Lessons from multiplication
Is the mind already yelling as to what could possibly be common between subtraction and multiplication? While we will see a detailed connection between the two towards the end of the book, let us not forget that both are arithmetical operations, and there are bound to be some similarities between multiplication and subtraction.
That both are a means of counting, i.e., quantifying, and multiplication is much faster in quantification than counting needs no special mention. What else can we learn from the knowledge of multiplication (relevant for understanding subtraction)? Here are a few interesting insights that are true for both the operations:
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Multiplication is a binary operation, does it imply that subtraction is highly likely to be applicable only on two numbers at a time (because addition is also binary)
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Of the four operations, only multiplication and subtraction have three distinct components in their expressions. The three components of multiplication are multiplier, multiplicand and product, while the three for subtraction are minuend, subtrahend, and ‘difference’.
This may seem to be ‘not worthy of mention’ similarity, but a definite 3-component understanding of multiplication does indeed help in visualising the need and role of three components in subtraction situations. Addition is essentially 2-component operation (addends and sum), and division is 4-component operation (dividend, divisor, quotient, and remainder).
Thus, multiplication is the first level of complexity (of a kind) over addition and makes the mind ready for understanding a somewhat similar 3-component operation – and this is a helpful step up in understanding subtraction.
- Manipulatives are more important to learn multiplication and subtraction (as compared to addition wherein manipulatives are important but not as much as it is for subtraction, for example)
- If we recall, 3 x 4 is not same as 3 x 2 x 2. In quite a similar manner, 8 – 6 is not the same as 8 – 4 – 2, or 8 – 3 – 3, in the sense of what the expressions represent in everyday situations. Of course, it is true for addition expressions too.
- Multiplication can also express repeated subtraction; detailed discussion on it is in a later Learning Outcome.
Knowledge of the multiplication operation ensures better preparation to understand subtraction, compared to just knowing the addition operation.
Summary
Surprising as it may be, it is important and interesting to appreciate that prior knowledge of multiplication is also helpful in a better understanding of subtraction.
Excerpted from the book ‘Foundations of Subtraction (Mathematics as a language)’ by Sandeep Srivastava and Saloni Srivastava