Easily Convert Kilometres to Miles

This is a useful method for when travelling between imperial and metric countries and need to know what kilometres to miles are.

The formula to convert kilometres to miles is number of (kilometres / 8 ) X 5

So lets try 80 kilometres into miles
80/8 = 10

multiplied by 5 is 50 miles!

Another example
40 kilometres
40 / 8 = 5
5 X 5= 25 miles

Easy way for Converting Fractions into Decimals

With a little practice, it's not hard to recall the decimal equivalents of fractions up to 10/11!

First, there are 3 you should know already:
1/2 = .5
1/3 = .333...
1/4 = .25

Starting with the thirds, of which you already know one:
1/3 = .333...
2/3 = .666...

You also know 2 of the 4ths, as well, so there's only one new one to learn:
1/4 = .25
2/4 = 1/2 = .5
3/4 = .75

Fifths are very easy. Take the numerator (the number on top), double it, and stick a decimal in front of it.
1/5 = .2
2/5 = .4
3/5 = .6
4/5 = .8

There are only two new decimal equivalents to learn with the 6ths:
1/6 = .1666...
2/6 = 1/3 = .333...
3/6 = 1/2 = .5
4/6 = 2/3 = .666...
5/6 = .8333...

What about 7ths? We'll come back to them at the end. They're very unique.

aren't that hard to learn, as they're just smaller steps than 4ths. If you have trouble with any of the 8ths, find the nearest 4th,and add .125 if needed:

1/8 = .125
2/8 = 1/4 = .25
3/8 = .375
4/8 = 1/2 = .5
5/8 = .625
6/8 = 3/4 = .75
7/8 = .875

9ths are almost too easy:
1/9 = .111...
2/9 = .222...
3/9 = .333...
4/9 = .444...
5/9 = .555...
6/9 = .666...
7/9 = .777...
8/9 = .888...

10ths as u all know are very easy.

Just put a decimal in front of the numerator:


1/10 = .1
2/10 = .2
3/10 = .3
4/10 = .4
5/10 = .5
6/10 = .6
7/10 = .7
8/10 = .8
9/10 = .9

Remember how easy 9ths were? 11th are easy in a similar way, assuming you know your multiples of 9:

1/11 = .090909...
2/11 = .181818...
3/11 = .272727...
4/11 = .363636...
5/11 = .454545...
6/11 = .545454...
7/11 = .636363...
8/11 = .727272...
9/11 = .818181...
10/11 = .909090...

As long as you can remember the pattern for each fraction, it is quite simple to work out the decimal place as far as you want or need to go!


One-seventh is an interesting number:

1/7 = .142857142857142857...

For now, just think of one-seventh as: .142857

See if you notice any pattern in the 7ths:
1/7 = .142857...
2/7 = .285714...
3/7 = .428571...
4/7 = .571428...
5/7 = .714285...
6/7 = .857142...

Notice that the 6 digits in the 7ths ALWAYS stay in the same order and the starting digit is the only thing that changes!

If you know your multiples of 14 up to 6, it isn't difficult to, work out where to begin the decimal number. Look at this:

For 1/7, think "1 * 14", giving us .14 as the starting point.
For 2/7, think "2 * 14", giving us .28 as the starting point.
For 3/7, think "3 * 14", giving us .42 as the starting point.
For 4/14, 5/14 and 6/14, you'll have to adjust upward by 1:
For 4/7, think "(4 * 14) + 1", giving us .57 as the starting point.
For 5/7, think "(5 * 14) + 1", giving us .71 as the starting point.
For 6/7, think "(6 * 14) + 1", giving us .85 as the starting point.

Practice these, and you'll have the decimal equivalents of everything from 1/2 to 10/11 at your finger tips!
 

Temperature Conversions

This is a shortcut to convert Fahrenheit to Celsius and vice versa.

The answer you will get will not be an exact one,but it will give an idea of the temperature you are looking at.

Fahrenheit to Celsius:
Take 30 away from the Fahrenheit, and then divide the answer by two.

This is your answer in Celsius.

Example:

74 Fahrenheit - 30 = 44. Then divide by two, 22 Celsius.

So 74 Fahrenheit = 22 Celsius.

Celsius to Fahrenheit just do the reverse:

Double it, and then add 30.

30 Celsius double it, is 60, then add 30 is 90

30 Celsius = 90 Fahrenheit

Remember, the answer is not exact but it gives you a rough idea.

Adding Time

Here is a simple way to add hours and minutes together:

Let's add 1 hr and 35 minutes and 3 hr 55 minutes together.

What you do is this:

Make the 1 hr 35 minutes into one number, which will give us 135 and do
the same for the other number, 3 hours 55 minutes, giving us 355

Now you want to add these two numbers together:
135
355
___
490

So we now have a sub total of 490.
What you need to do to this and all sub totals is
 
add the time constant of 40.

No matter what the hours and minutes are,
just add the 40 time constant to the sub total.

490 + 40 = 530
So we can now see our answer is 5 hrs and 30 minutes!

Converting Kilos to Pounds

Let’s start off with looking at converting Kilos to pounds.
86 kilos into pounds:

1. Multiply the Kilos by 2.

To do this, just double the kilos.
86 x 2 = 172    ( Answer-1)

2. Divide the answer by 10.

To do this, just put a decimal point one place in from the right.
172 / 10 = 17.2 ( Answer- 2)

3.Add Answer 2 AND Answer 1

17.2 + 172 = 189.2

86 Kilos = 189.2 pounds

Let's try:

50 Kilos to Pounds:
1. Multiply the Kilos by 2.

To do this, just double the kilos.
50 x 2 = 100

2. Divide the Answer by 10.

To do this, just put a decimal point one place in from the right.
100/10 = 10

3.Add Answer 2 AND Answer 1

100 + 10 = 110

50 Kilos = 110 pounds

Shortcut to Multiplying By 12

So how does the 12's shortcut work?                                       

Let's take a look.
12 X 7

The first thing is to always multiply the 1 of the twelve by the
number we are multiplying by, in this case 7. So 1 X 7 = 7.

Multiply this 7 by 10 giving 70.


Now multiply the 7 by the 2 of twelve giving 14. Add this to 70 giving 84.

Therefore 7 X 12 = 84

Let's try another:
 17 X 12

Remember, multiply the 17 by the 1 in 12 and multiply by 10

(Just add a zero to the end)
1 X 17 = 17, multiplied by 10 giving 170.

Multiply 17 by 2 giving 34.
Add 34 to 170 giving 204.
So 17 X 12 = 204

lets go one more
24 X 12


Multiply 24 X 1 = 24. Multiply by 10 giving 240.

Multiply 24 by 2 = 48. Add to 240 giving us 288
24 X 12 = 288

Whether a Number is divisible by 4 or not ?

This little math trick will show you whether a number is divisible by four or not.

 
So, this is how it works.

Let's look at 1234

Does 4 divide evenly into 1234?

For 4 to divide into any number we have
to make sure that the last number is even

If it is an odd number, there is no way it will go in evenly.

So, for example, 4 will not go evenly into 1233 or 1235
Now we know that for 4 to divide evenly into any
number the number has to end with an even number.

Back to the question...
4 into 1234, the solution:

Take the last number and add it to 2 times the second last number

If 4 goes evenly into this number then you know
that 4 will go evenly into the whole number.

So
4 + (2 X 3) = 10

4 goes into 10 two times with a remainder of 2 so it does not go in evenly.

Therefore 4 into 1234 does not go in completely.
Let’s try 4 into 3436546

So, from our example, take the last number, 6 and add it to
two times the penultimate number, 4
6 + (2 X 4) = 14
4 goes into 14 three times with two remainder.

So it doesn't go in evenly.

Let's try one more.
4 into 212334436
6 + (2 X 3) = 12
4 goes into 12 three times with 0 remainder.

Therefore 4 goes into 234436 evenly.



You can use it in working out whether the year you are calculating is a leap year or not.

Easy Way to Divide By 9

Easy Way to Divide By 9

23 / 9 = 2 remainder 5

The first figure of 23 is 2, and this is the answer.

The remainder is just 2 and 3 added up!
43 / 9 = 4 remainder 7

The first figure 4 is the answer
and 4 + 3 = 7 is the remainder - could it be easier?

Divide by 9:

1)  61 / 9 =        remainder        

2)  33 / 9 =        remainder     

3)  44 / 9 =       remainder      

4)  53 / 9  =       remainder     

5)  80 / 9  =       remainder     


In 134 / 9 = 14 remainder 8
The answer consists of 1,4 and 8.

1 is just the first figure of 134.

4 is the total of the first two figures 1+ 3 = 4,
and 8 is the total of all three figures 1+ 3 + 4 = 8.

Divide by 9:

1)  232 =          remainder     

2)  151 =          remainder     

3)  303 =         remainder      

4)  212 =          remainder      

5)  2121 =      remainder      

842 / 9 = 8₁2 remainder 14 = 92 remainder 14

Actually a remainder of 9 or more is not usually
permitted because we are trying to find how
many 9's there are in 842.

Since the remainder, 14 has one more 9 with 5
left over the final answer will be 93 remainder 5

Divide these by 9:

1)  771 / 9  =          remainder   
2)  942 / 9  =          remainder   
3)  565 / 9 =           remainder   
4)  555  / 9 =          remainder   
5)  2382 / 9  =        remainder   
6)  7070 / 9  =        remainder   

Multiplying a number by 11.

