e - pre-algebra vol1 worksheet 5 subtracting integers find the difference of the following positive...
Post on 07-Apr-2018
224 Views
Preview:
TRANSCRIPT
© 2010 Math TutorDVD.com The Pre-Algebra Tutor: Vol 1 Section 5 – Subtracting Integers
Page 1
Supplemental Worksheet Problems To Accompany:
The Pre-Algebra Tutor: Volume 1 Section 5 – Subtracting Integers
Please watch Section 5 of this DVD before working these problems.
The DVD is located at:
http://www.mathtutordvd.com/products/item66.cfm
© 2010 Math TutorDVD.com The Pre-Algebra Tutor: Vol 1 Section 5 – Subtracting Integers
Page 2
Part 1: Subtracting Positive Integers
1) Find the difference of the following positive integers.
2) Find the difference of the following positive integers.
3) Find the difference of the following positive integers.
4) Find the difference of the following positive integers.
5) Find the difference of the following positive integers.
6) Find the difference of the following positive integers.
© 2010 Math TutorDVD.com The Pre-Algebra Tutor: Vol 1 Section 5 – Subtracting Integers
Page 3
Part 2: Subtracting Positive Integers from Negative Integers
7) Find the difference of the following integers.
8) Find the difference of the following integers.
9) Find the difference of the following integers.
10) Find the difference of the following integers.
11) Find the difference of the following integers.
12) Find the difference of the following integers.
© 2010 Math TutorDVD.com The Pre-Algebra Tutor: Vol 1 Section 5 – Subtracting Integers
Page 4
Part 3: Subtracting Negative Integers from Positive Integers
13) Find the difference of the following integers.
14) Find the difference of the following integers.
15) Find the difference of the following integers.
16) Find the difference of the following integers.
17) Find the difference of the following integers.
18) Find the difference of the following integers.
© 2010 Math TutorDVD.com The Pre-Algebra Tutor: Vol 1 Section 5 – Subtracting Integers
Page 5
Part 4: Subtracting Negative Integers from Negative Integers
19) Find the difference of the following negative integers.
20) Find the difference of the following negative integers.
21) Find the difference of the following negative integers.
22) Find the difference of the following negative integers.
23) Find the difference of the following negative integers.
24) Find the difference of the following negative integers.
© 2010 Math TutorDVD.com The Pre-Algebra Tutor: Vol 1 Section 5 – Subtracting Integers
Page 6
Part 5: Evaluate and solve for the following expressions
28)
29)
30)
31) 32)
33)
34)
35)
© 2010 Math TutorDVD.com The Pre-Algebra Tutor: Vol 1 Section 5 – Subtracting Integers
Page 7
Question
Answer
1) Find the difference of the following positive integers.
Begin
(bigger #) - (smaller #) = positive
Final result:
First we notice that we are subtracting a smaller number from a bigger number, which tells us we will end up with a positive answer. What we have is bigger in quantity than what will be taken away, which means we will still have some left over. We then subtract 6 from 12 as we are used to doing in regular subtraction. If we also picture a number line and start at 12, we can move 6 units to the left since we are taking away something and we see we end up at 6.
Ans: 6
© 2010 Math TutorDVD.com The Pre-Algebra Tutor: Vol 1 Section 5 – Subtracting Integers
Page 8
2) Find the difference of the following positive integers.
Begin
(bigger #) - (smaller #) = positive
Final result:
First we notice that we are subtracting a smaller number from a bigger number, which tells us we will end up with a positive answer. What we have is bigger in quantity than what will be taken away, which means we will still have some left over. We then subtract 5 from 25 as we are used to doing in regular subtraction. If we also picture a number line and start at 25, we can move 5 units to the left since we are taking away something and we see we end up at 20.
Ans: 20
© 2010 Math TutorDVD.com The Pre-Algebra Tutor: Vol 1 Section 5 – Subtracting Integers
Page 9
3) Find the difference of the following positive integers.
