How do you do percentages mental math?

Sales Tax

I grew up in Washington state and our sales tax was about 8.5%. Let’s say I am purchasing an item that costs $39.95 and would like to know how much sales tax I’ll be paying.

Let’s begin by taking 10% of $39.95. Using the 10% Trick from last lesson, simply move the decimal point one position left.

At this point I know that the tax on my item will be less than $4. Suppose I want a more exact estimate. I could utilize the 1% Trick to get closer to 8.5%.

Now take 1% of $39.95.

If I subtract the 1% value from the 10% value, I will have 9% of $39.95.

That’s a pretty good estimation, but I can get even closer. I now know that 1% of $39.95 is 40 cents, if I cut this in half I can determine what 0.5% of $39.95 is.

Lastly I will subtract 20 cents from $3.60 to obtainexactly 8.5% of $39.95.

So 8.5% of $39.95 is exactly $3.40.

Pretty nifty isn’t it? With practice you’ll be surprised by how much you can do mentally!


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Finding the Percentage

The general rule for finding a given percentage of a given whole is:

Work out the value of 1%, then multiply it by the percentage you need to find.

This is easiest to understand with an example. Let’s suppose that you want to buy a new laptop computer. You have checked local suppliers and one company has offered to give you 20% off the list price of £500. How much will the laptop cost from that supplier?

In this example, the whole is £500, or the cost of the laptop before the discount is applied. The percentage that you need to find is 20%, or the discount offered by the supplier. You are then going to take that off the full price to find out what the laptop will cost you.

  1. Start by working out the value of 1%

    One percent of £500 is £500 ÷ 100 = £5.

  2. Multiply it by the percentage you are looking for

    Once you have worked out the value of 1%, you simply multiply it by the percentage you are looking for, in this case 20%.

    £5 × 20 = £100.

    You now know that the discount is worth £100.

  3. Complete the calculation by adding or subtracting as necessary.

    The price of the laptop, including the discount, is £500−20%, or £500−£100 = £400.

The easy way to work out 1% of any number

1% is the whole (whatever that may be) divided by 100.

When we divide something by 100, we simply move the place values two columns to the right (or move the decimal point two places to the left).

You can find out more about numbers and place values on our Numbers page, but here’s a quick recap:

£500 is made up of 5 hundreds, zero tens and zero units. £500 also has zero pence (cents if you are working in dollars) so could be written as £500.00, with zero tenths or hundredths.

Hundreds Tens Units Point Tenths Hundredths
5 .

When we divide by 100, we move our number two columns to the right. 500 divided by 100 = 005, or 5. Leading zeros (zeros on the ‘outside left’ of a number, such as those in 005, 02, 00014) have no value, so we do not need to write them.

You can also think of this as moving the decimal point two places to the left.

Hundreds Tens Units Point Tenths Hundredths
5 .

This rule applies to all numbers, so £327 divided by 100 is £3.27. This is the same as saying that £3.27 is 1% of £327. £1 divided by 100 = £0.01, or one pence. There are one hundred pence in a pound (and one hundred cents in a dollar). 1p is therefore 1% of £1.

Once you have calculated 1% of the whole, you can then multiply your answer to the percentage you are looking for (see our page on multiplication for help).

Mental Maths Hacks

As your maths skills develop, you can begin to see other ways of arriving at the same answer. The laptop example above is quite straightforward and with practise, you can use your mental maths skills to think about this problem in a different way to make it easier. In this case, you are trying to find 20%, so instead of finding 1% and then multiplying it by 20, you can find 10% and then simply double it. We know that 10% is the same as 1/10th and we can divide a number by 10 by moving the decimal place one place to left (removing a zero from 500). Therefore 10% of £500 is £50 and 20% is £100.

A useful mental maths hack is that percentages are reversible, so 16% of 25 is the same as 25% of 16. Invariably, one of those will be much easier to work out in our head…try it!

Use our Percentage Calculators to quickly solve your percentage problems.

How do I turn numbers into percentages?

Multiply by 100 to convert a number from decimal to percent then add a percent sign %.

