Some fractions are a part of everyday life; dimes, quarters, nickels, hours, minutes, seconds, etc. These are relatively easy to manage mainly because we deal with them so often. Everyone just “knows” that 1/2 is 0.5, and 1/4 is .25, and 1/10 is 0.1; we’ve had it ingrained in us through massive amounts of repetition. I go one step further; I can usually estimate the decimal equivalent of just about any fraction that comes up in my life. Super useful? Maybe not, but it has good show-off value, and I think it’s fun!
Joe commented below and suggested using 0.[3] to denote a 0. followed by an endlessly repeating 3. I thought it was a good idea, so I changed the text below to use it. Hope it’s not confusing.
Learning the first 12 fractions can make it super-easy to do division in your head and produce answers down to the 10ths or even 1000ths quickly and easily. Let’s take a look:
| Denominator | Values | Tips |
| 1/1 | 1 | This is the easy one, put here for completeness. It could be beneficial to remember that any non-zero number N over N = N/N = 1. |
| 1/2 | 1/2 = 0.5 | Sure, it’s simple, but it’s useful when trying to compute 1/20th, etc. |
| 1/3 |
1/3 = 0.[333] 2/3 = 0.[666] |
That’s 0.[333], where the 3s never stop, also called 0.3 repeating. And yes, 0.9 repeating does equal 1! |
| 1/4 |
1/4 = 0.25 2/4 = 0.5 3/4 = 0.75 |
Here’s the first one where just memorizing keeps you from having to reduce 2/4 = 1/2. |
| 1/5 |
1/5 = 0.2 2/5 = 0.4 3/5 = 0.6 4/5 = 0.8 |
N/5 = 0.(2*N). Note you’re really multiplying N by 2, then dividing by 10 (which just moves the decimal): 3/5 = (3*2)/10 = 0.6! |
| 1/6 |
1/6 = 0.1[6] 2/6 = 0.[3] 3/6 = 0.5 4/6 = 0.[6] 5/6 = 0.8[3] |
Ok, this one’s not so simple. It helps to realize that 0.[3] / 2 = 0.1[6], and go from there. Having 3/6 = 0.5 in the middle can help too, since 5/6 = 3/6 + 2/6 = 0.5 + 0.[3] = 0.8[3], see? |
| 1/7 |
1/7 = 0.[142857] 2/7 = 0.[285714] 3/7 = 0.[428571] 4/7 = 0.[571428] 5/7 = 0.[714285] 6/7 = 0.[857142] |
This is by far my favorite fraction. Note that in all cases, all six digits repeat, so 1/7 = 0.142857142857… Also note that the same six digits appear in the same order for all 6 fractions, you just start with a different digit. I use the fact that 14 is half 28 is half (just about) 57 to help remember the digits, too. This is the impressive one, guys. Someone asks, “what’s 1/7th of 100?” and you say “14.2857″ instantly. Nice. |
| 1/8 |
1/8 = 0.125 2/8 = 0.25 3/8 = 0.375 4/8 = 0.5 5/8 = 0.625 6/8 = 0.75 7/8 = 0.875 |
Seems like a lot to know, but most are easily computable from knowing 1/8 and reducing the rest. 5/8 = 4/8 + 1/8 = 0.5 + 0.125 = 0.625 |
| 1/9 |
1/9 = 0.[1] 2/9 = 0.[2] … 7/9 = 0.[7] 8/9 = 0.[8] |
Just take the numerator and repeat it over and over. And again, 9/9 = 0.[9] = 1. Also of note, any number N (up to 99) over 99 0.[N] too, but use both digits, so 5/99 = 0.[05], 63/99 = 0.[63], etc. This continues for 999, 9999, etc. |
| 1/10 |
1/10 = 0.1 2/10 = 0.2 … 8/10 = 0.8 9/10 = 0.9 |
These are pretty self-evident. You’re dividing by 10, so just slide the decimal place. |
| 1/11 |
1/11 = 0.[09] 2/11 = 0.[18] 3/11 = 0.[27] 4/11 = 0.[36] 5/11 = 0.[45] 6/11 = 0.[54] 7/11 = 0.[63] 8/11 = 0.[72] 9/11 = 0.[81] 10/11 = 0.[90] |
See what’s happening? N/11 = 0.[N*9] repeating, with both digits repeating (Note, 1*9 = 09 in this case). This becomes obvious when you think that 11/11 must equal 0.[9], so dividing that by 11 must divide each of those 99s in the decimal by 11 as well: 0.[9] / 11 = 0.[09]. |
| 1/12 |
1/12 = 0.08[3] 2/12 = 0.1[6] 3/12 = 0.25 4/12 = 0.[3] 5/12 = 0.41[6] 6/12 = 0.5 7/12 = 0.58[3] 8/12 = 0.[6] 9/12 = 0.75 10/12 = 0.8[3] 11/12 = 0.91[6] |
I must admit, I don’t really have these memorized. I know that 1/12 = 0.08[3] and work from there. 7/12 = 6/12 + 1/12 = 0.5 + 0.08[3] = 0.58[3], etc. Since half the values for N reduce to smaller fractions, this is where I leave off memorizing. |
There you have them, the first 12 fractions for easy memorization. Amaze your friends! Astound your kids! Become even more of a know-it-all than you already are! I joke, but I guess you’d be surprised how often I use these, I know I am.
The Count
P.S. Please excuse my use of * to denote repeating decimals, I’d be happy to hear of a better symbol, since my font doesn’t allow lines across the top of text
