8 Math Tricks for Quick Calculations in Your Head

No matter where you go, you will always see mathematicians being used as calculators by their friends. However, digging deeper, you will find that most mathematicians aren’t great at arithmetics.

I can never forget in university; my math professor would solve these complex problems and solve them until he got to the algebraic portion. Looking at the incomplete problem, he would say, “We did our job; the rest is for the engineers to solve.” Not once did I see that teacher complete an entire question.

These days, complex calculators are made for engineers, but we see that even at the elementary level, students are using calculators for simple arithmetic processes. Despite this, many arithmetic problems can be solved using simple tricks, often even faster than a calculator.

Doing arithmetic in your mind is also helpful in training your brain. After doing arithmetic in your head, you will start to feel that your brain is under serious strain. You can also learn mathematical magic with your kids using the techniques below. [For further reading, you can get Arthur Benjamin’s Secrets of Mental Math]

Before I start, this article is not for the mathematicians among you. I would appreciate it if you did not sound like Albert Einstein in the comments below.

Multiplying a number by 11

There are two tricks to multiplying a number by 11. The first method is: Multiply the number by 10 and then add our result to our original number.

For example, let's try (333 x 11) and (15 x11)

10 × 333 = 3330 and 3330 + 333 = 3663

15 x 10 = 150 ve 150 + 15 = 165.

In the second example, you will notice a neat occurrence. The “6” in the tens place is just the addition of the 1 and 5 in the number being multiplied. Simply, we just wrote “1 + 5 = 6” in between 1 and 5.

We can write this occurrence as a rule: when multiplying a two-digit number by 11, we write the addition of the digits in the number in between the digits.

Let's try another example and multiply 11 and 22.

2+2=4. Therefore 22 x 11 = 242.

However, this rule does not always work, as in the example of 88 x 11, where 8+8=16, a two-digit number. Therefore, we can amend this rule: We will add the first digit in the middle and 1 to the digit on the left.

For instance, you can apply this rule when you multiply 88 and 11.

88 x 11 => 8 + 8 = 16 and (8+1) 6 8 => 968.

Multiplying a number by a number with one in the ones place

For this trick, we will use a simple approach. Let’s take 62 x 21 as our example. First, let’s multiply 62 x 2. Then we can add a 0 at the end of the number we get. Finally, we will add 62 to the final number.

To find 62 x 21:

62 x 2 = 124.

Add a zero to the end, 1240. 

Finally, add 62 to it; 1240 + 62 = 1302.

Multiplying a number with a number with 5 in the ones place

Multiplying any number ending in 5 is significantly harder than multiplying one ending in 0. Therefore we will get our result by multiplying half of what we want to multiply with double what we want to multiply it by. I will clarify this process with an example.

Let's try 36 times 25.

First, we take half of 36, which is 18. 

Then we take double of 25, 50. It is much simpler to multiply these two.

In other words, 36 x 25 = 18 x 50 = 900.

Multiplying a number by 15

To get the same answer as multiplying by 15, we can replace the number with one that we can multiply by 10, then add half of the number back to itself, and then multiply it by 10.

Let’s try with an example and multiply 24 and 15.

24 x 15 = [24 + (24/2)] x 10 = (24 + 12) x 10 = 36 x 10 = 360.

As you can see, we add half of 24 to itself, then multiply the answer by 10, getting 360.

While it looks like witchcraft, the above technique is simply logic put into use. If you think about it, 15 is just half of 10 added to 10. Therefore if you do the same process to what you want to multiply, you can multiply it by 10.

Now let’s try this method on larger numbers:

62 x 15 = (62+31) x 10 = 93 x10 = 930

122 x 15 = (122 + 61) x 10 = 183 x 10 = 1830

37 x 15 = ( 37 x 18.5) x 10 = 55.5 x 10 = 555

Multiplying a number by 45

Using logic, we know that 5 is one-tenth of 50. Therefore, to multiply a number by 45, first, we will multiply it by 50, then take out one-tenth of it.

For example, let’s try 24 x 45.

24 x 50 = 1200. 

One-tenth of 1200 is 120. Thus,

1200–120 = 1080.

Multiplying a number by 55

Multiplying by 55 is the exact opposite of multiplying by 45. Where in 45, you take out one-tenth; in 55, you add one-tenth.

For example let’s do 24 x 55.

24 x 50 = 1200. 

One-tenth of 1200 is 120. 

Therefore 1200 + 120= 1320.

Multiplying a number by 9

Because 9 is one less than 10, if you multiply a number by 10, then take out the number from the result, you will get your answer. For example:

12 x 9 = [12 x (9+1)] - 12 = 120 -12 = 108.

145 x 9 = [145 x (9+1)] - 145 = 1450 - 145 = 1305

Multiplication of two-digit numbers ending in 9

You can also use the same method we used for numbers ending in 1 here. Replace the multiplier with one that ends in 0, and multiply by the tens place of the multiplier. Now do the reverse of this method and subtract the multiplied from the answer.

32 x 19 = [32 x (19+1)] - 32 = (32 x 20) - 32 = 640 - 32 = 608

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