How to multiply any two digits number by 11
Let’s say that you want to find the product of 36 and 11. One way to find it would be to multiply 36 by 10 and then add 36 on the result. There is, however, a simple trick that’ll do the job for any two digits number. To find out the result, write the first digit followed by the addition of the first and second digit, followed by the second digit.
What happens if the sum of the two numbers is bigger than 9? In this case you add 1 to the first number, followed by the last digit of the addition of the two numbers, and then again you add the second number
Square any two digits number that ends with 5
Calculating the square of a number below 100 is extremely simple. If you want to find the square of 25 for example, you simply have to take the first digit (2), multiply it for the next higher number (3), and then add 25 to the result.
Multiply any two digits numbers with the same first digit and the second digit that sums up to 10
Let’s say that you want to multiply 42 and 48 together. Notice that they both start with 4, and that the sum of their second digit is 10. In this case there’s a simple rule that you can use to find their product. Simply multiply the first digit (4) for the next higher number (5) and then append the product of their second digits.
Note that if the product of the second digits is below ten, you have to add a 0 in front of it.
Multiply by 9
To multiply by 9, simply multiply by 10 and then subtract the number itself.
Quickly find percentages
To find out the 15% of a number, divide it by 10 and the add half of it.
To find out the 20% of a number, divide it by 10 and multiply the result by two.
When we were at school, we have been taught how to sum two or more numbers together by using the right to left approach. With this method, you first sum the decimal part of the number, then you move to the hundreds and so on. This works good on paper, but it’s a pain when you’re doing mental calculations. Fortunately, the solution is very easy.
Left to right approach
Instead of using a right to left approach, we can start from the left and move to the right. Take the following example:
Usually, you would first sum up 4 to 45, and then and 30 to the result. But by using the left to right approach, you first sum up 30 to 45, and then you add 4 to the result. Although this example is very simple, you’ll see the advantages of this method as you start to use it.
If you’re working with three digits numbers, the process is the same.
This example is a bit more complicated than the previous one, yet it’s very easy to solve using the left to right approach. You first start by adding 600 to 459, which results in 1059. Now the problem is simplified to 1049 + 37. You simplify it even further by adding 30 to 1049, and then you finally add 7 to the result.
Like with addition, you can use the left to right approach for subtracting to numbers together. This time, however, it may feel uncomfortable to keep track of borrowings (a borrowing occurs when you subtract a number to a bigger one, like 16 – 9). Let’s see an example of this.
In this case, you first start by subtracting 10 to 64, resulting in 54, and now you only have to subtract 7 to 54. You can, however, subtract 20 to 64 and add 3 to the result. This way you don’t have to worry about borrowings.
Using complements to simplify subtractions even more
There is a way to easily calculate 3 or 4 digits subtractions very quickly in your head. This technique makes use of complements. For example. let’s say that you’re facing the following problem:
Instead of following the standard left to right approach, you could solve this problem by subtracting 400 to 674 and then add 42 back to the result. 42 is the difference from 100 and 58. A good question is: how do you find 42?
Note that there’s a simple pattern for calculating the second number. In particular, the sum of the first digits always sum up to 9, and the sum of the second digits always sum up to 10. The only exception is when the number ends with 0, which is simpler.
You can use this technique to solve any subtraction very easily.
In order to solve simple multiplications, it’s helps a lot being comfortable with the multiplication table for numbers below 10.
As you may have already guessed, we’re going to use the left to right approach to solve simple multiplication very easily. Take the following example:
We can reduce it by first calculating 30 × 7 (which is like 3 × 7 plus a 0) and then add 6 × 7 on the result.
This approach can be used for even larger numbers. Note that you can also round up instead of rounding down: