Adding and Subtracting Fractions and Decimals

Change everything into one form first, then calculate. For 3/5 + 0.75, either turn the fraction into a decimal, 3/5 = 0.6, and add: 0.6 + 0.75 = 1.35; or turn the decimal into a fraction, 0.75 = 3/4, and add 3/5 + 3/4 = 12/20 + 15/20 = 27/20, which is also 1.35. Subtracting works the same way.

Decimals are usually faster, because you can add or subtract them directly. Fractions are better when a fraction does not make an exact decimal: 1/3 and 1/7 give long recurring decimals, so the decimal route would mean rounding. Check the fractions first: if every one converts exactly, use decimals; if not, convert everything to fractions.

Convert the decimal into a fraction instead, so nothing is rounded. For 1/3 + 0.25, write 0.25 as 1/4; the common denominator of 3 and 4 is 12, so 1/3 = 4/12 and 1/4 = 3/12, and the answer is 7/12. Working in decimals would mean 0.333… + 0.25, which can only be written approximately.

Combining the decimals you can in one step leaves fewer numbers to convert. In an expression such as 1/3 + 0.55 − 0.3, subtract 0.3 from 0.55 first to get 0.25; it becomes 1/3 + 0.25, which needs one conversion and one addition instead of two. Then convert 0.25 to 1/4 and add to get 7/12.

Because the denominator says how big each part is, and you can only add parts of the same size. Fifths and quarters are different sizes, so 3/5 + 3/4 cannot be added as they are. A common denominator is a shared one: the lowest common multiple of 5 and 4 is 20, so 3/5 = 12/20 and 3/4 = 15/20, which add to 27/20.