Multiplying a number by 11.

To multiply any 2-figure number by 11 we just put
the total of the two figures between the 2 figures.

26 x 11 = 286

Notice that the outer figures in 286 are the 26
being multiplied.

And the middle figure is just 2 and 6 added up.
So 72 x 11 = 792

Try These :
Multiply by 11-
1) 43 =

2) 81 =

3) 15 =

4) 44 =

5) 11 =

In 77 x 11 = 847 

This involves a carry figure because 7 + 7 = 14

 
we get 77 x 11 = 7₁47 = 847.


Multiply by 11:
1) 11 x  88 =

2)  11 x 84 =

3)  11 x 48 =

4)  11 x 73 =

5)  11 x 56 =

234 x 11 = 2574
 
We put the 2 and the 4 at the ends.

We add the first pair 2 + 3 = 5.
and we add the last pair: 3 + 4 = 7.

Multiply by 11:

1) 151 =

2) 527 =

3) 333 =

4) 714 =

5) 909 =

An elegant way of multiplying numbers

An elegant way of multiplying numbers using a simple pattern

21 x 23 = 483

This is normally called long multiplication but actually
the answer can be written straight down using the
VERTICALLY AND CROSSWISE formula.

We first put, or imagine, 23 below 21:

There are 3 steps:

a) Multiply vertically on the left: 2 x 2 = 4.
This gives the first figure of the answer.

b) Multiply crosswise and add: 2 x 3 + 1 x 2 = 8
This gives the middle figure.

c) Multiply vertically on the right: 1 x 3 = 3
This gives the last figure of the answer.

And thats all there is to it.

Similarly 61 x 31 = 1891

6 x 3 = 18; 6 x 1 + 1 x 3 = 9; 1 x 1 = 1

Try these :

1) 14 x 21

2) 22 x 31

3) 21 x 31

4) 21 x 22

5) 32 x 21


Multiply any 2-figure numbers together by mere mental arithmetic!
If you want 21 Bottles at 26 Rupees each you can
easily find the total price in your head.
There were no carries in the method given above



However, there only involve one small extra step.
21 x 26 = 546


The method is the same as above
except that we get a 2-figure number, 14, in the
middle step, so the 1 is carried over to the left
(4 becomes 5).
So 21 Bottles cost 546 Rupees

Practise a few:

1) 21 x 47

2) 23 x 43

3) 32 x 53

4) 42 x 32

5) 71 x 72



There may be more than one carry in a sum:

33 x 44 = 1452

Vertically on the left we get 12.
Crosswise gives us 24, so we carry 2 to the left
and mentally get 144.

Then vertically on the right we get 12 and the 1
here is carried over to the 144 to make 1452.

1) 32 x 56

2) 32 x 54


3) 31 x 72

4) 44 x 53

5) 54 x 64

Any two numbers, no matter how big, can be
multiplied in one line by this method. 

Easy way for MULTIPLYING

Method for multiplying numbers where the first
figures are the same and the last figures add up to 10.

32 x 38 = 1216

Both numbers here start with 3 and the last figures (2 and 8) add up to 10.

So we just multiply 3 by 4 (the next number up)
to get 12 for the first part of the answer.

And we multiply the last figures: 2 x 8 = 16 to
get the last part of the answer.

Diagrammatically:

And 81 x 89 = 7209

We put 09 since we need two figures as in all the other examples.

Try some by Urself:

1)  43 x 47 =

2)  24 x 26 =

3)  62 x 68 =

4)  17 x 13 =

5)  59 x 51 =

6)  77 x 73 =

A quick way to square numbers that end in 5 using the formula

A quick way to square numbers that end in 5 using
the formula
BY ONE MORE THAN THE ONE BEFORE.

75² = 5625

75² means 75 x 75.

The answer is in two parts: 56 and 25.

The last part is always 25.

The first part is the first number, 7, multiplied
by the number "one more", which is 8:
so 7 x 8 = 56



Similarly 85² = 7225 because 8 x 9 = 72.


Try these:
1) 45² =

2) 65² =

3) 95² =

4) 35² =

5) 15² =

Easy way to ADD and SUBTRACT Fractions

Use VERTICALLY AND CROSSWISE
to write the answer straight down!




Multiply crosswise and add to get the top of the answer:
2 x 5 = 10 and 1 x 3 = 3. Then 10 + 3 = 13.
The bottom of the fraction is just 3 x 5 = 15.

You multiply the bottom number together.
So:




Subtracting is just as easy: multiply
crosswise as before, but the subtract:



Try a few: