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 Questions

Example Question #11 : Expressions & Equations

Simplify the following:

Possible Answers:

Correct answer:

Explanation:

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 

Example Question #12 : Expressions & Equations

Simplify:

Possible Answers:

Correct answer:

Explanation:

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.

Example Question #206 : Algebra

Simplify:

Possible Answers:

Correct answer:

Explanation:

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

Example Question #13 : Expressions & Equations

Which of the answer choices is equivalent to the following expression:

Possible Answers:

Correct answer:

Explanation:

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. 

Example Question #14 : Expressions & Equations

Which of the answer choices is equivalent to the following expression:

Possible Answers:

Correct answer:

Explanation:

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. 

Example Question #13 : Expressions & Equations

Which of the answer choices is equivalent to the following expression:

Possible Answers:

Correct answer:

Explanation:

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. 

Example Question #16 : Apply Properties Of Operations To Expand Linear Expressions With Rational Coefficients: Ccss.Math.Content.7.Ee.A.1

Which of the answer choices is equivalent to the following expression:

 

Possible Answers:

Correct answer:

Explanation:

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. 

Example Question #17 : Apply Properties Of Operations To Expand Linear Expressions With Rational Coefficients: Ccss.Math.Content.7.Ee.A.1

Which of the answer choices is equivalent to the following expression:

Possible Answers:

Correct answer:

Explanation:

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. 

Example Question #18 : Apply Properties Of Operations To Expand Linear Expressions With Rational Coefficients: Ccss.Math.Content.7.Ee.A.1

Which of the answer choices is equivalent to the following expression:

 

Possible Answers:

Correct answer:

Explanation:

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. 

Example Question #19 : Apply Properties Of Operations To Expand Linear Expressions With Rational Coefficients: Ccss.Math.Content.7.Ee.A.1

Which of the answer choices is equivalent to the following expression:

Possible Answers:

Correct answer:

Explanation:

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. 

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