Arithmetic Computation - Six Easy Ways of Performing Arithmetic Computations

Maybe you have been wondering why your colleagues perform arithmetic computations faster than you do. You might think you are not good at doing it. You are rather not informed that there are easy ways of doing that. In my country, Ghana, most people do not like arithmetic computation with the reason that it is difficult. On the contrary, I stand to say that, it is not because it is difficult, it is because most people are not informed that there are ways to make arithmetic computations very beautiful and lovey. See this article as an introduction to the field that I think is worth promoting to entice basic school kids to like mathematics. The following ways might be awesome to you:

1. Multiplication of numbers from one to ten by nine.

See these computations below:

9 × 1 = 09

9 × 2 = 18

9 × 3 = 27

9 × 4 = 36

9 × 5 = 45

9 × 6 = 54

9 × 7 = 63

9 × 8 = 72

9 × 9 = 81

9× 10 = 90

Look at the answers critically from top to bottom. What can you see? Can you see that the first digits (the tens) in the answers increased from zero (0) to nine (9)? I hope you can see also that the second digits (ones) in the answers also decreased from nine (9) to zero (0) by looking at them from top to bottom as well. Can you see that? Awesome! Isn’t it? You can also do it this way; 9 × 1 = 09. When you want to compute 9 × 2, subtract 1 from the second digit in the answer just above it. In this case, subtract 1 from 9 in 09 and add it to 0 in the same 09. That is, 9 × 2 = 18 and so on. Simply put, to compute 9 × n (where 0 < n < = 10 , n an integer), subtract 1 from the unit digit in the answer for 9 × (n - 1) and add it to the tens digit in the answer for the same 9 × (n - 1)

1. 2. Multiplying numbers by 11

It should be noted that a single digit number apart from zero, when multiplied by 11 is double the number. For example 9 × 11 is 99. what happens if the number is not a single digit? In this page, let us look at double digit numbers. Using the calculator to compute 52 × 11, the answer is 572. How can you amaze your friends with this arithmetic computation without the use of a calculator? You can easily do this with the use of the formula below:

AB × 11 = A (A + B) B where A and B are the digits that make up the number, where the space occupied by A+B must by occupied by a single digit. When A + B is equal to ten or greater, the first digit (the tens) in the answer is carried forward to A. This means that 52 × 11 = 5 (5+2) 2 = 572. Also, 98 × 11 = 9 (9+8) 8 =9 (17) 8 but since 17 is greater than 10, we carry the first digit (the tens) which is 1 in the brackets and add it to 9 (in front of the bracket) making it 10. So the answer becomes 1078. Awesome! Isn’t it? You can use this to amaze your friends everywhere!!

Note: Numbers with more than two digits can also be calculated in the same way but it is only cumbersome. You will see it on later days.

1. 3. Multiplying a number by 5

Sometimes it is time wasting trying to divide a number by 5. You can make it easier by sticking to this formula; let the number be A.

A × 5 = (A × 10) ÷ 2. So for example 26 × 5, this can be computed arithmetically as;

(26 × 10) ÷ 2 which become 260 ÷ 2 and it is simpler to now state the answer as 130. Also 120 × 5 can be computed as (120 × 10) ÷ 2= 1200 ÷ 2 = 600.

Again decimal numbers can also be computed in the same way. For example, 0.04 × 5 =(0.04 × 10) ÷ 2 = 0.4 ÷ 2 = 0.2.

NOTE: 0.04 × 10 = 0.4 (since 10 has one zero, the decimal point is run once to the right)

1. 4. Dividing a number by 5

This in a way, is a reverse of the above; to divide a number by 5, stick to the formula below;

Let the number be A

A ÷ 5 = (A × 2) ÷10. For example, 36 ÷ 5 = (36 × 2) ÷ 10 =72 ÷10 =7.2.

Also, decimals can also be computed arithmetically in the same vain; for example, 0.34 ÷ 5 =0.68 ÷10 = 0.068. it is amazing. Isn’t it?

1. 5. Multiplying double digit numbers ranging from 10 to 19

I have my own way with which I compute double digits numbers ranging from 10 to 19. It has been working for me and I believe you will also enjoy it. To multiply two numbers ranging from 10 to 19;

1. Add the second digits in each of the two double digit numbers
2. Add the result to 10
3. Add a zero to the back of the answer as if to make it 100
4. Find the product of those second two digits in the two numbers
5. Add the result in D to the result in C

For example, we want to multiply 16 by 13

We add 6 and 3 and the answer is 6. We then add the 9 to ten making 19. We we suffix 19 with 0 making it 190. We find the product of 6 and 3 which is 18. We then add this 18 to 190 making it 208. Therefore, 16 × 13 = 208.

Also, for 14 by 17, we add 4 and 7 and that gives 11. We add 11 to 10 and that becomes 21. We then suffix 21 with a 0 and it becomes 210. Now, we find the product of 4 and 7 which is 28. We finally add 28 to 210 and it results in 238. Therefore, 14 × 17 = 238. You can use the procedure to compute numbers arithmetically and very fast if you keep practicing it for some time. I actually started doing this at a slow pace, but I can now give out the answer in a few seconds. They say “practice makes man perfect”.

1. 6. Finding the square of a number ending with a 5

You might find this also very amazing. To find the square of a number such as 25, ignore the 5. Multiply the 2 by the number after it as it comes when counting. That is 2 × 3 and the answer is 6. We then place 25 at the back of 30 which becomes 625. Also, to find the square of 65, we drop the 5. We then multiply 6 by 7 which gives 42. We then attach 25 to the back of 42 and that becomes 4225.

There is something about arithmetic that people forget of. That is constant practicing. Do practice arithmetic computations at your own leisure time.

I have been researching on ways to make arithmetic computations very interesting especially to kids in the basic and high schools. This will, in a way, reduce the problem of hatred for maths. The video below is also an insightful one and is very helpful.