In this tutorial on Mathematical shortcuts, and over the course of next few articles, we will focus on division. In the previous tutorial, we saw how to divide a number when the divisor ends in digit 9 and digits ending in 8. Here, we will discuss how to divide a number when the divisor ends in digit 1.

Again, we will break the discussion into 2 parts. You can refer to the second part of the discussion here.

Let us understand the shortcut with an example. Consider the simple division 42รท131.

**Step 1 :** The first step, subtract both the numerator and the denominator by 1.

**Step 2 :** This is where the division steps changes. Notice the division is similar to long division. When 87 is divided by 13, we get a quotient of 6 and a reminder of 9. In a long division method, you would put a zero in-front of 9 to continue the division.

However, when using this shortcut, instead of putting a zero, you would **subtract** the last quotient from 9 and append the difference to the reminder to continue the division. Notice the difference between the long division on the left and the shortcut on the right.

## Long Division Method |
## Shortcut technique |

Notice the first step, when 41/13, you get a quotient of 3 and reminder 3. In the second step, the difference ( 9 โ quotient) is appended to reminder 2 to get 26.

**Step 3 :** This step is continued and at each step, the last quotient is appended to the reminder and the added to the number to continue the division process.

Very easy right ๐

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**Example 2 :** Let us consider another example, Divide 234/241

**Solution : Step 1 :** Reduce 234รท241 as follows :

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**Step 2 :** Now divide 23.3 by 24 like normal division, instead of putting a zero in each step, the last quotient is subtracted from 9 and is appended to the reminder to continue the division process as shown.

Try yourself :

Divide the following:

- 51/131
- 132/151
- 162/251
- 21/31
- 53/321

I hope, you find this article very useful. If you have any doubts or have any comments concerning this tutorial, Please leave a comment or contact me. I would be glad to help.

Good content! Please allow me to re-post to my site. Thanks! ๐

Wacks Formula