Common Core: 7th Grade Math : The Number System

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

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Example Questions

Example Question #6 : Solve Problems With The Four Operations With Rational Numbers: Ccss.Math.Content.7.Ns.A.3

Possible Answers:

Correct answer:

Explanation:

We need to take care of the parentheses first because of PEMDAS. Parentheses has priority over everything. The product is  is . Because there is a negative sign outside the parentheses, we need to add it to our answer which now becomes 

Example Question #1 : Solve Problems With The Four Operations With Rational Numbers: Ccss.Math.Content.7.Ns.A.3

Possible Answers:

Correct answer:

Explanation:

Remember PEMDAS. Parentheses comes first then multiplication. . We are multiplying two negatives which make a positive number, in this case . Next, we have  since there is only one negative number, the answer is negative.

Example Question #8 : Solve Problems With The Four Operations With Rational Numbers: Ccss.Math.Content.7.Ns.A.3

Possible Answers:

Correct answer:

Explanation:

Remember PEMDAS. Parenthesis comes first then multiplication. . We are multiplying two negatives which make a positive number, in this case . Next, we have just multiplication of . Since there are two negative numbers and one positive number being multiplied, the answer is positive.  and 

Example Question #9 : Solve Problems With The Four Operations With Rational Numbers: Ccss.Math.Content.7.Ns.A.3

Solve: 

Possible Answers:

Correct answer:

Explanation:

We know the following information:

In this particular case, do the negative numbers change our answer? There are a couple of rules that we need to remember when multiplying with negative numbers to help us answer this question:

  • A negative number multiplied by a positive number will always equal a negative number
  • A negative number multiplied by a negative number will always equal a positive number 

Thus,

Example Question #311 : The Number System

Solve: 

Possible Answers:

Correct answer:

Explanation:

We know the following information:

However, the  changes our answer, in this particular case. There are a couple of rules that we need to remember when multiplying with negative numbers:

  • A negative number multiplied by a positive number will always equal a negative number
  • A negative number multiplied by a negative number will always equal a positive number 

Thus,

Example Question #11 : Solve Problems With The Four Operations With Rational Numbers: Ccss.Math.Content.7.Ns.A.3

Solve: 

Possible Answers:

Correct answer:

Explanation:

We know the following information:

However, the  changes our answer, in this particular case. There are a couple of rules that we need to remember when multiplying with negative numbers:

  • A negative number divided by a positive number will always equal a negative number, and a positive number divided by a negative number will always equal a negative number.
  • A negative number divided by a negative number will always equal a positive number 

Thus,

Example Question #12 : Solve Problems With The Four Operations With Rational Numbers: Ccss.Math.Content.7.Ns.A.3

Solve: 

Possible Answers:

Correct answer:

Explanation:

We know the following information:

However, the  changes our answer, in this particular case. There are a couple of rules that we need to remember when multiplying with negative numbers:

  • A negative number divided by a positive number will always equal a negative number, and a positive number divided by a negative number will always equal a negative number.
  • A negative number divided by a negative number will always equal a positive number 

Thus,

Example Question #13 : Solve Problems With The Four Operations With Rational Numbers: Ccss.Math.Content.7.Ns.A.3

Solve: 

Possible Answers:

Correct answer:

Explanation:

We know the following information:

In this particular case, do the negative numbers change our answer? . There are a couple of rules that we need to remember when multiplying with negative numbers:

  • A negative number divided by a positive number will always equal a negative number, and a positive number divided by a negative number will always equal a negative number.
  • A negative number divided by a negative number will always equal a positive number 

Thus,

Example Question #12 : Solve Problems With The Four Operations With Rational Numbers: Ccss.Math.Content.7.Ns.A.3

Solve:

 

Possible Answers:

Correct answer:

Explanation:

In order to solve this problem, we need to start at  on the number line. 

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Next, we have  which means we need to move  places to the right on the number line. When we have an addition sign   we move to the right because that is towards the positive side of the number line. When we have a subtraction sign  we move to the left because that is towards the negative side of the number line. 

 12 5

The orange arrow moved  places to the right, and ended at ; thus,

Example Question #13 : Solve Problems With The Four Operations With Rational Numbers: Ccss.Math.Content.7.Ns.A.3

Solve:

Possible Answers:

Correct answer:

Explanation:

In order to solve this problem, we need to start at  on the number line. 

6

Next, we have  which means we need to move  places to the right on the number line. When we have an addition sign   we move to the right because that is towards the positive side of the number line. When we have a subtraction sign  we move to the left because that is towards the negative side of the number line. 

 6 6

The orange arrow moved  places to the right, and ended at ; thus,

Remember,  and  are opposite numbers. A number and its opposite always have a sum of 

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