Algebra I.
Lesson 2
Rational Numbers (Grades 9-12)
Instruction 2-2
Integers and the Number Line | Adding and Subtracting Integers | Inequalities and the Number Line | Comparing and Ordering Rational Numbers | Dividing Rational Numbers | Summary
| Adding and Subtracting Integers |
| CCSTD HS Grades Algebra 13.0 |
A good way to add or subtract integers is to understand
the concept of absolute value. Knowing this idea, you can add and subtract
integers easily.
Absolute Value
Absolute value of an integer is its distance from zero. Opposite numbers have
the same absolute value. For example, the absolute values of –3 and 3 or –5 and
5 are the same (Figure 2.7).

Figure 2.7
The absolute value of any number is a whole number. Absolute value of a
number usually shown by placing the number between segments | |. These are
some samples of showing absolute values of numbers.
Practice 4. Which number is at the furthest point from zero on a
number line?
–2, 23, –34, 8, 29, 32, –22
Answer
How to Add and Subtract Integers?
In adding and subtracting integers, we always deal with two cases.
In all such cases, add the absolute values of the numbers. Then choose
the sign of the numbers as the sign of the result.
For example, in (a) the sign of the result is +. In (b), the sign of the
result is –.
Practice 5. Calculate.
(a) 32 + 121 + 22 + 56 + 11
(b) –11 – 32 – 43 – 11 – 54
(c) 21 + 11 – 5 + 23 – 7 – 23
Answer
Practice 6. Place the sum of each row in the right column. Then add up
the numbers in this column. This should be zero.
| 5 | -11 | 8 | -16 | 25 | 21 | |
| 21 | 6 | -14 | 6 | -42 | 11 | |
| 19 | -32 | -20 | 22 | 27 | 28 | |
| -32 | 18 | 7 | 24 | 17 | -35 | |
|
Sum of Numbers in Right Column |
||||||
Table 2.8
Answer
Real Life Application 3. In Table 2.10, the operations of a company
are shown during five days. Using integers, find the final profit of the
company.
| Day | Income | Expenditure |
|---|---|---|
| First Day | $1,200 | $320 |
| Second Day | $1,000 | $240 |
| Third Day | $1,900 | $430 |
| Fourth Day | $1,700 | $110 |
| Fifth Day | $1,100 | $100 |
Table 2.10
General Rules for Combing Integers
If a and b are integers, then
a + (–b) = a – b
a – (+b) = a – b
a – (–b) = a + b
a + (+b) = a + b
Practice 7. Compute
(a) 32 – (+45)
(b) –49 + (–23)
(c) 31 + (+28)
(d) –46 – (–26)
Answer
Practice 8. Calculate
(a) 12 + (–32) – 25
(b) –21 – (+43) + 19
(c) 15 – (–32) + 17
Answer
Real Life Application 4. The altitudes of Valley A and Mountain B are
–84 ft and 63 ft. What is the difference between these altitudes?
Answer
Practical Exercise 1 Compute
(a) –11 + 23 – (+31) – (–87)
(b) 34 – 43 – (–11) + (–34)
(c) –24 – (–11) – (–29)
Answer
Links for Students, Parents and Teachers
Now let's do Practice
Exercise 2-2 (top).
Inequalities and the Number Line (top)Next Page: