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

When solving this problem we need to remember our order of operations, or PEMDAS.

PEMDAS stands for parentheses, exponents, multiplication/division, and addition/subtraction. When you have a problem with several different operations, you need to solve the problem in this order and you work from left to right for multiplication/division and addition/subtraction.

Parentheses: We are not able to add a variable to a number, so we move to the next step.

Multiplication: We can distribute (or multiply) the .

Addition/Subtraction: Remember, we can't add a variable to a number, so the is left alone.

When solving this problem we need to remember our order of operations, or PEMDAS.

PEMDAS stands for parentheses, exponents, multiplication/division, and addition/subtraction. When you have a problem with several different operations, you need to solve the problem in this order and you work from left to right for multiplication/division and addition/subtraction.

Parentheses: We are not able to add a variable to a number, so we move to the next step.

Multiplication: We can distribute (or multiply) the .

Addition/Subtraction: Remember, we can't add a variable to a number, so the is left alone.

Now we have

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:

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:

Begin by distributing the :

Multiply each factor:

Change the double negation to addition:

Combine like terms:

Begin by distributing the :

Multiply all factors:

Group together the only like factor ():

Combine like terms:

When solving this problem we need to remember our order of operations, or PEMDAS.

PEMDAS stands for parentheses, exponents, multiplication/division, and addition/subtraction. When you have a problem with several different operations, you need to solve the problem in this order and you work from left to right for multiplication/division and addition/subtraction.

Parentheses: We are not able to add a variable to a number, so we move on to the next step

Multiplication: We can distribute the negative sign to the and

Remember, a negative times a negative will equal a positive, so we have a

Finally we can combine like terms

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.

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 .

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.

In order to answer this question, we need to write the given expression is standard form.

First, we will need to use the distributive property, which tells us to multiply each component inside the parenthesis by the value outside the parenthesis. In this case we will multiply by the and the by the following fraction:

For the variable ,

For the number ,

Next, we put our products together:

This expression is considered to be simplified because we are not able to perform any other operations on its constituent components.

In other words, we can't add the to because the rules of operations tell us that these are unlike terms due to the presence of the variable, , in the enumerator and we cannot add unlike terms.

In order to answer this question, we need to write the given expression is standard form.

First, we will need to use the distributive property, which tells us to multiply each component inside the parenthesis by the value outside the parenthesis. In this case we will multiply by the and the by the following fraction:

For the variable ,

For the number ,

Next, we put our products together:

This expression is considered to be simplified because we are not able to perform any other operations on its constituent components.

In other words, we can't add the to because the rules of operations tell us that these are unlike terms due to the presence of the variable, , in the enumerator and we cannot add unlike terms.

In order to answer this question, we need to write the given expression is standard form.

First, we will need to use the distributive property, which tells us to multiply each component inside the parenthesis by the value outside the parenthesis. In this case we will multiply by the and the by the following fraction:

For the variable ,

For the number ,

Next, we put our products together:

This expression is considered to be simplified because we are not able to perform any other operations on its constituent components.

In other words, we can't add the to because the rules of operations tell us that these are unlike terms due to the presence of the variable, , in the enumerator and we cannot add unlike terms.

In order to answer this question, we need to write the given expression is standard form.

First, we will need to use the distributive property, which tells us to multiply each component inside the parenthesis by the value outside the parenthesis. In this case we will multiply by the and the by the following fraction:

For the variable ,

For the number ,

Next, we put our products together:

This expression is considered to be simplified because we are not able to perform any other operations on its constituent components.

In other words, we can't add the to because the rules of operations tell us that these are unlike terms due to the presence of the variable, , in the enumerator and we cannot add unlike terms.

In order to answer this question, we need to write the given expression is standard form.

First, we will need to use the distributive property, which tells us to multiply each component inside the parenthesis by the value outside the parenthesis. In this case we will multiply by the and the by the following fraction:

For the variable ,

For the number ,

Next, we put our products together:

This expression is considered to be simplified because we are not able to perform any other operations on its constituent components.

In other words, we can't add the to because the rules of operations tell us that these are unlike terms due to the presence of the variable, , in the enumerator and we cannot add unlike terms.

In order to answer this question, we need to write the given expression is standard form.

First, we will need to use the distributive property, which tells us to multiply each component inside the parenthesis by the value outside the parenthesis. In this case we will multiply by the and the by the following fraction:

For the variable ,

For the number ,

Next, we put our products together:

This expression is considered to be simplified because we are not able to perform any other operations on its constituent components.

In other words, we can't add the to because the rules of operations tell us that these are unlike terms due to the presence of the variable, , in the enumerator and we cannot add unlike terms.

In order to answer this question, we need to write the given expression is standard form.

First, we will need to use the distributive property, which tells us to multiply each component inside the parenthesis by the value outside the parenthesis. In this case we will multiply by the and the by the following fraction:

For the variable ,

For the number ,

Next, we put our products together:

This expression is considered to be simplified because we are not able to perform any other operations on its constituent components.

In other words, we can't add the to because the rules of operations tell us that these are unlike terms due to the presence of the variable, , in the enumerator and we cannot add unlike terms.