Fractions can take two forms, and whichever form you use, you can use your calculator or your notepad to find two-thirds of a number. For example, you can write two-thirds in fractional form – 2/3 – or as a decimal – 0.667 – and either way, you calculate two-thirds of a number by multiplying by that number. The operations are equivalent, although if you're using your notepad, you may prefer to use the fractional form.
Type in two divided by three and press the equals sign on your calculator. You should receive a decimal similar to 0.666 repeating.
Press the multiplication sign and type in the number of interest. For example, if you are finding two-thirds of 100, after you press multiplication sign type in "100." Then press the equals sign.
Interpret your result. If you have 66.66 repeating, then you may wish to round this to the tenths place of 66.7. Thus, two-thirds of 100 is approximately 66.7.
Divide the number of interest by 3. If you are finding two-thirds of 60, then first divide 60 by 3. You will get the number 20 as your result.
Round your result to the tenths place. In some cases, you may get a repeating decimal and it may be easier to use a smaller approximation. For instance, if you divide 250 by 3 you get 83.333 repeating. You may want to use 83.3 as your result instead of the entire decimal.
Multiply the result by 2. If you have 20 as your result, then 20 times two is 40. Therefore, two-thirds of 60 is 40. By the same token, two-thirds of 250 is 83.333 x 2 = 166.667.
TL;DR (Too Long; Didn't Read)
You can also multiply by two first and then divide your result by three, when calculating two-thirds by hand.