What are the reciprocals of 1, 2, 3, 4, 5, 6, 8, 9, 10?
1, 1/2, 1/3, 1/4, 1/5, 1/6, 1/8, 1/9, 1/10
What are the decimal values of these reciprocals?
| Fraction | Decimal | Think |
| 1 | 1 | |
| 1/2 | 0.5 | |
| 1/3 | 0.333… | Each 3 comes from 10/3 with 1 left over which becomes 10/3 |
| 1/4 | 0.25 | 4 quarters in a dollar |
| 1/5 | 0.2 | 20 nickels in a dollar 1/5 = 2/10 = 2 x 0.1 |
| 1/6 | 0.16666… | 1/6 = 1/2 of 1/3 32/2 = 16, but there is a little more it is the 6 that keeps repeating |
| 1/8 | 0.125 | 1/8 = 1/2 of 1/4 25/2 = 12.5 |
| 1/9 | 0.111… | 1/9 = 1/3 of 1/3 0.333… / 3 = 0.111… |
| 1/10 | 0.1 |
Why is 7 not included?
The decimal expansion of 1/7 = 0.142857… repeats six digits which is much more complicated than the others. It is helpful to recognize that 1/7 is approximately 14%.
What is the decimal value of 2/3?
2/3 = 0.666… which is just 0.333… doubled.
What is the decimal value of 3/4?
0.75
1/4 is 0.25, just like a quarter equals 25 cents. Three quarters is 75 cents.
What are the decimal values of 2/5, 3/5, and 4/5?
1/5 = 0.2
Multiplying 0.2 by 2, 3 and 4, gives 0.4, 0.6 and 0.8, respectively.
You could also multiply the top and bottom of each fraction by 2 to get 4/10, 6/10 and 8/10, respectively.
What are the decimal values of 2/6, 3/6, and 4/6?
2/6 = 1/3 = 0.333…
3/6 = 1/2 = 0.5
4/6 = 2/3 = 0.666…
What are the decimal values of 2/8, 3/8, 4/8, 5/8, and 6/8?
2/8 = 1/4 = 0.25
3/8 = 3(0.125) = 0.375
4/8 = 0.5
5/8 = 5(0.125) = 0.625 (Think 5(25) = 5(4+1) = 100 + 25. 5(0.125) = 5(0.1 + 0.025)
6/8 = 3/4 = 0.75
What are the decimal values of 2/9, 3/9, 4/9, 5/9, 6/9, 7/9, and 8/9?
1/9 = 0.111…
Multiplying 0.111… by 2, 3, 4, 5, 6, 7, and 8 gives 0.222…, 0.333…, 0.444…, 0.555…, 0.666…, 0.777…, and 0.888…, respectively. This is consistent with 3/9 = 1/3 and 6/9 = 2/3
Which is greater, 3/5 or 5/8?
3/5 = 0.6, 5/8 = 0.625
16% is approximately what fraction?
1/6 = 0.1666…
What is 8/3 as a decimal?
8/3 = 6/3 + 2/3 = 2 + 0.666.. = 2.666…
Why is this important?
You will greatly benefit from being able to rapidly do all of these fractions in your head.
It is easiest to compare fractions by converting to decimals.
It is often helpful to think of percents as fractions or fractions as percents.
Once you know these, you can do improper fractions as well.
CoMo Science 
Leave a comment