A fraction is a numerator over a denominator: 3/4 is three of four equal parts. The calculator works exactly, on whole numbers, never on rounded decimals, and always gives the answer in lowest terms, as a mixed number and as a decimal.
Adding and subtracting need a common denominator. The smallest one is the lowest common multiple of the two denominators: for 3/4 + 5/6 it is 12, so the sum is 9/12 + 10/12 = 19/12, which is 1 7/12. Multiplying needs none, since you multiply the tops and the bottoms: 3/4 × 5/6 = 15/24 = 5/8. Dividing is multiplying by the reciprocal: 3/4 ÷ 5/6 = 3/4 × 6/5 = 9/10.
Mixed numbers such as 2 1/4 are turned into improper fractions first (9/4), which is where most hand-worked mistakes happen. Type them with a space between the whole number and the fraction. A negative sign in front applies to the whole mixed number: −1 1/2 is −3/2.
Decimals. A terminating decimal is an exact fraction over a power of ten: 0.625 = 625/1000 = 5/8. A rounded decimal is not: 0.333 is 333/1000, not 1/3. For those the decimal panel also shows the nearest fraction with a denominator up to 64, the resolution of an inch ruler, so 0.3125 reads as 5/16 and 0.333 as 1/3.