Do arithmetic on two fractions and get the answer in lowest terms, as a mixed number and as a decimal. The converter works the other way too, turning a decimal into the simplest fraction that represents it rather than a technically-correct monster like 333333/1000000.
You can only add parts of the same size, so both fractions need a common denominator first. Multiplying the two denominators always produces one: 1/2 + 1/3 becomes 3/6 + 2/6 = 5/6. Using the lowest common denominator instead just saves you reducing at the end.
Dividing by a number is the same as multiplying by its reciprocal. Dividing by 1/2 gives twice as much because the question is "how many halves fit in this", and two do. So 3/4 divided by 1/2 is 3/4 x 2/1 = 3/2.
Multiplying by a power of ten and reducing turns 0.333333 into 333333/1000000, which is technically correct and useless. The continued-fraction method finds the simplest fraction within a tolerance, giving 1/3. The same method turns pi into 355/113 - accurate to seven decimal places, and known to Chinese mathematicians in the fifth century.
Put them over a common denominator first, then add the numerators. Multiplying the denominators together always works: 1/2 + 1/3 becomes 3/6 + 2/6 = 5/6. Using the lowest common denominator instead just saves reducing afterwards.
By using continued fractions, which find the simplest fraction within a tolerance rather than the literal decimal expansion. The same method gives 355/113 for pi - an approximation accurate to seven decimal places that has been known since the fifth century.
Dividing by a number is multiplying by its reciprocal, and the reciprocal of 2/3 is 3/2. Dividing by 1/2 gives twice as much because you are asking how many halves fit, and two do.
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