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 #489 : Grade 7

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 #1 : Multiply And Divide Rational Numbers Using Properties Of Operations: Ccss.Math.Content.7.Ns.A.2c

Possible Answers:

Correct answer:

Explanation:

Let's work from left to right since it's only multiplication and division. Since there is only one negative number, the product of  is negative which is . Now we have . Two negative numbers in a  division problem makes the answer positive. 

Example Question #311 : Operations

Solve:  

Possible Answers:

Correct answer:

Explanation:

When solving this problem remember our orders of operation, 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.

Simplify the quantities inside the parentheses.  Then multiply and distribute the coefficient in front.

Example Question #93 : Negative Numbers

Solve:

 

Possible Answers:

Correct answer:

Explanation:

When solving this problem remember our orders of operation, 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.

Evaluate the quantities inside the parentheses first.

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

Solve:

Possible Answers:

Correct answer:

Explanation:

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. The parentheses comes first. When adding a negative value, the operation is subtraction. We now have . The answer in the parentheses is , but since there is a negative sign outside, we need to add that in so final answer becomes 

Example Question #2 : Solve Problems With The Four Operations With Rational Numbers: Ccss.Math.Content.7.Ns.A.3

Possible Answers:

Correct answer:

Explanation:

When given multiple operations, remember PEMDAS. Division comes before subtraction. So we divide  by  first to get an answer of . Now we have an expression of . To determine the answer, it's best to compare the values without doing any math. Since  is bigger than  and the  has the negative sign in front, the answer is negative. So, just subtract  with  to get . Since the answer should be negative, the final answer is 

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

Possible Answers:

Correct answer:

Explanation:

Remember PEMDAS. The parentheses comes first so let's work what's inside. When adding a negative sign, the operation becomes negative. So, we have . To determine the answer, it's best to compare the values without doing any math. Since  is bigger than  and the  has the negative sign in front, the answer is negative. So, we subtract normally to get  but the actual answer should be . Now, we hae . Two negatives make a positive so the final answer is 

Example Question #4 : Solve Problems With The Four Operations With Rational Numbers: Ccss.Math.Content.7.Ns.A.3

Possible Answers:

Correct answer:

Explanation:

Remember PEMDAS. Let's work the parantheses first. For  we have opposite signs in the product so the answer should be negative.  is . Next, on the last parantheses, . First we will do . When multiplying two negatives, we get a positive value.  is . Next, we need to divide  by .  When that positive value is divided by a negative value, the answer is negative. So  is Now, we have:

. We can now work from left to right. When adding positive with negative, the sign becomes negative. Since  is greater than  and it's negative, the expression becomes subtraction. We get . Next, with two negative signs, we get a positive value. The expression is now . We can add all the positive values and get an expression of . Since  is greater than  and  is positive, the answer is positive. We treat this as a subtraction problem because of the  and the difference is . The answer we want is positive so the answer is still 

Example Question #5 : Solve Problems With The Four Operations With Rational Numbers: Ccss.Math.Content.7.Ns.A.3

Possible Answers:

Correct answer:

Explanation:

Remember PEMDAS. The parantheses come first. On the left we have  is greater than  and it's negative. We turn that expression into a subtraction problem and get  in the first paranthesis. On the other parentheses, two negatives make a positive so now it becomes  or . Now we have . Now we can work left to right. On the left, since we are multiplying two negative values, the answer is positive. So we have  or . On the right, with opposite signs, we get a negative answer. So that becomes . Now we have . Since we are dividing opposite signs, the answer is negative. The quotient is  but we want a negative value so final answer is 

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