Begin
(smaller #) - (bigger #) = negative
Final result:
First we notice we are subtracting a bigger number from a smaller number. This means we will end up with a negative number or owing some value since we don’t have enough to continue taking more of what we have away. Next we simply subtract the numbers as a regular subtraction (smaller number from bigger number) and put the negative sign in front of the answer.
Final result:
Another way of solving for this is we can rewrite the expression to something we are familiar to and solve that way. Recall that we will take the sign of the larger absolute value of the two integers which in this case is negative (-32). We then simply subtract the two numbers in a way we are used to doing and place the negative sign in front.
Ans: -10
© 2010 Math TutorDVD.com The Pre-Algebra Tutor: Vol 1 Section 5 – Subtracting Integers
Page 10
4) Find the difference of the following positive integers.
Begin
(smaller #) - (bigger #) = negative
Final result:
First we notice we are subtracting a bigger number from a smaller number. This means we will end up with a negative number or owing some value since we don’t have enough to continue taking more of what we have away. Next we simply subtract the numbers as a regular subtraction (smaller number from bigger number) and put the negative sign in front of the answer.
Final result:
Another way of solving for this is we can rewrite the expression to something we are familiar to and solve that way. Recall that we will take the sign of the larger absolute value of the two integers which in this case is negative (-14). We then simply subtract the two numbers in a way we are used to doing and place the negative sign in front.
Ans: -7
© 2010 Math TutorDVD.com The Pre-Algebra Tutor: Vol 1 Section 5 – Subtracting Integers
Page 11
5) Find the difference of the following positive integers.
Begin
(bigger #) - (smaller #) = positive
Final result:
First we notice that we are subtracting a smaller number from a bigger number, which tells us we will end up with a positive answer. What we have is bigger in quantity than what will be taken away, which means we will still have some left over. We then subtract 8 from 16 as we are used to doing in regular subtraction. If we also picture a number line and start at 16, we can move 8 units to the left since we are taking away something and we see we end up at 8.
Ans: 8
© 2010 Math TutorDVD.com The Pre-Algebra Tutor: Vol 1 Section 5 – Subtracting Integers
Page 12
6) Find the difference of the following positive integers.
Begin
(smaller #) - (bigger #) = negative
Final result:
First we notice we are subtracting a bigger number from a smaller number. This means we will end up with a negative number or owing some value since we don’t have enough to continue taking more of what we have away. Next we simply subtract the numbers as a regular subtraction (smaller number from bigger number) and put the negative sign in front of the answer.
Final result:
Another way of solving for this is we can rewrite the expression to something we are familiar to and solve that way. Recall that we will take the sign of the larger absolute value of the two integers which in this case is negative (-21). We then simply subtract the two numbers in a way we are used to doing and place the negative sign in front.
Ans: -11
© 2010 Math TutorDVD.com The Pre-Algebra Tutor: Vol 1 Section 5 – Subtracting Integers
Page 13
7) Find the difference of the following integers.
Begin
(negative #) - (positive #) = negative
Final result:
First thing we notice is we are subtracting from a negative number, which means we are going to increase the number of things we owe by the number we are subtracting with. If we visualize a number line and start at -14, then go 9 places to the left since we are subtracting, we notice we land on -23. So we notice the result is simply the sum of the two numbers with a negative sign in front. This is because we are taking away from something that is already negative. I owed 14 already, now I am going to owe 9 more, which means in total, I owe 23, hence the -23 of something we owe.
Final result:
Another way of looking at this problem is to use what we learned in adding integers. We can rewrite the expression into an addition. This is the exact same thing; we are adding the total number of things we owe. So we simply add the two values and place a negative sign in front to get the total of things we owe.
Ans: -23
© 2010 Math TutorDVD.com The Pre-Algebra Tutor: Vol 1 Section 5 – Subtracting Integers
Page 14
8) Find the difference of the following integers.
