Introduction:

If 1 bowl of rice is cooked in 2 and a half bowls of water, how much water is required to cook 3 and a half bowls of rice? In real life and the pace at which modern world operates, students need to know how to convert fractions to decimals and vice versa. In today’s real world, fractions less than 1/8 are not generally used except in very specific fields like wood working. If the beginners are familiar with the eights, they are through to most of the calculations they come up in the day to day tasks. Before computers and calculators, 1 or 2 digit fraction calculations were easier than performing computing 3 or more digit decimals. Presently, the practical world demands mathematicians, engineers, and scientists to work with English system fractions. Therefore, to assist these professionals and also beginners or students, mixed fraction calculators nowadays, are available in the form of web applications, desktop software and even as mobile or tablet apps. These calculators offer math calculations with mixed numbers (mixed fractions) allowing to perform operations on fractions, whole numbers, integers, proper fractions and improper fractions. The mixed numbers calculator also has the capability to add, subtract, multiply and divide mixed numbers and fractions.

Generally, the online versions of the calculators handle simple operations on whole numbers, integers, mixed numbers, improper and proper fractions by adding, subtracting, dividing or multiplying. The answer is provided in a reduced fraction and a mixed number if the conversion allows.

The Algorithm:

The mixed fraction calculators add mixed number using the adding fractions formula. It includes firstly, conversion of mixed numbers to improper fractions. Then use the algebraic formula i.e. ‘a/b +c/d = (ad+bc) / bd’,  for addition of fractions. The last step involves expression reduction and simplification if possible. Similarly subtracting mixed numbers also involves the conversion of mixed number to an improper fraction, applying the algebraic formula ‘a/b -c/d = (ad-bc) / bd’ and at last simplifying the expression. The multiplication operation also involves the mixed fraction to improper fraction conversion. Then the algebraic formula ‘a/b * c/d = ac / bd’ is employed to multiply fractions, and finally, reduction and simplifications are done if required. Last but not the least, division operation in mixed numbers calculators is performed using the dividing fractions formula. As done in the other three arithmetic operations earlier, the initial step involves mixed fraction to improper fraction conversion. Then the algebraic formula of division of fractions i.e. ‘a/b ÷ c/d = ad / bc’ is used. The final step involves simplification process as previously done. The simplification process performed by the software calculators involves a code that utilizes Euclid’s theorem for reducing fractions.

Real world applications:

Mixed numbers or fractions are used in every walk of life, all round us. For example, for a carpenter the problem could be like while building a wooden house and framing the walls, the outer wall is 30  Feet long, and he wants to put a stud every 1 foot, 6 inches. How many studs would be needed for this particular job? Students at a beginner level are taught these operations by problems that involve the division of cake pieces or pizza slices. That makes it easier for them to proceed towards complex problems.