This post departs from the pattern of presenting an interesting concept from number theory or presenting a solution to a classic problem. We will look at a basic concept and at understanding it in a way that makes some daily mathematical tasks simpler. The concept is difference or the result of subtracting one number from another.
What difference means
The sum of two numbers is the result of their addition. The difference of two numbers, or between two numbers to use more common terms, is the result of subtracting the smaller of the numbers from the larger one.
Looking at the image above, the question may be, “What is the difference in the heights of the two buildings?” The usual way to answer is this: . Hopefully, the numbers were simple enough to be done without a calculator.
Another way of thinking about that difference would be to say, “If I were standing on top of the 15m building, how high must I leap in the air in order to be level with the 28m one?” In this case, you might want to leap 3m to get to 18m above the ground, then you’ll leap another 10m to get to 28m above the ground. In total, the distance that you have to breach is 13m, the sum of the bolded numbers.
To those who think it silly to think of ourselves as leaping 13m (42 ft 8 in), I say, “What are your jet packs for?”
What if the numbers were tricky?
Instead of heights of buildings, what if we had to calculate change at the supermarket? It is not as though we have a portable calculator in our pocket, or the sales assistants have one on their counters! We absolutely need to calculate the change in our heads: You handed a shiny, green, plastic $100 (Australian) dollar note for a $28.35 purchase. Would you ask for a pen and paper to line up the digits and do the subtraction? Of course not!
Like we did above, we will calculate the change by asking, “How many more dollars and cents does it take to breach the gap between $28.35 and $100?” In other words, let’s count up from the smaller number to the larger one.
- From $28.35, let’s add $0.65 to get to the next whole number, $29.
- Now, we’ll $1 and get to the next round number, $30
- How much do I add to $30 in order to get to $100? Yes, indeed, $70.
In total, the change will be:
That was an example of how addition can be used to calculate the result of a subtraction. Over the years, I have encountered many students who do not realise that they can use this strategy and this has surprised me. Maybe this is something that is taught rather than intuited.
I hope that this was a useful post for my favourite “words people” out there. Let me know if there are any other concepts that you want me to cover.
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