how to find percentages without calculator

how to find percentages without calculator

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Percentage Questions on Non-Calculator Numeracy Tests

By Colin Beveridge

When you’re reduced to working on paper on a numeracy test,
you need to know some techniques for quickly dealing with percentage questions.
Luckily, you have several ways of dealing with percentages.

Converting percentages into other forms

Converting a percentage into a decimal is as easy as converting pennies into pounds –
in fact, it’s the same sum!

If you have a two-digit percentage (such as 25%),
all you need to do is put a zero and a dot in front of the first number.
For this example, 25% is the same as 0.25.

If you have a one-digit percentage,
you have to put a zero,
a dot and another zero in front of your number –
so 9% is the same as 0.09.

how to find percentages without calculator
Colorful Sale Discount Price Tag From 10 – 50 Percent Discount Isolated on White Background

Finding a percentage

Percentage questions in non-
calculator tests tend to work with comparatively easy percentages,
and here are the steps you take to work out a number as a percentage of another, for example,
45 as a percentage of 180:

  1. Label the smaller number as the ‘part’ and the larger number the ‘whole thing.’

  2. Divide the ‘whole thing’ number by 10. This gives you 10%.

    If you’re looking for 45 as a percentage of 180, you can work out that 18 is 10%.

  3. Double your answer from step 1.

    This gives you 20% of the number. In this example, you have 36.

  4. Repeatedly add your 10% number until you go past your part number.

    Be sure to write down which percentage you’ve figured out at each stage. If you reach your number exactly,
    the percentage you got to is your answer!

  5. If the ‘part’ number is halfway between two of your answers, split the difference.

    For example, you know that 20% is 36 and 30% is 54.
    45 is halfway between 36 and 54,
    so the percentage is halfway between 20 and 30: 25%.
    This is your answer.

This method works in almost all non-
calculator percentage questions.

If you need to find a percentage of a number,
here’s what you do – for example, to find 35% of 240:

  1. Divide the number by 10 to find 10%.

    In this case,
    10% is 24.

  2. Multiply this number by how many tens are in the percentage you’re looking for –
    in this case, that’s 3, so you work out 30% to be 24 x 3 = 72.

    If your percentage number was a multiple of ten, this is your answer!

  3. If your percentage number isn’t a multiple of ten, you need to find 1%.

    You do this by dividing your answer from Step 1 by 10 again. In this case, 1% is 2.4.

  4. Multiply this number by the number of units in your answer – here, that’s 5, and you get 5% = 5 x 2.4 = 12.

  5. Add your answers from Steps 2 and 4 to get your answer.

    Here, it’s 72 + 12 = 84.

Percentage increase and decrease

Percentage increase and decrease aren’t any more difficult than simply finding percentages,
except that there’s an extra step involved. Here are some situations where you might need to work out a percentage increase or decrease:

  • A price has gone up or down by a given percentage.

  • You want to give a certain percentage of a meal price as a tip.

  • You’re given a price without tax and need to add the tax rate.

  • You’re given an investment or a loan and an interest rate.

  • You’re told that a value has gone up or down by a given percentage since the previous year.

This type of question is fairly common in numeracy tests,
and as long as you keep your head it’s quite straightforward. In this recipe,
you can work out what happens if the price of a £180 bike goes up or down by 15%. Here are the steps you take if you want to find the value after an increase or decrease:

  1. Work out the given percentage of the full price. Fifteen per cent of £180 is £27.

  2. If it’s an ‘increase’ question, add this on to the original value; this is your answer. If the price of the bike went up 15%, it would now cost £207.

  3. If it’s a ‘decrease’ question, take this away from the original value. If the price of the bike had dropped by 15%, it would now be £153. Bargain!

how to find percentages without calculator
how to find percentages without calculator

About the Book Author

Colin Beveridge, PhD, holds a doctorate in mathematics from the University of St Andrews.
He gave up a position as a researcher at Montana State University (working with NASA, among other projects) to become a full-time maths tutor,
helping adults and GCSE, A-level,
and university students overcome their fear of maths –
a position he finds ‘far more enjoyable than real work’.

