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Remember Reciprocals of Numbers with Shortcuts in PDF When giving exams, you need to calculate decimal equivalents of fractions quickly! If you want to succeed in Banking and Government Exams like IBPS PO, SSC CGL, SBI Clerk etc., you need to make sure that you don’t waste time calculating things manually, if you can avoid it. You will encounter such calculations in problems involving Data Interpretation, Time & Work, Pipes & Cisterns, Approximation, Probability etc. So let us look at the reciprocals of numbers till 20, and then some more! 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! 1|Page 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 2|Page 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 = 0.65, which rounded off gives us 0.7. 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 1428557 → 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|Page 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! 4|Page Liked these Shortcuts to Remember Reciprocals of Numbers? More Quant Tips, Tricks & Shortcuts here! Divisibility Tests for Quick Calculations Trick to Multiply Numbers Close to 100 Quickest Way to Solve Mensuration Problems Shortcut for Pipes & Cistern (Tank) Problems Shortcut to Find Square Root of a Number Shortcut to Find Cube Root of a Number Shortcut to Solve Compound Interest Problems Quickly Find Rate of Simple Interest 5|Page