Solve Problems with the Four Operations with Rational Numbers: CCSS.Math.Content.7.NS.A.3 - 7th Grade Math
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Solve:
Solve:
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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 
.
When given multiple operations, remember PEMDAS. Division comes before subtraction. So we divide
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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 
.
Remember PEMDAS. The parentheses comes first. When adding a negative value, the operation is subtraction. We now have
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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 
.
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
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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 
.
Remember PEMDAS. The parantheses come first. On the left we have
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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 
.
Remember PEMDAS. Let's work the parantheses first. For
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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 
We need to take care of the parentheses first because of PEMDAS. Parentheses has priority over everything. The product is
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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.
Remember PEMDAS. Parentheses comes first then multiplication.
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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 
.
Remember PEMDAS. Parenthesis comes first then multiplication.
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Solve the following:
Solve the following:
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,
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,
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Solve:
Solve:
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,
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,
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Solve:
Solve:
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,
We know the following information:
However, the
- 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,
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Solve:
Solve:
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,
We know the following information:
However, the
- 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,
Compare your answer with the correct one above
Solve:
Solve:
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,
We know the following information:
However, the
- 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,
Compare your answer with the correct one above
Solve:
Solve:
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,
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,
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Solve:
Solve:
In order to solve this problem, we need to start at 
on the number line.
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.
The orange arrow moved 
places to the right, and ended at 
; thus,
In order to solve this problem, we need to start at
Next, we have
The orange arrow moved
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Solve:
Solve:
In order to solve this problem, we need to start at 
on the number line.
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.
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 
.
In order to solve this problem, we need to start at
Next, we have
The orange arrow moved
Remember,
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Solve:
Solve:
In order to solve this problem, we need to start at 
on the number line.
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.
The orange arrow moved 
places to the right, and ended at 
; thus,
In order to solve this problem, we need to start at
Next, we have
The orange arrow moved
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Solve:
Solve:
In order to solve this problem, we need to start at 
on the number line.
Next, we have 
which means we need to move 
places to the left 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.
The orange arrow moved 
places to the left, and ended at 
; thus,
In order to solve this problem, we need to start at
Next, we have
The orange arrow moved
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Solve:
Solve:
In order to solve this problem, we need to start at 
on the number line.
Next, we have 
which means we need to move 
places to the left 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.
The orange arrow moved 
places to the left, and ended at 
; thus,
In order to solve this problem, we need to start at
Next, we have
The orange arrow moved
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