Adding Mixed Numbers with Different Denominators

Adding and subtracting mixed numbers can become complicated when the fractions have different denominators, such as 7 3/4 + 2 1/5. One way to solve this equation is to convert each side of the equation into one improper fraction by multiplying the denominator by the whole number and add the numerator. Using the previous example, (4*7) + 1 = 31. This gives you 31/4 for the first improper fraction. (5*2) + 1 = 11, which gives you 11/5 for the second improper fraction. Now your equation is 31/4 + 11/5, which still needs a common denominator. The LCM between 4 and 5 is 20, so multiply the improper fractions in a way that results in a denominator of 20. Your result will be 155/20 and 44/20, which you will add together to reach 199/20 and reach your final answer of 9 19/20.

Last updated: 07/10/2018