Common Core: 7th Grade Math : Apply Properties of Operations to Expand Linear Expressions with Rational Coefficients: CCSS.Math.Content.7.EE.A.1

Study concepts, example questions & explanations for Common Core: 7th Grade Math

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Example Question #1 : Apply Properties Of Operations To Expand Linear Expressions With Rational Coefficients: Ccss.Math.Content.7.Ee.A.1

If  is added to  of another number, the result is . What is the other number?

Possible Answers:

Correct answer:

Explanation:

The first step is to translate the words, "if  is added to  of another number, the result is ," into an equation. This gives us:

Subtract  from each side. 

Multiply each side by

Therefore,  is the correct answer. 

Example Question #2 : Apply Properties Of Operations To Expand Linear Expressions With Rational Coefficients: Ccss.Math.Content.7.Ee.A.1

Simplify the following expression: 

Possible Answers:

Cannot be computed

Correct answer:

Explanation:

When adding and subtracting variable, you can only combine like variables.  

That means all of the  variables are solved separately from the  variables.  

Then you just add and subtract the constants normally so  and .  

So the final answer is .

Example Question #3 : Apply Properties Of Operations To Expand Linear Expressions With Rational Coefficients: Ccss.Math.Content.7.Ee.A.1

Simplify the followng:

Possible Answers:

Correct answer:

Explanation:

When adding variables together, you must first make sure you are combining the same variable.  So, in this case

we can see that both terms contain the variable a.  Therefore, we can combine them. 

Now, when we combine them, we can think of the variables as objects.  So, we can say were are combining an apple and 4 apples together.  So,

We can simplify our problem the same way.

Example Question #81 : Algebra

Simplify:

Possible Answers:

Correct answer:

Explanation:

Example Question #2 : How To Subtract Variables

Simplify:

Possible Answers:

Correct answer:

Explanation:

Example Question #4 : Apply Properties Of Operations To Expand Linear Expressions With Rational Coefficients: Ccss.Math.Content.7.Ee.A.1

Simplify:

Possible Answers:

Correct answer:

Explanation:

This problem is just a matter of grouping together like terms.  Remember that terms like  are treated as though they were their own, different variable:

The only part that might be a little hard is:

If you are confused, think of your number line.  This is like "going back" (more negative) from 15.  Therefore, you ranswer will be:

Example Question #5 : Apply Properties Of Operations To Expand Linear Expressions With Rational Coefficients: Ccss.Math.Content.7.Ee.A.1

Simplify:

Possible Answers:

Correct answer:

Explanation:

You need to begin by distributing the minus sign through the whole group .  This gives you:

Simplifying the double negative, you get:

Now, you can move the like terms next to each other:

Finally, simplify:

Example Question #13 : How To Subtract Variables

Simplify:

Possible Answers:

Correct answer:

Explanation:

Begin by distributing the :

Multiply each factor:

Change the double negation to addition:

Combine like terms:

Example Question #6 : Apply Properties Of Operations To Expand Linear Expressions With Rational Coefficients: Ccss.Math.Content.7.Ee.A.1

Simplify:

Possible Answers:

Correct answer:

Explanation:

Begin by distributing the :

Multiply all factors:

Group together the only like factor ():

Combine like terms:

Example Question #7 : Apply Properties Of Operations To Expand Linear Expressions With Rational Coefficients: Ccss.Math.Content.7.Ee.A.1

Simplify:

Possible Answers:

Correct answer:

Explanation:

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