Finding the subtraction rules

Here are some very important things we have discovered so far:

Important understandings of ADDITION

  • Adding a positive number goes to the right.
  • Adding a negative number goes to the left.
Important understandings of SUBTRACTION
  • Subtracting a positive number goes to the left. 
  • Subtracting a negative number goes to the right.

 

 

Putting these understandings together we find that 

  • Subtracting a negative number is the same as adding a positive number.
  • Subtracting a positive number is the same as adding a negative number. 

Here are two examples showing that each subtraction problem has a related addition problem that gives the exact same answer.

5 – (-8) = 13
5 + 8 = 13

 

5 – 2 = 3
5 + (-2) = 3
 

 

Let's practice a little:

Change the subtraction expression into an addition expression. Then simplify.

(-4) – (+6)
 

(-4) – (+6) will result in the same answer as (-4) + (-6).

(-4) – (+6) = (-4) + (-6) = -10

(-7) – (-9)

(-7) – (-9) will result in the same answer as (-7) + (+9)

(-7) – (-9) = (-7) + (+9) = +2

(+3) – (+5)

(+3) – (+5) will result in the same answer as (+3) + (-5)

(+3) – (+5) = (+3) + (-5) = -2

(+8) – (-2)

(+8) – (-2) will result in the same answer as (+8) + (+2)

(+8) – (-2) = (+8) + (+2) = +10

 

By looking at the four examples above, we can see a pattern that occurs in each of the examples:

  • The first integer stays the same;
  • The subtraction sign turns into an addition sign;
  • The second integer turns into its opposite.

In fact, the rule for subtracting positives and negatives is:

To subtract two integers:
The first integer stays the same and add the opposite of the second integer

 

Self-Check


Question 1

Write the following expression using addition. Then simplify.

(+8) – (-5)

[show answer]


Question 2

Write the following expression using addition. Then simplify.

(-3) – (-4)

[show answer]


Question 3

Write the following expression using addition. Then simplify.

(-6) – (+7)

[show answer]


 

 

 

 

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