Begin
(negative #) - (positive #) = negative
Final result:
First thing we notice is we are subtracting from a negative number, which means we are going to increase the number of things we owe by the number we are subtracting with. If we visualize a number line and start at -2, then go 10 places to the left since we are subtracting, we notice we land on -12. So we notice the result is simply the sum of the two numbers with a negative sign in front. This is because we are taking away from something that is already negative. I owed 2 already, now I am going to owe 10 more, which means in total, I owe 12, hence the -12 of something we owe.
Final result:
Another way of looking at this problem is to use what we learned in adding integers. We can rewrite the expression into an addition. This is the exact same thing; we are adding the total number of things we owe. So we simply add the two values and place a negative sign in front to get the total of things we owe.
Ans: -12
© 2010 Math TutorDVD.com The Pre-Algebra Tutor: Vol 1 Section 5 – Subtracting Integers
Page 15
9) Find the difference of the following integers.
Begin
(negative #) - (positive #) = negative
Final result:
First thing we notice is we are subtracting from a negative number, which means we are going to increase the number of things we owe by the number we are subtracting with. If we visualize a number line and start at -18, then go 2 places to the left since we are subtracting, we notice we land on -20. So we notice the result is simply the sum of the two numbers with a negative sign in front. This is because we are taking away from something that is already negative. I owed 18 already, now I am going to owe 2 more, which means in total, I owe 20, hence the -20 of something we owe.
Final result:
Another way of looking at this problem is to use what we learned in adding integers. We can rewrite the expression into an addition. This is the exact same thing; we are adding the total number of things we owe. So we simply add the two values and place a negative sign in front to get the total of things we owe.
Ans: -20
© 2010 Math TutorDVD.com The Pre-Algebra Tutor: Vol 1 Section 5 – Subtracting Integers
Page 16
10) Find the difference of the following integers.
Begin
(negative #) - (positive #) = negative
Final result:
First thing we notice is we are subtracting from a negative number, which means we are going to increase the number of things we owe by the number we are subtracting with. If we visualize a number line and start at -1, then go 1 place to the left since we are subtracting, we notice we land on -2. So we notice the result is simply the sum of the two numbers with a negative sign in front. This is because we are taking away from something that is already negative. I owed 1 already, now I am going to owe 1 more, which means in total, I owe 2, hence the -2 of something we owe.
Final result:
Another way of looking at this problem is to use what we learned in adding integers. We can rewrite the expression into an addition. This is the exact same thing; we are adding the total number of things we owe. So we simply add the two values and place a negative sign in front to get the total of things we owe.
Ans: -2
© 2010 Math TutorDVD.com The Pre-Algebra Tutor: Vol 1 Section 5 – Subtracting Integers
Page 17
11) Find the difference of the following integers.
Begin
(negative #) - (positive #) = negative
Final result:
First thing we notice is we are subtracting from a negative number, which means we are going to increase the number of things we owe by the number we are subtracting with. If we visualize a number line and start at -7, then go 12 places to the left since we are subtracting, we notice we land on -19. So we notice the result is simply the sum of the two numbers with a negative sign in front. This is because we are taking away from something that is already negative. I owed 7 already, now I am going to owe 12 more, which means in total, I owe 19, hence the -19 of something we owe.
Final result:
Another way of looking at this problem is to use what we learned in adding integers. We can rewrite the expression into an addition. This is the exact same thing; we are adding the total number of things we owe. So we simply add the two values and place a negative sign in front to get the total of things we owe.
Ans: -19
© 2010 Math TutorDVD.com The Pre-Algebra Tutor: Vol 1 Section 5 – Subtracting Integers
Page 18
12) Find the difference of the following integers.
Begin
(negative #) - (positive #) = negative
Final result:
First thing we notice is we are subtracting from a negative number, which means we are going to increase the number of things we owe by the number we are subtracting with. If we visualize a number line and start at -9, then go 11 places to the left since we are subtracting, we notice we land on -20. So we notice the result is simply the sum of the two numbers with a negative sign in front. This is because we are taking away from something that is already negative. I owed 9 already, now I am going to owe 11 more, which means in total, I owe 20, hence the -20 of something we owe.
Final result:
Another way of looking at this problem is to use what we learned in adding integers. We can rewrite the expression into an addition. This is the exact same thing; we are adding the total number of things we owe. So we simply add the two values and place a negative sign in front to get the total of things we owe.
Ans: -20
© 2010 Math TutorDVD.com The Pre-Algebra Tutor: Vol 1 Section 5 – Subtracting Integers
Page 19
13) Find the difference of the following integers.
Begin
(a #) - (negative #) = (a #) + (positive #)
We are adding the opposite of the negative
number
Final result:
First, we notice we are attempting to subtract with a negative number. This means we have a minus sign in front of a negative and as you recall, this is where we are going to “add the opposite.” This means the two negative signs next to each other cancel out and you end up with a plus sign. We then simply add the two integers and the result is our final answer.
Ans: 15
© 2010 Math TutorDVD.com The Pre-Algebra Tutor: Vol 1 Section 5 – Subtracting Integers
Page 20
14) Find the difference of the following integers.
Begin
(a #) - (negative #) = (a #) + (positive #)
We are adding the opposite of the negative
number
Final result:
First, we notice we are attempting to subtract with a negative number. This means we have a minus sign in front of a negative and as you recall, this is where we are going to “add the opposite.” This means the two negative signs next to each other cancel out and you end up with a plus sign. We then simply add the two integers and the result is our final answer.
Ans: 9
© 2010 Math TutorDVD.com The Pre-Algebra Tutor: Vol 1 Section 5 – Subtracting Integers
Page 21
15) Find the difference of the following integers.
Begin
(a #) - (negative #) = (a #) + (positive #)
We are adding the opposite of the negative
number
Final result:
First, we notice we are attempting to subtract with a negative number. This means we have a minus sign in front of a negative and as you recall, this is where we are going to “add the opposite.” This means the two negative signs next to each other cancel out and you end up with a plus sign. We then simply add the two integers and the result is our final answer.
Ans: 30
© 2010 Math TutorDVD.com The Pre-Algebra Tutor: Vol 1 Section 5 – Subtracting Integers
Page 22
16) Find the difference of the following integers.
Begin
(a #) - (negative #) = (a #) + (positive #)
We are adding the opposite of the negative
number
Final result:
First, we notice we are attempting to subtract with a negative number. This means we have a minus sign in front of a negative and as you recall, this is where we are going to “add the opposite.” This means the two negative signs next to each other cancel out and you end up with a plus sign. We then simply add the two integers and the result is our final answer.
Ans: 47
© 2010 Math TutorDVD.com The Pre-Algebra Tutor: Vol 1 Section 5 – Subtracting Integers
Page 23
17) Find the difference of the following integers.
Begin
(a #) - (negative #) = (a #) + (positive #)
We are adding the opposite of the negative
number
Final result:
First, we notice we are attempting to subtract with a negative number. This means we have a minus sign in front of a negative and as you recall, this is where we are going to “add the opposite.” This means the two negative signs next to each other cancel out and you end up with a plus sign. We then simply add the two integers and the result is our final answer.
Ans: 20
© 2010 Math TutorDVD.com The Pre-Algebra Tutor: Vol 1 Section 5 – Subtracting Integers
Page 24
18) Find the difference of the following integers.
Begin
(a #) - (negative #) = (a #) + (positive #)
We are adding the opposite of the negative
number
Final result:
First, we notice we are attempting to subtract with a negative number. This means we have a minus sign in front of a negative and as you recall, this is where we are going to “add the opposite.” This means the two negative signs next to each other cancel out and you end up with a plus sign. We then simply add the two integers and the result is our final answer.
Ans: 8
© 2010 Math TutorDVD.com The Pre-Algebra Tutor: Vol 1 Section 5 – Subtracting Integers
Page 25
19) Find the difference of the following negative integers.
Begin
(a #) - (negative #) = (a #) + (positive #)
We are adding the opposite of the negative
number
The first thing we should notice right away is that we are attempting to subtract with a negative number. This means we have a minus sign in front of a negative and as you recall, this is where we are going to “add the opposite.” This means the two negative signs next to each other cancel out and you end up with a plus sign.
Final result:
Now we are left with an addition problem where we are adding two integers with opposite signs. Recall from the previous section (Adding Integers) that it doesn’t matter if we are adding a negative to a positive or a positive to a negative. The sign of your result will always be carried by the sign of the largest absolute value in the expression. In this case, the absolute value of 15 is greater so the final result will be negative. Remember that when adding two integers with opposite signs, we are really in fact subtracting. So next we subtract the absolute values from each other as we would with a regular subtraction. Once you get your result don’t forget to indicate the sign of the result you found earlier, which is negative.
Ans: -10
© 2010 Math TutorDVD.com The Pre-Algebra Tutor: Vol 1 Section 5 – Subtracting Integers
Page 26
20) Find the difference of the following negative integers.
Begin
(a #) - (negative #) = (a #) + (positive #)
We are adding the opposite of the negative
number
The first thing we should notice right away is that we are attempting to subtract with a negative number. This means we have a minus sign in front of a negative and as you recall, this is where we are going to “add the opposite.” This means the two negative signs next to each other cancel out and you end up with a plus sign.
Final result:
Now we are left with an addition problem where we are adding two integers with opposite signs. Recall from the previous section (Adding Integers) that it doesn’t matter if we are adding a negative to a positive or a positive to a negative. The sign of your result will always be carried by the sign of the largest absolute value in the expression. In this case, the absolute value of 8 is greater so the final result will be positive. Remember that when adding two integers with opposite signs, we are really in fact subtracting. So next we subtract the absolute values from each other as we would with a regular subtraction. Once you get your result don’t forget to indicate the sign of the result you found earlier, which is positive.
Ans: 6
© 2010 Math TutorDVD.com The Pre-Algebra Tutor: Vol 1 Section 5 – Subtracting Integers
Page 27
21) Find the difference of the following negative integers.
Begin
(a #) - (negative #) = (a #) + (positive #)
We are adding the opposite of the negative
number
The first thing we should notice right away is that we are attempting to subtract with a negative number. This means we have a minus sign in front of a negative and as you recall, this is where we are going to “add the opposite.” This means the two negative signs next to each other cancel out and you end up with a plus sign.
Final result:
Now we are left with an addition problem where we are adding two integers with opposite signs. Recall from the previous section (Adding Integers) that it doesn’t matter if we are adding a negative to a positive or a positive to a negative. The sign of your result will always be carried by the sign of the largest absolute value in the expression. In this case, the absolute value of 50 is greater so the final result will be negative. Remember that when adding two integers with opposite signs, we are really in fact subtracting. So next we subtract the absolute values from each other as we would with a regular subtraction. Once you get your result don’t forget to indicate the sign of the result you found earlier, which is negative.
Ans: -30
© 2010 Math TutorDVD.com The Pre-Algebra Tutor: Vol 1 Section 5 – Subtracting Integers
Page 28
22) Find the difference of the following negative integers.
Begin
(a #) - (negative #) = (a #) + (positive #)
We are adding the opposite of the negative
number
The first thing we should notice right away is that we are attempting to subtract with a negative number. This means we have a minus sign in front of a negative and as you recall, this is where we are going to “add the opposite.” This means the two negative signs next to each other cancel out and you end up with a plus sign.
Final result:
Now we are left with an addition problem where we are adding two integers with opposite signs. Recall from the previous section (Adding Integers) that it doesn’t matter if we are adding a negative to a positive or a positive to a negative. The sign of your result will always be carried by the sign of the largest absolute value in the expression. In this case, the absolute value of 14 is greater so the final result will be positive. Remember that when adding two integers with opposite signs, we are really in fact subtracting. So next we subtract the absolute values from each other as we would with a regular subtraction. Once you get your result don’t forget to indicate the sign of the result you found earlier, which is positive.
Ans: 11
© 2010 Math TutorDVD.com The Pre-Algebra Tutor: Vol 1 Section 5 – Subtracting Integers
Page 29
23) Find the difference of the following negative integers.
Begin
(a #) - (negative #) = (a #) + (positive #)
We are adding the opposite of the negative
number
The first thing we should notice right away is that we are attempting to subtract with a negative number. This means we have a minus sign in front of a negative and as you recall, this is where we are going to “add the opposite.” This means the two negative signs next to each other cancel out and you end up with a plus sign.
Final result:
Now we are left with an addition problem where we are adding two integers with opposite signs. Recall from the previous section (Adding Integers) that it doesn’t matter if we are adding a negative to a positive or a positive to a negative. The sign of your result will always be carried by the sign of the largest absolute value in the expression. In this case, the absolute value of 9 is greater so the final result will be negative. Remember that when adding two integers with opposite signs, we are really in fact subtracting. So next we subtract the absolute values from each other as we would with a regular subtraction. Once you get your result don’t forget to indicate the sign of the result you found earlier, which is negative.
Ans: -1
© 2010 Math TutorDVD.com The Pre-Algebra Tutor: Vol 1 Section 5 – Subtracting Integers
Page 30
24) Find the difference of the following negative integers.
Begin
(a #) - (negative #) = (a #) + (positive #)
We are adding the opposite of the negative number
The first thing we should notice right away is that we are attempting to subtract with a negative number. This means we have a minus sign in front of a negative and as you recall, this is where we are going to “add the opposite.” This means the two negative signs next to each other cancel out and you end up with a plus sign.
Final result:
Now we are left with an addition problem where we are adding two integers with opposite signs. Recall from the previous section (Adding Integers) that it doesn’t matter if we are adding a negative to a positive or a positive to a negative. The sign of your result will always be carried by the sign of the largest absolute value in the expression. In this case, the absolute value of 22 is greater so the final result will be negative. Remember that when adding two integers with opposite signs, we are really in fact subtracting. So next we subtract the absolute values from each other as we would with a regular subtraction. Once you get your result don’t forget to indicate the sign of the result you found earlier, which is negative.
Ans: -2
© 2010 Math TutorDVD.com The Pre-Algebra Tutor: Vol 1 Section 5 – Subtracting Integers
Page 31
28)
Begin
First, let’s evaluate the expression by substituting the values expressed by the letters. We also notice there is an absolute value expression. We substitute for that as well. Now we can use what we have learned previously to find the difference.
(a #) - (negative #) = (a #) + (positive #)
We are adding the opposite of the negative number
Final result:
First, we notice we are attempting to subtract with a negative number. This means we have a minus sign in front of a negative and as you recall, this is where we are going to “add the opposite.” This means the two negative signs next to each other cancel out and you end up with a plus sign. We then simply add the two integers and the result is our final answer.
Ans: 17
© 2010 Math TutorDVD.com The Pre-Algebra Tutor: Vol 1 Section 5 – Subtracting Integers
Page 32
29)
Begin
First, let’s evaluate the expression by substituting the values expressed by the letters. Now we can use what we have learned previously to find the difference.
(bigger #) - (smaller #) = positive
Final result:
First we notice that we are subtracting a smaller number from a bigger number, which tells us we will end up with a positive answer. What we have is bigger in quantity than what will be taken away, which means we will still have some left over. We then subtract 4 from 10 as we are used to doing in regular subtraction. If we also picture a number line and start at 10, we can move 4 units to the left since we are taking away something and we see we end up at 6.
Ans: 6
© 2010 Math TutorDVD.com The Pre-Algebra Tutor: Vol 1 Section 5 – Subtracting Integers
Page 33
30)
Begin
First, let’s evaluate the expression by substituting the values expressed by the letters. Now we can use what we have learned previously to find the difference.
(negative #) - (positive #) = negative
Final result:
First thing we notice is we are subtracting from a negative number, which means we are going to increase the number of things we owe by the number we are subtracting with. If we visualize a number line and start at -12, then go 4 places to the left since we are subtracting, we notice we land on -16. So we notice the result is simply the sum of the two numbers with a negative sign in front. This is because we are taking away from something that is already negative. I owed 12 already, now I am going to owe 4 more, which means in total, I owe 16, hence the -16 of something we owe.
Final result:
Another way of looking at this problem is to use what we learned in adding integers. We can rewrite the expression into an addition. This is the exact same thing; we are adding the total number of things we owe. So we simply add the two values and place a negative sign in front to get the total of things we owe.
Ans: -16
© 2010 Math TutorDVD.com The Pre-Algebra Tutor: Vol 1 Section 5 – Subtracting Integers
Page 34
31)
Begin
First, let’s evaluate the expression by substituting the values expressed by the letters. We also notice there is an absolute value expression. We substitute for that as well. Now we can use what we have learned previously to find the difference. We now have three integers that we need to find the difference for. We can make it easier by tackling two integers at a time from left to right and then finding the difference between that result and the remaining integer in the expression.
(smaller #) - (bigger #) = negative
result:
First we notice we are subtracting a bigger number from a smaller number. This means we will end up with a negative number or owing some value since we don’t have enough to continue taking more of what we have away. Next we simply subtract the numbers as a regular subtraction (smaller number from bigger number) and put the negative sign in front of the answer.
Re-evaluate original expression with new result.
(negative #) - (positive #) = negative
First thing we notice is we are subtracting from a negative number, which means we are going to increase the number of things we owe by the number we are subtracting with. If we visualize a number line and start at -5, then go 10 places to the left since we are
© 2010 Math TutorDVD.com The Pre-Algebra Tutor: Vol 1 Section 5 – Subtracting Integers
Page 35
Final result:
subtracting, we notice we land on -15. So we notice the result is simply the sum of the two numbers with a negative sign in front. This is because we are taking away from something that is already negative. I owed 5 already, now I am going to owe 10 more, which means in total, I owe 15, hence the -15 of something we owe.
Ans: -15
© 2010 Math TutorDVD.com The Pre-Algebra Tutor: Vol 1 Section 5 – Subtracting Integers
Page 36
32)
Begin
First, let’s evaluate the expression by substituting the values expressed by the letters. Now we can use what we have learned previously to find the difference.
(a #) - (negative #) = (a #) + (positive #)
We are adding the opposite of the negative number
The first thing we should notice right away is that we are attempting to subtract with a negative number. This means we have a minus sign in front of a negative and as you recall, this is where we are going to “add the opposite.” This means the two negative signs next to each other cancel out and you end up with a plus sign.
Final result:
Now we are left with an addition problem where we are adding two integers with opposite signs. Recall from the previous section (Adding Integers) that it doesn’t matter if we are adding a negative to a positive or a positive to a negative. The sign of your result will always be carried by the sign of the largest absolute value in the expression. In this case both absolute values are equal. This should give us a clue to what the final answer will be. Remember that when adding two integers with opposite signs, we are really in fact subtracting. So next we subtract the absolute values from each other as we would with a regular subtraction. We see that we end up with 0, which is why there was no clear sign to pick from since zero is neutral (neither negative or positive).
© 2010 Math TutorDVD.com The Pre-Algebra Tutor: Vol 1 Section 5 – Subtracting Integers
Page 37
Ans: 0
33)
Begin
First, let’s evaluate the expression by substituting the values expressed by the letters. We also notice there is an absolute value expression. We substitute for that as well. Now we can use what we have learned previously to find the difference. We now have three integers that we need to find the difference for. We can make it easier by tackling two integers at a time from left to right and then finding the difference between that result and the remaining integer in the expression.
(negative #) - (positive #) = negative
result:
Next thing we notice is we are subtracting from a negative number, which means we are going to increase the number of things we owe by the number we are subtracting with. If we visualize a number line and start at -8, then go 9 places to the left since we are subtracting, we notice we land on -17. So we notice the result is simply the sum of the two numbers with a negative sign in front. This is because we are taking away from something that is already negative. I owed 8 already, now I am going to owe 9 more, which means in total, I owe 17, hence the -17 of something we owe.
Re-evaluate original expression with new result.
© 2010 Math TutorDVD.com The Pre-Algebra Tutor: Vol 1 Section 5 – Subtracting Integers
Page 38
(negative #) - (positive #) = negative
Final result:
Next thing we notice is we are subtracting from a negative number. We just finished doing a similar problem. This means we are going to increase the number of things we owe by the number we are subtracting with. If we visualize a number line and start at -17, then go 4 places to the left since we are subtracting, we notice we land on -21. So we notice the result is simply the sum of the two numbers with a negative sign in front. This is because we are taking away from something that is already negative. I owed 17 already, now I am going to owe 4 more, which means in total, I owe 21, hence the -21 of something we owe.
Ans: -21
© 2010 Math TutorDVD.com The Pre-Algebra Tutor: Vol 1 Section 5 – Subtracting Integers
Page 39
34)
Begin
First, let’s evaluate the expression by substituting the values expressed by the letters. Now we can use what we have learned previously to find the difference. We now have three integers that we need to find the difference for. We can make it easier by tackling two integers at a time from left to right and then finding the difference between that result and the remaining integer in the expression.
(a #) - (negative #) = (a #) + (positive #)
We are adding the opposite of the negative
number
result:
First, we notice we are attempting to subtract with a negative number. This means we have a minus sign in front of a negative and as you recall, this is where we are going to “add the opposite.” This means the two negative signs next to each other cancel out and you end up with a plus sign. We then simply add the two integers and the result is our final answer.
Re-evaluate original expression with new result.
(a #) - (negative #) = (a #) + (positive #)
We are adding the opposite of the negative
number
Next, we notice we are attempting to subtract with a negative number. This means we have a minus sign in front of a negative and as you recall, this is where we are going to “add the opposite.” This means the two negative signs next
© 2010 Math TutorDVD.com The Pre-Algebra Tutor: Vol 1 Section 5 – Subtracting Integers
Page 40
Final result:
to each other cancel out and you end up with a plus sign. We then simply add the two integers and the result is our final answer.
Ans: 30
© 2010 Math TutorDVD.com The Pre-Algebra Tutor: Vol 1 Section 5 – Subtracting Integers
Page 41
35)
Begin
First, let’s evaluate the expression by substituting the values expressed by the letters. Now we can use what we have learned previously to find the difference.
(negative #) - (positive #) = negative
Final result:
First thing we notice is we are subtracting from a negative number, which means we are going to increase the number of things we owe by the number we are subtracting with. If we visualize a number line and start at -12, then go 10 places to the left since we are subtracting, we notice we land on -22. So we notice the result is simply the sum of the two numbers with a negative sign in front. This is because we are taking away from something that is already negative. I owed 12 already, now I am going to owe 10 more, which means in total, I owe 22, hence the -22 of something we owe.
Final result:
Another way of looking at this problem is to use what we learned in adding integers. We can rewrite the expression into an addition. This is the exact same thing; we are adding the total number of things we owe. So we simply add the two values and place a negative sign in front to get the total of things we owe.
Ans: -22
top related