Percentage using mental math

How to do percentage using mental math in 10 seconds

The concept of percentages is applicable in various day-to-day operations of our lives. May it be, filling taxes, computer loading screen, restaurant bill tip or calculating interest rates, It just everywhere. Hence, It becomes important for an indivdual to be well versed in doing percentages quickly. Students with learning disorders, specially dyscalculia, are often seen having trouble doing percentages. Usually, they mess up numbers,decimals and symbols.

There is a fine line between ‘too hard’ and ‘that’s so easy’ in solving percentages. It all depends upon how you see the question. If you have strong mental math capabilities, then its a cake walk for you. However, It couldn’t be expected from everybody. In such cases, practicing mental math for percentages is the best option. A good thing about practicing percentages is that the learner will also enhance their mental math abilities for several other math operations, such as multiplication and division.

Keeping this in mind, We brought you easy ways to do percentages. So easy that you don’t have to pick pen or paper after practicing it for couple of times. With persistence efforts, you will reach a level where you will be able to do it within 10 secs.

A little about Percentages

Before diving a little deep into the concept. First, we got to know what percentages is ?

The word ‘percent’ suggests the part/section/portion of something. It could be anything. So, when we say the percentage of water in a glass, then that means the portion of the glassis filled with water. Similarly, when we say our savings is around 10 percent, then it means out of salary (100%), we save 10% and rest 90% is spent.

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In practical terms,

  • 100% means the whole complete thing
  • 75% means 3/4th amount of the thing
  • 50% means Half of the thing
  • 25% means 1/4th of thing
  • 10% means 1/10th of the thing
  • 0% means no amount of the thing

It is advised that above given percentages must be memorized as these are used very often. Other percentages can be derived from these easily. We can go beyond the hundred percent also

200%, 300%, 400% means the double, triple, quadruple respectively and so on.

Rest calculating percentage is just the game of how you want to simplify the number? In all, it rests on how you approach the question.

Let’s talk about different approach to simplify the question by taking different examples

1.) Nearest to the milestone

’50’ and ‘100’ are considered milestone numbers. This approach works best for calculating percentage near to these numbers, say upto +5 to -5 to the milestones.

Let’s take the 51% of 140.

Here, the milestone will be 50. From the question, percentage value is 1 more than the milestone. So, we will rearrange it as follow:

51% of 140

= (50 + 1) % of 140

Here, 51% of 140 will be equal to the addition to the 50% of 140 and 1% of 140.

As we know already that 50% is just half of the number and rearranging zeroes of 1% to 140 will give 1 x 1.4

The answer becomes = (50% of 140 + 1% of 140) => 70 + 1.4 => 71.4

Let’s take another example of 97% of 208.

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Here, the milestone will be 100. From the question, percentage value is 3 less than the milestone. So, we will rearrange it as follow:

97% of 208

= (100 – 3)% of 208

Here, 97% of 208 will be equal to the subtraction between the 100% of 208 and 3% of 208.

As we know already that 100% is complete whole of the number and rearranging zeroes of 3% to 208 will give 6.24 (3 x 2.08).

The answer becomes = (100% of 208 – 3% of 208) => 208 – 6.24 => 201.76

2.) Break It up

It is better to break the numbers in the percentages that are not covered in milestone approach. Breaking the numbers simplify it to a great extent. Numbers should be separated as such that we use as much milestones as we could to reach the number. Let us take an example to understand it better

Let us take an example of 382% of 150

Here, we will break 382 into smaller numbers as such that their addition equals 382.

382 => (300 + 80 + 2)

Further simplifying it,

=> (100 + 100 +100 +100 – 20 +2)

=> (100+100+100+100 -10 -10 +2) % of 150

As we know, 100% is complete of the number, 10 is 1/10th of the number and 2 is 1/50th

=> (150 + 150 + 150 + 150 – 15 – 15 + 3)

=> (600-30+3) => 573

This does look like a lot of work on paper. But, once you get a good hold of this by practicing daily than It will be a matter of just seconds.

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3.) a% of b = b% of a

This is pretty basic concept of percentage. It depends upon your comfortability with the arrangement of the operation. This, alongwith milestone break up method, can really make the question so easy.

Let us take the example of 38% of 400

This can also be written as, 400% of 38,

We already discussed that 400% means quadruple of the number.

So, 400% of 38 = 4 x 38 = 152

Upping one level, we will now solve 187% of 350

This can also be written as, 350% of 187,

We will further divide the 350 into smaller numbers as per the milestone breaking method,

350% of 187 => (300 +50)% of 187

=> (100+100+100+50)% of 187

=> (187 + 187 + 187 + 93.5)

=> 654.5

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