Before Science, Let’s Revisit Arithmetic１ – Starting with the Distributive Property

As children, we all learned how to do simple addition and subtraction.
But when someone says “the distributive property”, doesn’t it make you go, “Wait… what?”

So before we dive into the world of science, I thought it would be a good idea to go back and take another look at the basics of arithmetic.
Who knows—it might offer us a fresh new perspective for tackling complex topics in the future.

What Is the Distributive Property?

Let’s try to understand the distributive property in simple terms.

There are two basic forms:

1.   a × (b + c) = a × b + a × c
2.   (a + b) × c = a × c + b × c

It also applies to more terms, like this:

a × (b + c + d) = a × b + a × c + a × d

Makes sense, right?

The Opposite of Distribution: Factoring

The reverse process of distribution is called factoring.

For example:

AB + AC = A × (B + C)

Simple and elegant!

Applying the Concept to Real Calculations

Let’s try applying this idea to actual numbers.

12 × 2998
= 12 × (3000 − 2)
= 12 × 3000 − 12 × 2
= 36000 − 24
= 35976

That definitely made the calculation easier!

Another one:

99 × 99＝□—99
= (100 − 1) × (100 − 1)
= 100 × 100 − 100 × 1 − 1 × 100 + 1 × 1
= 10000 − 100 − 100 + 1
= (10000 − 100) − (100 − 1)
= 9900 – 99

□= 9900

Whoa! That’s clever—and surprisingly easy!

Rethinking the Obvious

Sometimes, the best insights come when we stop taking the “obvious” for granted.
Looking at everyday math from different angles can reveal surprisingly powerful tools.

Coming Up Next: Continued Fractions!

Next, I plan to study continued fractions.
Stay tuned—this is going to be an exciting journey through the hidden beauty of numbers!

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