This post is the continuation of my previous post Mathematics Tricks

## Division by Subtraction

**Example 1:**

340 / 85 = 4 means Quotient is 4 & Reminder is 0

Step 1: 340 – 85 = 255

Step 2: 255 – 85 = 170

Step 3: 170 – 85 = 85

Step 4: 85 – 85 = 0

Continue subtracting until it can be subtracted. Now we have 4 steps so the answer is 4 & left over(reminder) is 0

**Example 2:**

82 / 30 = 2.7333.. means Quotient is 2 & Reminder is

Step 1: 82 – 30 = 52

Step 2: 52 – 30 = 22

Here number of steps is 2 so Quotient is 2 and it Reminder is the left over 22

## Trick to Remember Square

We all know N x N is Square of the N

So how do we achieve the same square in a different way? The answer is ((N-1) x (N+1)) + 1

See for yourself from the below table 🙂

N x N | ((N-1) x (N+1)) + 1 |

1 x 1 = 1 | 0 x 2 = 0 + 1 |

2 x 2 = 4 | 1 x 3 = 3 + 1 |

3 x 3 = 9 | 2 x 4 = 8 + 1 |

4 x 4 = 16 | 3 x 5 = 15 + 1 |

5 x 5 = 25 | 4 x 6 = 24 + 1 |

6 x 6 = 36 | 5 x 7 = 35 + 1 |

7 x 7 = 49 | 6 x 8 = 48 + 1 |

8 x 8 = 64 | 7 x 9 = 63 + 1 |

… | … |

25 x 25 = 625 | 24 x 26 = 624 + 1 |

… | … |

100 x 100 = 10000 | 99 x 101 = 9999 + 1 |