Maths Made Easy

Who needs a brain?

For most people, whenever a mathematical problem arises, it’s time to get the calculator out. If there isn’t one to hand, then it’s pen and paper. If that isn’t an option, they’ll either struggle to come up with the correct answer and then stand and ponder over the solution they guessed at, or else let someone else do the working out for them.

But what about the times when it’s inappropriate or awkward or even against the rules to whip the old faithful out? Or suppose you want to calculate something secretly. For example, if you think a checkout operator or restaurant has short-changed you, and you don’t want to make it obvious to them that you are challenging their competence.

Often, it’s an embarrassing time – letting someone see you struggle with a relatively easy sum. Take for example: 15 X 8. You know it’s elementary, primary school stuff. You shouldn’t require a calculator, nor should you spend very long working it out.

Not forgetting the importance of mental exercise. Just like all the muscles in your body, the brain gets stronger with regular challenges, tasks and exercise - and conversely, the brain gets weaker through little or mundane use.

Using these techniques, your brain will be able to solve a high percentage of the number puzzles that you face on a regular basis, without the need for any of the usual crutches. All you have to do is study them, practice them and remember them,The more you practice, the more certain you are to remember the techniques.

Of course calculators are still a vital tool for any complicated numerical problem. In many professions they will always be an essential aid. But with regards to the simple, everyday stuff, (or if there isn't a calculator close by) the ability to use your own grey matter for the job comes in very handy.

It doesn't matter if Albert Einstein is not one of your ancestors. If you have a rock bottom understanding of addition, subtraction, multiplication and division, plus the desire to learn, you will be able to improve your number power using these techniques. Have fun.

N.B. Remember to ignore any decimal points or zeros when starting the calculation, then re-affix to complete the calculation.

Does it make sense?

When you arrive at a figure, you must look at it and use common sense or logic to decide if it is the final answer. It should appear obvious if the figure needs to be somewhere in the hundreds or thousands, for example. This is the final stage necessary to determine your answers in all cases.

Here goes, the first one is easy.

1. To multiply any number by 4 All you do is double it, then double it again.

Example. - 18 X 4.

First Double the 18: 18 X 2 = 36

Then Double the 36: 36 X 2 = 72

2. To multiply any number by 5 Just divide the number by 2, and then re-affix any necessary decimal points or zeroes. (Having disregarded them on starting the calculation).

Example. - 36 X 5.

First Divide: 36 ÷ 2 = 18.

Then Make sense?: 18 is obviously too small to be the answer to 36 X 5. It's clear that the answer is somewhere in the 100s. So you add a zero to the 18 and you have the correct answer – 180.

3. To multiply by 9

An easy one - Simply multiply the number by 10, and then subtract the number itself from the result.

Example. – 16 X 9

First Multiply: 16 X 10 = 160.

Then Subtract: 160 - 16 = 144

4. To multiply any two-digit number by 11. First, write the number, leaving a space in between the two digits. Then insert the sum of the two digits in between the two digits themselves.

Example. – 34 X 11.

First Write down the two digit number, leaving a gap between the two digits: 3 _4.

Then Add the two digits: 3+4 = 7.

Then Insert the sum between the 3 and the 4, which gives you the answer – 374.

You will have to ‘carry’ when the sum of the two digits exceeds 9.

Example. – 48 X 11.

First Write 4 _8.

Then Add the two digits: 4 + 8 = 12.

Then Because the two digits total more than 9, you must insert the 2, which gives you 428,

Then ‘carry’ the 1 (add it to the 4), giving the answer - 528.

5. To multiply any number by 25,

To do this, just divide the number by 4, and then add any necessary decimal points or zeroes.

Example. – 32 X 25.

First. 32 ÷ 4 = 8.

Then. Make sense? 8 and 80 both seem too small to be the correct answer to 32 X 25.

Then. Add two noughts to the 8 giving the correct answer - 800.

6. To divide any number by 25,

Here, you multiply the number by 4, and then add any necessary decimal points or zeroes.

Example. – 900 ÷ 25.

First Ignore the zeroes and multiply 9 X 4 = 36.

Then Make sense? Yes it does.

7. To multiply any two-digit number by 99,

First, subtract 1 from the number to obtain the left hand part of the answer. Then, subtract the number from 100 to get the right hand part. Sounds a bit complicated, I know. Look at the example below and it will become clear.

Example. – 15 x 99.

First Subtract: 15 – 1 =14. (left- hand part of the answer).

Then Subtract. 100 – 15 = 85. (right-hand part of the answer).

Then Put both parts together: 1,485 is the answer.

8. To multiply any two-digit numbers from 11 to 19.

Example. – 18 x 16.

First Take the whole of the higher number: (18) and add to the second digit in the smaller number: 18 + 6 = 24.

Then Add a zero to the end of the answer (multiply by 10): 240.

Then Multiply the second digits of the original sum: 8 X 6 = 48 and add it to the answer from step 2: 240 + 48 = 288

Example 2. – 430 X 9

First Ignore the zero and multiply: 43 X 10 = 430.

Then Subtract: 430 - 43 = 387

Then Make sense? It's obvious that 387 cannot be the answer as it's lower than the number you are multiplying. Add a nought and you have the correct answer - 3,870

9. To multiply by 12.

First multiply the number by 10. To that product, add twice the number to reach the answer.

Example. –35 X 12

First Multiply: 35 x 10 = 350.

Then Multiply: 35 x 2 = 70.

Then Add 350 + 70 = 420

10. To multiply by 15.

As above, first multiply the number by 10. What you do then is add half of that product to the product to get the answer.

Example 1. – 42 X 15

First Multiply: 42 X 10 = 420.

Then Divide: 420 ÷ 2 = 210

Then Add: 420 + 210 = 630

11. To multiply by 1.5, 2.5, 3,5 etc.

This is made a lot easier if you first double the 1.5, 2.5 or other multiplier and then halve the other number, before multiplying the two products. (It's a lot easier when multiplying even numbers than odd numbers).

Example 1. – 3.5 X 16

First Double: 3.5 X 2 = 7.

Then Halve: 16 ÷ 2 = 8.

Then Multiply: 7 X 8 = 56

Example 2. – 2.5 X 13

First Double: 2.5 X 2 = 5.

Then Halve: 13 ÷ 2 = 6.5.

Then Multiply: 5 X 6.5 = 32.5

12. To divide by 1.5, 2.5, 3,5 etc.

This technique is very similar to number 4. What you do hear is double both the divisor and the dividend, before dividing.

Example 1. – 28 ÷ 3.5

First Double: 28 X 2 = 56.

Then Double: 3.5 X 2 = 7.

Then Divide: 56 ÷ 7 = 8

Example 2. – 17 ÷ 1.5

First Double: 17 X 2 = 34.

Then Double: 1.5 X 2 = 3.

Then Divide: 34 ÷ 3 = 11.333 (the answer). As you can see, the even numbers work a lot easier than the odds.

13. Not forgetting - percentages.

It is common knowledge that 'percent' literally means 'for every hundred'. However, this quick way to solve any percentage problem is not so widely known. All you do is multiply the two numbers and then move the decimal point two spaces left (divide by 100). Remember to ignore any decimal points and zeroes and re-affix them at the end.

Example. – 8% of 26

First Multiply: 8 X 26 = 208.

Then Move the decimal point two spaces left = 2.08

Also it’s useful to know that you can always spin percentages and arive at the same answer, e.g. 4% of 52 is the same as 52% of 4.

Don’t forget – practice.