What Does ‘Percent’ Mean?

It is valuable to know the origin of the term ​percent​ if you want to truly understand how to calculate a percentage. The word ​percent​ comes from the phrase per cent. ​Cent​ is a root that means one hundred,
so per cent literally means per one hundred.
For example,
if you know that 30 percent of the students in a school are boys, that means that there are 30 boys per one hundred students.
Another way to say this is that 30 out of 100 students are boys.

Generally,
the way to figure out any percentage is to multiply the number of items in question, or ​X​, by the ​decimal​ form of the percent.
To figure out the decimal form of a percent, simply move the decimal two places to the left. For example, the decimal form of 10 percent is 0.1. Then,
to calculate what 10 percent of is, say, 250 students, simply multiply the number of students by 0.1.

10 percent of 250 students =0.1×250 students=25 students 10 \text{ percent of } 250 \text{ students } = 0.1 × 250 \text{ students} = 25 \text{ students}

Some Easy Percentages to Remember

If you can commit the percentage list below to memory, you will be able to calculate a wide variety of percentages without a calculator.

50 percent​ means ​half​. To calculate 50 percent of a number, simply divide it by 2. For example, 50 percent of 26 is 26 divided by 2, or 13.

25 percent​ means ​one fourth​. To calculate 25 percent of a number, simply divide it by 4. For example, 25 percent of 12 is 12 divided by 4, or 3.

10 percent​ means ​one tenth​. To calculate 10 percent of a number, simply divide it by 10 or move the decimal point one place to the left. For example, 10 percent of 230 is 230 divided by 10, or 23.

5 percent​ is ​one half of 10 percent​. To calculate 5 percent of a number, simply divide 10 percent of the number by 2. For example, 5 percent of 230 is 23 divided by 2, or 11.5.

How to Do Percentages In Your Head

So how much is 15 percent of 210? You can use the four key percentages you memorized to figure this out.
Consider that 15 percent is 5 percent added to 10 percent. Since 10 percent of 210 is 21,
and 5 percent is half that, or 10.5,
then 15 percent is 21 added to 10.5, or 31.5.

How about 75 percent of 440? Here you can figure that 75 percent is 50 percent added to 25 percent.
Since 50 percent of 440 is half that,
or 220,
and 25 percent of 440 is one fourth,
or 110,
then 75 percent is 220 added to 110, or 330.

In this way you can combine 5 percent,
10 percent, 25 percent, and 50 percent to calculate a wide variety of percentages in your head.
If you need to calculate a percentage that is not a multiple of 5,
you can use this technique to estimate the answer very closely.

How to Compute Percentage Greater Than 100 Percent

To calculate a percentage greater than 100 percent,
simply move the decimal of the percent ​two spaces​ to the left and use the answer to multiply the number in question.
You can do this to figure out what is 350 percent of 20. Moving the decimal of the percent two spaces to the left gives you 3.5. Multiplying 20 by 3.5 then gives you the answer, which is 70.

how to find percentages without calculator
how to find percentages without calculator

How to Calculate Percentages with a Calculator

1. If your calculator has a “%” button.

Let’s say you wanted to find 19 percent of 20. Press these buttons:

1 9 % * 2 0 =
The answer is 3.8.

2. If your calculator does not have a “%” button

Step 1: Remove the percent sign and add a couple of zeros after the decimal point.
19% becomes 19.00
Step 2: Convert the percent to a decimal by moving the decimal point two places to the left:
19.00 > .1900
Step 3: Press these buttons:

. 1 9 * 2 0 =

A different type of question

19 is what percentage of 20?
Step 1: Rewrite the question as a fraction. “19 out of 20” becomes:
19/20.
Step 2: Multiply Step 1 by 100:
(19/20) * 100 = 95

Percentage

In mathematics, a percentage (from Latin per centum “by a hundred”) is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, “%”, although the abbreviations “pct.”, “pct” and sometimes “pc” are also used.A percentage is a dimensionless number (pure number); it has no unit of measuremen

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