# Browsing category fractions

## The Mathematical Ninja’s Rules of Fractions

The student, wisely, stammered an apology and the Mathematical Ninja pulled him back in through the window by the ankle. "But I just…" "Shht." "I mean…" "Shht." The Mathematical Ninja took a step towards the student and the student, finally shhted1. "Never," said the Mathematical Ninja, "let me catch you

## Recurring Decimals – Secrets of the Mathematical Ninja

— Thanks to Rosalind for showing me this trick. It’s one of the questions in the GCSE that looks like it ought to be easy: What is $0.1\dot{4}3\dot{6}$ as a fraction? But it’s a lot less easy than it seems at first. I’ve taught the longwinded way for years. It

Oo, a question to answer! This one’s from Deborah. How would you solve: $\frac{1}{x-2} + \frac{1}{x} = \frac{3}{4}$ and $\frac{1}{x}+\frac{1}{2x+1}=\frac{7}{10}$? When I substitute my answer back in, I can’t get it to work out! Forgive me if my working is a bit pedestrian — I figure it’s better to err

## Thirteenths (Part 3/3): Secrets of the Mathematical Ninja

The final installment, the big reveal: why does the ninja trick of multiplying by 77 and finding the nine’s complement work? My friend, that is an excellent question. The reason is this: $77 \times 13 = 1,001$. And it turns out, 1001ths are not all that hard to work out.

## Thirteenths (Part 2/3): Secrets of the Mathematical Ninja

This is the second of a three-part series about working out thirteenths. In the first part, you learned that the first step of finding thirteenths was to multiply by 77. The second part is to work out the nine’s complement of one less than your number. What’s the nine’s complement?

## Thirteenths (Part 1/3): Secrets of the Mathematical Ninja

I’ve always liked the number 13, perhaps because it’s got a bad reputation. However, until Matt Parker’s recent ZOMG tweet, I couldn’t do thirteenths in my head. If you asked me ‘what’s 7/13?’, I’d have screwed my face up and said “a bit more than a half.” Now I know.

## A Co-Proof of the Birthday Problem

“[In this context] Co- just means ‘opposite’ — so a co-mathematician is a machine for turning theorems into ffee.” — Miles () Matt Parker () laid down a challenge on Day 1 of the MathsJam conference: he said that proof by MathsJam was acceptable, because if it wasn’t true, you

## Cancelling Fractions – Secrets of the Mathematical Ninja

I was merrily ninjaing away in class the other day, teaching binomial expansion my favourite way, and found that one of the rows gave the slightly awful $$\frac{-5}{81} \cdot \frac{1}{256} \cdot 27$$ My student, quite understandably, reached for a calculator. And because one of the main attributes of a

## The secrets of the mathematical ninja: converting awkward fractions to decimals.

The true mathematical ninja gets immense satisfaction from one thing above all others: showing off. And so, when you can eyeball a messy fraction and say 'that's about...' and get it right to two decimal places or so... well, you earn the baffled respect of everyone around you, and gain

## Four fraction failures you’d be a fool not to fix

Good God, will you get your fractions sorted out? You're meant to have been on top of them since primary school, but you've been studiously avoiding them for the last half-decade, haven't you? If you'd put half as much effort into learning four simple rules as you have into convincing