee.A.3

Simplify the expression:

Possible Answers:

Correct answer:

Explanation:

To solve this question you must use the distrubitive property by multiplying x by -2 and the 2 by -2, making sure to distribute the negative as well. This gives you:

Example Question #3 : Apply The Properties Of Operations To Generate Equivalent Expressions: Ccss.Math.Content.6.Ee.A.3

Which answer correctly simplifies this expression?

Possible Answers:

Correct answer:

Explanation:

To simplify this expression, use the distributive property. This means that we have to multiply the 2 times both terms inside the parentheses. , and . So, our answer is .

Example Question #4 : Apply The Properties Of Operations To Generate Equivalent Expressions: Ccss.Math.Content.6.Ee.A.3

Simplify the following expression:

Possible Answers:

Correct answer:

Explanation:

Apply the distributive property of multiplication to remove the parenthesis from the given expression. Multiply the term outside of the parenthesis to each of the terms inside the parenthesis.

Example Question #5 : Apply The Properties Of Operations To Generate Equivalent Expressions: Ccss.Math.Content.6.Ee.A.3

Simplify the following:

 

Possible Answers:

Correct answer:

Explanation:

This is applying to distrubtive property and then combining like terms.

First you distrubute the negative to the two terms in the first parentheses, so:

Then do the same for the four:

Finally, combine like terms to get:

 

Example Question #6 : Apply The Properties Of Operations To Generate Equivalent Expressions: Ccss.Math.Content.6.Ee.A.3

Name the property used to solve the problem.

Possible Answers:

Distributive Property

Identity Property

Multiplication Property

Associative Property of Multiplication

Communitive Property of Multiplication

Correct answer:

Distributive Property

Explanation:

Multiplying each term on the outside of the parenthesis by each term on the inside refers to the distributive property.

Example Question #7 : Apply The Properties Of Operations To Generate Equivalent Expressions: Ccss.Math.Content.6.Ee.A.3

Simplify using distributive property.

Possible Answers:

Correct answer:

Explanation:

Distributive property is used to multiply a single term by two or more terms inside a set of parenthesis. Multiply the outside term (5) by 7 first.

Then multiply the outside term (5) by 9.

Combine the two remaining terms by keeping the sign that was originally inside the parenthesis.

Example Question #8 : Apply The Properties Of Operations To Generate Equivalent Expressions: Ccss.Math.Content.6.Ee.A.3

Which of the following is equivalent to ?

Possible Answers:

Correct answer:

Explanation:

We need to distribute -3 by multiplying both terms inside the parentheses by -3.:

 .

Now we can multiply and simplify. Remember that multiplying two negative numbers results in a positive number:

Example Question #9 : Apply The Properties Of Operations To Generate Equivalent Expressions: Ccss.Math.Content.6.Ee.A.3

Distribute:

Possible Answers:

Correct answer:

Explanation:

Remember that a negative multiplied by a negative is positive, and a negative multiplied by a positive is negative.

Distribute the  through the parentheses by multiplying it by each of the two terms: 

 

Example Question #10 : Apply The Properties Of Operations To Generate Equivalent Expressions: Ccss.Math.Content.6.Ee.A.3

Solve the equation using the distributive property.

Possible Answers:

Correct answer:

Explanation:

First, we must use the distributive property on both sides of the equation.

The distributive property states:

Therefore:

Now, we can solve the expression like a two-step equation with variables on both sides. Do not forget the properties of equality and perform the same operations on both sides.

Subtract  from both sides.

   

            

Simplify.

Now, the problem is a one-step equation.

Add  to both sides.

       

Solve.

Check the answer by substituting it back into the original equation. Both sides should equal to each other.

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