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1.3.3: Integer Subtraction

  • Page ID
    4289
  • Subtraction of Integers

    Molly goes shopping with $20. She buys a new notebook for $4 and a soda for $2. How much money does she have left?

    Subtracting Integers

    To subtract one signed number from another, change the problem from a subtraction problem to an addition problem and change the sign of the second number. In other words, to subtract signed numbers simply add the opposite. Then, follow the rules for adding signed numbers.

    The subtraction of integers can be represented with manipulatives such as color counters and algebra tiles. A number line can also be used to show the subtraction of integers.

    Let's practice subtracting positive and negative integers using color counters:

    1. Simplify 7−(−3)

    First change the subtraction to addition, and change the sign of the second number, so that 7−(−3)becomes 7+(+3). Now the problem can be represented with color counters. In this case, the red counters represent positive numbers.

    The answer is the sum of 7 and 3: 7+(+3)=10

    1. 4−(+6)

    Change the subtraction problem to an addition problem and change the sign of the second number:

    4−(+6)=−2

    Now the problem can be represented with color counters. In this case, the red counters are positive numbers, and the yellow counters are negative numbers.

    The remaining counters represent the answer. Therefore, 4−(+6)=−2.The answer is the difference between 6 and 4, and the answer takes the sign of the larger number in the addition problem.

    Now, let's subtract integers using algebra tiles:
    5−(+8)

    Rewrite the problem as addition, and change the sign of the second number: 5−(+8)=5+(−8)

    Now the problem can be represented with tiles. Here the green tiles represent positive numbers and the white represent negatives:

    The remaining tiles represent the answer. There are three negative tiles remaining. Therefore, (5)−(+8)=−3.

    Finally, let's subtract integers using a number line:
    (−4)−(+3)

    This is the same as (−4)+(−3). The solution to this problem can be determined by using a number line.

    Indicate the starting point of -4 by using a dot. From this point, add a -3 by moving three places to the left. You will stop at -7.

    The point where you stopped is the answer to the problem. Therefore, (−4)−(+3)=−7.

    Examples

    Example 1

    Example \(\PageIndex{1}\)

    Earlier, you were told that Molly goes shopping with $20. She buys a new notebook for $4 and a soda for $2. How much money does she have left?

    Solution

    You can find Molly's remaining money by subtracting the amount she spent from the amount she went shopping with.

    $20−$4−$2=$14

    Example 2

    Example \(\PageIndex{1}\)

    Subtract the integers: (−2)−(−6)

    Solution

    (−2)−(−6)=−2+6=6−2=4

    Example 3

    Example \(\PageIndex{1}\)

    Subtract the integers: 7−(+5)

    Solution

    7−(+5)=7−5=2.

    Example 4

    Example \(\PageIndex{1}\)

    Subtract the integers: (−8)−(−5)

    Solution

    (−8)−(−5)=−8+5=5−8=−3

    Example 5

    Example \(\PageIndex{1}\)

    Subtract the integers: (−4)−(+9)

    Solution

    (−4)−(+9)=−4−9=−13.

    Review

    Subtract the integers.

    1. (−9)−(−2)
    2. (5)−(+8)
    3. (5)−(−4)
    4. (−7)−(−9)
    5. (6)−(+5)
    6. (8)−(+4)
    7. (−2)−(−7)
    8. (3)−(+5)
    9. (−6)−(−10)
    10. (−4)−(−7)
    11. (−13)−(−19)
    12. (−6)−(+8)−(−12)
    13. (14)−(+8)−(−6)
    14. (18)−(+8)−(+3)
    15. (10)−(−6)−(+4)−(+2)

    For each of the following models, write and answer a subtraction problem that describes the situation.

    1. .
    1. .
    1. .
    1. .
    1. .

    Review (Answers)

    To see the Review answers, open this PDF file and look for section 1.4.

    Vocabulary

    Term Definition
    Integer The integers consist of all natural numbers, their opposites, and zero. Integers are numbers in the list ..., -3, -2, -1, 0, 1, 2, 3...
    number line A number line is a line on which numbers are marked at intervals. Number lines are often used in mathematics to show mathematical computations.

    Additional Resources

    PLIX: Play, Learn, Interact, eXperience: The Secret of Subtraction

    Video: Subtracting Integers - Overview

    Practice: Integer Subtraction

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