Mental Math Tricks by Kevin OConnor - HTML preview

Decimals Equivalents of Fractions

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.

 

8ths 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:

 

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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 are very easy, as well. 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 http://www.memorymentor.com/

 

the decimal place as far as you want or need to go!

 

Oh, I almost forgot! We haven't done 7ths yet, have we?

 

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!

If you want to demonstrate this skill to other people, and you know your multiplication tables up to the hundreds for each number 1-9, then give them a calculator and ask for a 2-digit number (3-digit number, if you're up to it!) to be divided by a 1-digit number.

If they give you 96 divided by 7, for example, you can think, "Hmm... the closest multiple of 7 is 91, which is 13 * 7, with 5 left over. So the answer is 13 and 5/7, or: 13.7142857!"

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