Remember Reciprocals of Numbers with Shortcuts

Reciprocal of 1

1 → 1 = 1.0
Easy no?  Wait, it gets harder.

Reciprocal of 2

2 → ½ = 0.5
You should know this already.

Reciprocal of 3 and 6

3 → 1/3 = 0.33
Again, an easy number to remember. Remember this number for reciprocal of 6.
6 → 1/6 = 0.166
Just try to memorize this, or half the reciprocal of 3.

Reciprocal of 4

4 → ¼ = 0.25
Remember! 4 parts of 25 make a hundred!

Reciprocal of 5

5 → 1/5 = 0.2
If ½ is 0.5 then 1/5 is 0.2! Obviously!

Reciprocal of 7 and its Multiples

1 4 2 8 5 7
Remember this sequence. How to do that?
Remember that this is for 7! So 2 Times 7 is 14. 2 Times 14 is 28. 2 Times 28 is 56, but we want to end it with a 7, so let’s make it 57. But it always forms a cycle.
1/7 = 0.142857 → starts with the smallest number in the sequence.
2/7 = 0.285714 → same cycle but starts with the second smallest number in the sequence.
3/7 = 0.428571 → same cycle but starts with the third smallest number in the sequence.
4/7 = 0.571428 → starts with the fourth smallest number in the sequence.
5/7 = 0.714285 → starts with the fifth smallest number in the sequence.
6/7 = 0.857142 → starts with the sixth smallest number in the sequence.

Reciprocal of 8 and its Multiples

1/8 = 0.125
2/8 = ¼ = 0.25
3/8 = 3 × 1/8 = 0.375
4/8 = ½ = 0.5
5/8 = 4/8 + 1/8 = 0.5 + 0.125 = 0.625
6/8 = ¾ = 0.75
7/8 = 6/8 + 1/8 = 0.75 + 1.25 = 0.875

Reciprocal of 9 and its Multiples

1/9 = 0.111111…
2/9 = 0.222222…
3/9 = 0.333333…
You get the picture…  All the way up to:
8/9 = 0.888888…

Reciprocal of 10

10 → 1/10 = 0.1
Another sitter!

Reciprocal of 11 and its Multiples

1/11 = 0.090909…
Observe that the reciprocal of 09 has a recurring 11. And the reciprocal of 11 has a recurring 09.
2/11 = 0.181818…
3/11 = 0.272727…
Just like with the reciprocal of 9  All the way up to:
10/11 = 0.909090…

Reciprocal of 12

1/12 → ½ × 1/6 = ½ × 0.166666 = 0.083333…
Now learn to compound your fractions mentally.

Reciprocal of 13

1/13 = 0.076923
Notice that there is a reversed 26 and a reversed 39 (both multiples of 13) in the fraction. Lastly, ½ of 13 = 6.5, which rounded off gives us 7. Don’t forget to add that extra 0 after the decimal point! So when we write the reciprocal of 13, let us start from the right.
__ → __ → __ → 9 → __ → 3
__ → __ → 6 → 9 → 2 → 3
__ → 7 → 6 → 9 → 2 → 3
0 → 7 → 6 → 9 → 2 → 3

Reciprocal of 14 and its Multiples

1 4 2 8 5 7
And the sequence is back! With a modification!
1/14 = 0.07 142857 142857 → this time it begins with 07, followed by the sequence starting with the smallest digit.
2/14 = 1/7 = 0.14 285714 285714 → beginning with the 2nd multiple of 07, followed by the sequence starting with the 2nd smallest digit.
3/14 = 0.21 428571 428571 → beginning with the 3rd multiple of 07, followed by the sequence starting with the 3rd smallest digit.
4/14 = 2/7 = 0.28 571428 571428 → beginning with the 4th multiple of 07, followed by the sequence starting with the 4th smallest digit.
5/14 = 0.35 714285 714285 → beginning with the 5th multiple of 07, followed by the sequence starting with the 5th smallest digit.
6/14 = 0.42 857142 857142 → beginning with the 6th multiple of 07, followed by the sequence starting with the 6th smallest digit.

Reciprocal of 15

1/15 = 1/3 × 1/5 = 0.33333 × 0.2
Don’t get frightened! Multiplication by 0.2 is not as terrifying as it seems! Just multiply the number by ‘2’ and add an extra ‘0’ after the decimal point!
1/15 = 0.066666…

Reciprocal of 16

1/16 = ½ × 1/8 = ½ × 0.125 = 0.0625
Once again, you can apply cascading fractions.

Reciprocal of 17

1/17 = 0.058823
This needs rote memorization! Sorry!

Reciprocal of 18

1/18 = ½ × 1/9 = ½ × 0.111111 = 0.055555…

Reciprocal of 19

1/19 = 0.052631
What’s one more to remember?! Give this one a shot too!

Reciprocal of 20

1/20 = 0.05
Now that you have seen how to remember fractions, we’re sure you can figure this one out!
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