  1. Converting from a decimal to a percentage is done by multiplying the decimal value by 100 and adding %.
  2. Example: 0.10 becomes 0.10 x 100 = 10%
  3. Example: 0.675 becomes 0.675 x 100 = 67.5%

How do you find the percent of a whole number?

Finding the percentage

For this type of problem, you can simply divide the number that you want to turn into a percentage by the whole. So, using this example, you would divide 2 by 5. This equation would give you 0.4. You would then multiply 0.4 by 100 to get 40, or 40%.

How do you find out the percentage? Percentage can be calculated by dividing the value by the total value, and then multiplying the result by 100. The formula used to calculate percentage is: (value/total value)×100%.

How do you calculate percentage online? To calculate a percentage of a percentage, convert both percentages to fractions of 100, or to decimals, and multiply them. For example, 50% of 40% is calculated; (50/100) x (40/100) = 0.50 x 0.40 = 0.20 = 20/100 = 20%.

3. Types of Calculations in Consulting Math

Basic Operations Add, subtract, multiply, divide – those four basic operations form the majority of calculations done by consultants. Simple, isn’t it? You do need to keep in mind however, that consultants usually deal with large numbers and a multitude of items in their calculations; that means you must be extra careful  – forgotten zeroes aren’t good for either business or case interviews.

Simple Equations Equations in management consulting context are mostly used to determine the conditions required for specific outcomes (e.g.: revenue to break even). These equations usually contain one or two variables and no power – only one step away from the most basic calculations.

Percentage Percentages are really useful to put things in perspective; effectively a fraction with a denominator of 100, percentages are often more intuitive and accurate than normal fractions (e.g.: 23% vs 3/13) The widespread use of percentages is a distinctive feature of business language: we usually say “revenue has increased by 50%” or “we need to cut costs by 20%”; we don’t usually say 1/2 or 1/5 in those contexts.

How to solve basic percent word problems

These two video lessons give examples and full solutions to several basic percentage word problems, most of which involve the concept of PART/TOTAL = PERCENTAGE.

First I present three problems that all involve a discount. The first asks for the discount percentage, the second for the discount price, and the third for the original price. Then I also solve a problem where the original price and a percentage price increase are given, and the new price is asked.

In the second video, we first find what percentage the area of one triangle is of the are of the other. Of course, to find the percentage, we simply write the fraction PART/TOTAL, and then convert that to a percentage. Then we solve a problem involving an overtime pay that is 160% of the normal.

The last problem states, “3.1 is 14% of what number?” — a typical algebra textbook problem. Essentially, we need to find the TOTAL when the part and the percentage are known. One way to do that is to use the little “formula” PART/TOTAL = PERCENTAGE. In this case, we get 3.1/x = 0.14 or 3.1/x = 14/100, and it’s easy to solve the latter equation with cross-multiplying.

Simple Interest

Suppose you invest $12,000 in a Certificate of Deposit that has an interest rate of 2.5% and plan to leave it for 5 years. Let’s calculate how much money you would earn on your investment.

For our purpose this investment is collecting simple interest. Althoughin real life, interest is usually compounded.

Compounding is the process of adding the amount you earn (or are charged) back into the principal (the amount you invested or borrowed)before the next time interest is calculated. This requires a more advanced formula than we’re ready for, so we’ll stick to simple interest today.

To compute simple interest, multiply the principal, interest rate and time in years together.

  • the principal = $12,000
  • the interest rate = 2.5%
  • the time = 5 years

We could enter this in a calculator, but that wouldn’t be practicing our mental math skills. So instead, begin by taking 2.5% of $12,000 mentally.

Step one: Find 1% of 12,000. Using the 1% Trick move the decimal point two digits left to yield $120.

Step two: Since 2% is twice that amount of 1%, double our previous answer.

Step three: To find 2.5% we need to find what half a percent is and add it to 2%. To obtain 0.5% divide the value for 1% by two.

After adding together the values for 2% and 0.5%, we have calculated that 2.5% of 12,000 is 300.

Step four: Now that we have 2.5% of 12,000 all that is left is to multiply by the number of years, which is five.

To do this mentally, split 300 into 3 x 100. Then multiply 5 x 3 together first, followed by 100.

Your investment will earn $1,500 in its lifetime.

And you could calculate it mentally while talking to your banker! How fancy!

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