Question
What two numbers give
a product of 21.5 and a difference of 6.1?

Introduction
This
question reminded me of a question that I set myself when I was in Primary 4 (» grade 4). I
imagined a rectangle with breadth 4
and length 2 units longer then
the breadth (i.e. 6) giving a area (product) of
24. Then I pretended that I did
not know the breadth and let it be x.
This led to a quadratic equation x(x
+ 2) which I did not know how to solve (if I did not know the answer). So I accidentally discovered quadratic
equations when I was in Primary 4. This
led me to a quest to learn the method of factorisation
(by “trial and error” or “guess and check”) and the quadratic formula. I never
liked trial and error. So I continued in
my quest to invent a method of
factorisation that did not require “guess and check”. I finally succeeded doing that in secondary 1
(» grade 7). This turned out to be a Pyrrhic victory. The method I invented was
quite similar to the quadratic formula.
There is a
place for “guess and check” in mathematics.
I present a simple solution to the above problem using just that.
Solution
smaller #

larger #

product


2

8.1

16.2

û

3

9.1

27.3

û

2.5

8.6

21.5

ü

Solved! J
H02. Use a
diagram / model (table)
H05. Work
backwards (if the smaller
number is this, what is the bigger number?)
H07. Use guess
and check
H09. Restate
the problem in another way (area =
product)
Suitable Levels
* Primary School Mathematics
* other syllabuses that involve decimal numbers
* anyone who loves to exercise their minds
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