Math 23 – Section 1.6 - Subtraction of Real Numbers - Page 1
Section 1.6
Subtraction of Real Numbers
I. Rules for Subtracting
A. To subtract a real number from another real number, change the sign and add.
B. Examples
1. 8 – 5 = 8 + (5)
Signs are different, take the sign of the biggest and
subtract.
Answer: 3
2. –12 – 7 = 12 + (7)
Answer: 19
Signs are the same, take the signs and add.
3. 18 – (6) = 18 + 6
Answer: 24
Signs are the same, take the signs and add.
4. Now you try one: 28 – 47
Answer: 19
5.
–13 + 6 – 5
7 – 5
Answer: 12
6.
4 7

9 9
Looking at the first two numbers, the signs are different,
take the sign of the biggest and subtract.
Signs are alike, take the sign and add.
We have a common denominator, so we notice that the
signs are different, so take the sign of the biggest and
subtract.

3
9
Reduce.
Answer: 
7.
Now you try one:
Answer: 
8.
1
3

4  1
  
5  5
3
5
9  7
Answer: 2 
Signs are different, take the sign of the biggest and
subtract.
9. Now you try one: 3  10 
Answer: 13 
© Copyright 2012 by John Fetcho. All rights reserved
Math 23 – Section 1.6 - Subtraction of Real Numbers - Page 2
10.
8  2 + 5 13
Group the numbers with the same signs together.
8 + 5  2  13
Use the rule that when the signs are alike, take the
signs and add.
Signs are different, take the sign of the biggest and
subtract.
13  15
Answer: 2
11.
2
3  7
  
4  8
First, a double negative gives us a positive.
2
3 7
 
4 8
Next, the common denominator is 8.
2
6 7
 
8 8
On the fractions, the signs are different, take the
sign of the biggest and subtract.
1
2
8
16 1

8 8
The common denominator is still 8!
Signs are alike, take the sign and add.
Answer:
17
8
12.
Now you try one:
Answer: 4.49
0.16  5.2  (0.87)
13.
5 + 9y  29y
First, we need to identify the like terms (9y and 29y).
Signs are different, take the sign of the biggest and
subtract.
Answer: 5  20y
14.
5  7b  13  4b
5  13  7b  4b
First, let's regroup so that the like terms are together.
On the constants, the signs are different, so take the sign
of the biggest and subtract. On the variable terms, the
signs are alike, so take the sign and add.
Answer: 6  11b
15. Now you try one:
Answer: 24 + 11x
13  (7x) + 4x  (11)
© Copyright 2012 by John Fetcho. All rights reserved
Math 23 – Section 1.6 - Subtraction of Real Numbers - Page 3
II.
Applications
A.
Process
1.
Read the problem.
2.
Determine what is unknown.
3.
Define a variable for the unknown.
4.
Write an equation expressing the problem algebraically (i.e. - translate from
English into Algebra).
5.
Solve the equation.
6.
Write a complete sentence answering the question.
B.
Examples - Follow the 6-step process from above to answer each question.
1.
The peak of Mount Whitney is 14,494 feet above sea level. Mount Whitney
can be seen directly above Death Valley, which is 282 feet below sea level.
What is the difference between these geographic locations? (Page 71, #96)
First, we see that what we don’t know is the “difference”. What operation
does this signal us to use?
Since we don’t know the “difference”,
Let d = The difference in elevation
Now we can write an equation expressing this “difference”:
14,494  (282) = x
We will now solve this equation:
14,494 – (282) = x
14,494 + 282 = x
14,776 = x
Now change the sign and add.
Finally, we will answer the question with a complete sentence:
Answer:
2.
The difference between the peak of Mt. Whitney and the lowest
point of Death Valley is 14,776 feet.
The bar graph (middle of right-hand column, page 71) shows the average
daily low temperature for each month in Fairbanks, Alaska. Use the graph to
solve Exercises 97 – 100.
What is the difference between the average daily low temperatures for
October and November? (Page 71, #98)
First, we determine that the difference in average daily low temperatures is
the unknown here. So, what operation should we use?
Let d = The difference in temperature
October = 6o F
November = 12o F
Our equation is:
6 – (12) = d
Change the sign and add.
6 + 12 = d
Simplifying the left-hand side, we get:
18 = d
So answering the question:
Answer: The difference between the October and November low temperatures
is 18o F.
© Copyright 2012 by John Fetcho. All rights reserved
Math 23 – Section 1.6 - Subtraction of Real Numbers - Page 4
3.
Now you try one: How many degrees warmer is February’s average low
temperature than January’s low temperature? (Page 71, #99)
Answer:
February is about 3o F warmer than January.
© Copyright 2012 by John Fetcho. All rights reserved