# Handling the Mischievous Negative Numbers

December 1, 2016

| Specialist Math Tutor

The little mischievous devil known as "Negative numbers" pops up every now and then and ruin the grades of my beloved students (Yes... even secondary 4 A-math students!). He preys on students with weak foundations in addition and subtraction of negative numbers. The best way to defend yourself against this arithmetic devil is to learn the mental processes behind how "Pros" deal with it.

Every secondary 1 student that comes for math tuition in Mr Ausome's coaching classes will inevitably go through a tutorial on "defense against the dark negative numbers". Here is the secret behind the mental process of how "Pros" with good math foundation handle negative numbers:

Follow these 4 steps to handle negative numbers:

Step 1) Convert all double negatives into positive.

Example: 2 - ( - 4 ) = 2 + 4

Example: - 7 - ( - 9 ) = - 7 + 9

The answer will be found in 2 parts: the sign (Step 2) and the number (Step 3)

Example: If Answer is - 2 ,  Sign is minus, Number is 2

Step 2) Determine the sign of the answer by following these 2 rules:

a) If both numbers are same sign, answer will have the same sign

Example: – 3 – 5 = – ⎕                  (both “3” and  “5” have negative, so answer is negative)

Example:  + 2 + 4 = + ⎕                 (both “2” and  “4” have positive, so answer is positive)

b) If both numbers have opposite sign, answer will follow the sign of the bigger number

Example: + 5 – 8 = – ⎕                  (“5” is “+” while “8 “is “–“, answer follows “– 8” & is “–“)

Example: – 7 + 9 = + ⎕                  (“7” is “–“, while “9 “is “+”, answer follows “+ 9” & is “+”)

Step 3) Next, determine number by following these 2 rules:

a) If both numbers are same sign, add numbers

Example: – 3 – 5 =⎕ 8                   (same sign, so we add 3 + 5 to get 8)

Example:  + 2 + 4 = ⎕ 6                 (same sign, so we add 2 + 4 to get 6)

b) If numbers are opposite sign, use bigger number minus smaller number

Example: + 5 – 8 = ⎕ 3                  (Opposite signs, so number is 8 – 5 = 3)

Example: – 7 + 9 = ⎕ 2                  (Opposite signs, so number is 9 – 7 = 2)

Step 4) Combine the sign and the number from steps 2 and 3 to get the final answer.

Example: + 2 + 4 = + 6

Example: – 3 – 5 = – 8

Example: + 5 – 8 = – 3

Example: – 7 + 9 = + 2

Of course, this is just the first part of your tuition on negative numbers. To be good, you need to practice, practice and practice even more!

To get more math practice on addition and subtraction of negative number, you can print out the 10 sets of worksheets from this link:

Hope you found this math tuition session helpful!