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The idea of subtraction as “reverse addition” is explored in greater detail in this document.

MATH MILESTONE #A3: SUBTRACTION

Subtraction is taking a quantity away from another quantity. For example, suppose you have 15 marbles; and you give 6 marbles to your friend. You can find the remaining marbles in two different ways:

1. Take 6 away from 15:  start from 15 and count back 6 to see the number you end up with.
2. Find 6 and “what” is 15: start from 6 and see how many counts it takes to arrive at 15.

The method in (a) requires a new skill of counting backwards. The method in (b) utilizes the already learned skill of addition. Both these methods work because

Subtraction is the opposite of addition.

The better one can do addition, the more skillful one gets at subtraction. In subtraction, one also learns the concept of regrouping the place values. The following videos from Khan Academy demonstrate subtraction.

Basic Subtraction

Subtraction 2

Subtraction 3: Introduction to Borrowing or Regrouping

Alternate mental subtraction method

Level 4 Subtraction

Why borrowing works

When we take away all the units, which are there, we are left with nothing. Thus, subtraction provides us with the idea of “nothing” as a “number.” We call it zero.

When we need to take away more than what is there, we are faced with a definite shortage. Thus, subtraction also provides us with a measure of “shortage.” We call it a negative number.

Calculators may be used to save time with subtraction; but still mental awareness is necessary to know if the calculated answer is correct. This awareness comes from the practice with mental math as outlined in the document above.

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