Multiply two consecutive numbers

Introduction

Ever wondered if there's a shortcut to multiply two numbers like 17 ✕18 or 49 ✕ 50? Here's a simple math trick that works only for consecutive numbers — and it's super quick! This approach will be useful while learning certain tricks that we'll be covering in our Maths tips & tricks series.

The Trick

If you want to multiply any two consecutive numbers, say n and n+1, just use this formula:

n(n + 1) = n2 + n

That's it!

Bonus: An Alternate Version of the Trick

There's another way to look at the same multiplication — starting from the larger number instead of the smaller one.

For any two consecutive numbers n and n+1, you can also use:

n(n + 1) = (n + 1)2 - (n + 1)

Why This Trick Works

This is a basic identity from algebra:

n(n + 1) = n2 + n

Because:

n(n + 1) = n × n + n × 1 = n2 + n

The alternate form works too:

n(n + 1) = (n + 1)2 - (n + 1)

As a simple algebraic expansion:

(n + 1)2 - (n + 1) = n2 + 2n + 1 - n - 1 = n2 + n

Our worksheets

Once you've learnt this trick, please do visit Practice drill on squares worksheet page and put your learnings into practice.

More Examples