Mathematical nuggets of information

MATHEMATICAL NUGGETS OF INFORMATION

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TIPS

To calculate the total of a bill including tax add 1 before multiplying.

Example 1 Price 150.95 plus tax of 0.065

Multiply 150.95 x 1.065 = 160.76

This also works in reverse -

160.76 divided by 1.065 = 150.95

Example 2 Price 150.95 plus 17.5% tax

Multiply 150.95 x 117.5% = 177.37

In reverse -

177.37 divided by 117.5% = 150.95

Thanks to KB for this one.

What this is actually doing is acknowledging the original figure is 100% and then adding on the additional percentage or (in this case) tax figure, giving a combined total as an answer.

Anything ending in an "even" number is divisible by 2.

Anything divisible by 9 is also divisible by 3.

Thanks to KB for these.

A quick way to do calculations is to drop the noughts at the ends of the numbers then replace them for your final answer.

Example - To add 120 + 90 add 12 + 9 = 21 then add back the 0 = 210

If you have to multiply a large number by 25, add two noughts to the number then divide by 4. This is much easier to do, especially mentally.

Example: 167 x 25 16700 Divide by 4 = 4175

When faced with a little poser like 27.5% of 50 for example, I find it easier to call it 50% or 27.5. It is easier to mentally divide 27.5 by 2. It works every time.

Thanks for these Harvey Alexander

When multiplying numbers ending in 5 by themselves e.g. 75 x 75

Deal with the left hand numbers first

In this example the left-hand number is 7

Add 1 to this number i.e. 7 + 1 = 8

Multiply the original number 7 x the new number 8 = 56

Now deal with the right-hand numbers which are always 5 x 5 = 25

Therefore the answer is 5625

Here is another example -

35 x 35

3 + 1 = 4

4 x 3 = 12

5 x 5 = 25

Answer 1225

Thanks to Allan Brown for this contribution

To make complex sums easier to handle, break down into simpler elements.

Example: 6 x 348

first multiply	6 x 300 = 1800
then	6 x 40 = 240
then	6 x 8 = 48
Then add up all the elements:-	2088

A quick way to convert kilometres to miles is to drop the last digit and multiply by 6.

Example: 72 kilometres = 7 x 6 = 42 miles (approximately)

10² means 10 x 10 (known as 10 squared)	= 100
10³ means 10 x 10 x 10 (known as 10 cubed)	= 1,000
10 (with a little 4 - I couldn't find the symbol) means 10 x 10 x 10 x 10 (I think is known as 10 to the power of 4) 10 to the 4th power - Thanks Brenda	= 10,000
10 (with a little 10) means 10x10x10x10x10x10x10x10x10x10	= 10,000,000,000 (1 followed by 10 noughts)

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