What Are Basic Operations With Fractions?

By Staff WriterLast Updated Apr 15, 2020 1:54:28 PM ET
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Basic operations with fractions involve addition, subtraction, multiplication and division. Addition and subtraction of fractions require a common denominator before making the calculations. When multiplying fractions, the numerators and denominators are multiplied separately to get the answer and when dividing fractions, the reciprocal of the divisor fraction is used, and the fractions are then multiplied.


Addition and subtraction of fractions require a common denominator. A denominator is the number in the fraction below the line. If there is a common denominator, the numerators, the numbers above the line, are simply added or subtracted, as in this example, 1/5 + 2/5 = 3/5. If the denominator is not the same, the least common denominator of the two numbers needs to be used. The least common denominator is the smallest multiple of both denominators. In the problem 1/ 3 - 1/6 = x, the least common denominator is 6. To solve the equation, the numerator and the denominator of the first fraction are multiplied by 2. The equation then can be solved as follows: 2/6 - 1/6 = 1/6.

Multiplication is the simplest basic fraction operation to perform. The numerators and the denominators are multiplied separately: 1/3 x 5/6 = 5/18. For division, it is necessary to use the reciprocal of the divisor fraction. This simply means that the fraction is flipped. Then, the factions are multiplied, as in this example: 2/3 / 3/5 = 2/3 x 5/3 = 10/9.