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

## Example Questions

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### Example Question #33 : How To Add Variables

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

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

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

Simplify the following expression:

Cannot be computed

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

Simplify the followng:

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.

Simplify:

Explanation:

Simplify:

Explanation:

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

Simplify:

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

Simplify:

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

Simplify:

Explanation:

Begin by distributing the :

Multiply each factor:

Change the double negation to addition:

Combine like terms:

### Example Question #8 : Apply Properties Of Operations To Expand Linear Expressions With Rational Coefficients: Ccss.Math.Content.7.Ee.A.1

Simplify:

Explanation:

Begin by distributing the :

Multiply all factors:

Group together the only like factor ():

Combine like terms:

Simplify: