TABE Level D Math: Integers

Whole numbers are 0,1,2,3,… on forever. Their opposites are −1, −2, −3,… (negative 1, negative 2, negative 3, and so forth), on forever. These whole numbers and their opposites are called integers.

Most of the numbers you use in day-to-day life are positive.

However, negative numbers have an important place in real life as well. When someone owes you money, it is a positive amount. When you owe someone else money, it is a negative amount. When a football team gains yards, it is positive yardage. When the team loses yards, it is negative yardage. There are temperatures above zero and below zero. Land may be above sea level (positive) or below sea level (negative).

It is useful to think of integers as the marks on an outdoor thermometer held sideways. Zero is in the middle. Positive integers go right and negative integers go left.



An integer and its opposite are the same distance from zero. They just go in opposite directions. For example 3 and −3 are both 3 away from 0.

You need to be able to add, subtract, multiply, and divide integers on the TABE D. When adding or subtracting integers, it might not be clear whether the − sign is part of a negative number or a subtraction.

There are certain rules for writing positive and negative numbers:


1. If a number is positive, it doesn’t need a + sign in front of it.

2. If a number is negative, it must have a − sign in front of it.

3. If a negative number comes first in a problem, it doesn’t need to be in parentheses, such as −3 + 7.

4. If a negative number doesn’t come first in a problem it must be in parentheses, such as 7 + (−3).

Let’s see how to read some examples.

Example A. − 1 + 5: 1 add 5
Example B. − 7 + (−6): −7 add −6
Example C. 4 + (−3): 4 add −3
Example D. 5 −8: 5 subtract 8
Example E. −3 −9: −3 subtract 9
Example F. 2 −(−6): 2 subtract −6
Example G. −3 (−7): −3 subtract −7

This is part of the language of math. You need to make sure you know how to read math correctly.

Adding Integers
If two integers are both positive, just add them like whole numbers. If they are negative, ignore the sign, add them, and put a negative sign in front of the answer.

For example, and .

If two integers have different signs, follow these steps:


1. Ignore the signs

2. Subtract the smaller number from the larger number.

3. Attach the minus sign to the answer if that number is larger.

Example A.

1. Ignore the signs: 8, 3.

2. Subtract the smaller number from the larger number: .

3. Since 8 is larger than 3, the answer is 5.

Example B.

1. Ignore the signs: 12, 3.

2. Subtract the smaller number from the larger number: .

3. Attach the negative sign, because 12 is larger than 3. The answer is −9.


Practice Adding Integers

1. −4 + 8

2. 5 + (−8)

3. −6 + (−14)

4. 7 + (−5)

5. −3 + 1

6. −7 + (−4)

Subtracting Integers
The word “subtract” means “add the opposite.” For example 5 − 7 (5 subtract 7) means 5 + (−7) (5 add −7). So you change a subtract problem to an add problem (add the opposite).

Example A.

: 6 subtract 2 means 6 add

Example B.

: 4subtract − 10 means 4 add

Example C.

: 9 subtract 12 means 9 add

Example D.

: 15 subtract 8 means 15 add

You could do Example D just like a regular whole number subtraction problem because both 15 and 8 are positive and 8 is smaller than 15.


Practice Subtracting Integers


1. 8 − (− 3)

2. − 4 − 13

3. − 1 −(− 8)

4. 12 − (− 1)

5. 10 − 12

6. − 11 − 4


Multiplying and Dividing Integers
Multiplying and dividing integers is easy. Just multiply or divide as you would with whole numbers. If the numbers have the same sign (both positive or both negative), the answer is positive. If the numbers have different signs, the answer is negative.

Example A.

Example B.

Example C.

Example D.

Example E.

Example F.

Practice Multiplying and Dividing Integers

1. − 7 × 4

2. 15 ÷ − 3

3. 9 × − 22

4. − 63 ÷ 7

5. − 13 ×(− 4)

6. − 66 ÷ 11

7. 3 × − 9

8. − 54 ÷ (− 6)


Mixed Practice on Integers

1. 21 − (− 8)

2. − 35 ÷ 7

3. − 19 + (− 6)

4. − 20 ÷ (− 5)

5. − 32 − (− 8)

6. − 3 × ÷ 7

7. − 9 + (− 13)

8. 42 × (− 1)

9. − 1 + (− 1)

10. − 15 ÷ (− 3)

11. 12 ÷ (− 2)

12. 6 −(− 5)

13. −7 ÷ (− 1)

14. 8 + (− 17)

15. − 4 × (− 4)

16. − 3 − 4

17. − 3 × − 12

18. 20 ÷ (− 10)

19. − 17 + (− 3)

20. 7 − 2

Answers: Practice Adding Integers

1. 4

2. −3

3. −20

4. 2

5. −2

6. −11

Answers: Practice Subtracting Integers

1. 11

2. −17

3. 7

4. 13

5. −2

6. −15

Answers: Practice Multiplying and Dividing Integers

1. −28

2. −5

3. −198

4. −9

5. 52

6. −6

7. −27

8. 9

Answers: Mixed Practice on Integers

1. 29

2. −5

3. −25

4. 4

5. −24

6. 21

7. −22

8. −42

9. −2

10. 5

11. −6

12. 11

13. 7

14. −9

15. 16

16. −7

17. −36

18. −2

19. −20

20. 5