### All Common Core: 7th Grade Math Resources

## Example Questions

### Example Question #302 : The Number System

Solve:

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**Correct answer:**

### Example Question #303 : The Number System

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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 #304 : The Number System

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

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

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

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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 .

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

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**Correct answer:**

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

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

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**Correct answer:**

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:

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**Correct answer:**

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,