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How To Add Fractions and Mixed Fractions

By Kathleen Cantor, 30 Sep 2020

Fractions are part of everyday life. They're used in every field, from statistics to cooking. From the estimating rainfall to telling time, they're a measurement of different quantities related to any measurable substance.

Fractions in simpler terms are a part of an equally divided segment. In more precise mathematical terms, the fraction is used to represent equal parts of a collection.

For example, let's imagine a boy is eating the 3/4th part of a cake. It means that the cake is divided into four equal parts, and the boy is eating three parts or portions of the cake.

How Fractions are Represented

A fraction is generally represented by two numbers separated by a line. The number that is written above the line is called the numerator. The denominator is the number beneath the line. The denominator is used to represent the total number of equal parts of a collection. The numerator is used to represent portions or parts of the collection.

Mixed Fractions

A mixed fraction is also sometimes called a mixed number. A mixed fraction consists of two parts a whole number part and a fractional part, i.e. 3 1/4.

An improper fraction is formed when the number in denominator is smaller than the number in the numerator, i.e. 3/4.

Generally, you would convert an improper fraction to a mixed fraction. For example, 23/4 is an improper fraction. When converted to mixed fraction, it becomes 5 ¾.

Steps To Convert An Improper Fraction Into Mixed Fraction

  1. Take the numerator of the fraction (the number above the line) by and divide it by the denominator of the improper fraction (the number below the line).
  2. The denominator is treated as the divisor, and the numerator is treated as the dividend.
  3. The quotient of the division performed in "step 1" is written as the whole number part of the mixed fraction.
  4. Write down the divisor as the denominator and the remainder as the numerator of the mixed fraction


Convert 9/4 into Mixed Fraction. You can convert an improper fraction 9/4 into a mixed fraction by following the steps.

  1. The numerator here is 9, and the denominator is 4. So, dividing 9 by 4
  2. After dividing 9 by 4 gives 2 as the quotient.
  3. By dividing 9 by 4 gives 1 as the remainder.

The resulting mixed fraction will be 2 ¼.

Steps To Convert  An Mixed Fraction Into Improper Fraction

  1. Multiply the denominator with the whole number, then add that product with the numerator.
  2. Write down the answer you found in step 1 as the numerator of the fraction. Keep the denominator unchanged.


Let’s consider the mixed fraction, 2 ¾, and convert it into an improper fraction.  To break it down, the denominator of the mixed fraction is 4, and the numerator is 3. The whole number part of the mixed fraction is 2. Following these steps:

  1. Multiply the denominator 4 with the whole number, 2. The result is 8. Then with 8, add the numerator 3.
  2. Write down 11 as the numerator of the fraction. Keep the same denominator. The resulting improper fraction is 11/4.

Adding a Fraction and a Mixed Fraction

Adding fractions with mixed fractions is, essentially, finding the sum of both of the fractions. The steps to find the addition of mixed fraction with the fraction is discussed below:

  1. Convert the mixed fractions into an improper fraction.
  2. Check the denominators of the fraction and find out the LCM (Least Common Multiple).
  3. Divide the result of the LCM with the denominator of each of the fractions and multiply the numerator by the quotient.
  4. Add the sum of the product and place the LCM in the denominator.

[(Numerator of fraction 1 *(LCM/denominator of fraction 1)]+ [Numerator of fraction 2 *(LCM/denominator of fraction 2)] /LCM


Finding the sum of  ¼  + 3 ½. You can add the two fractions, ¼ and 3 ½, by using the following steps:

  1. There is only one mixed fraction out of the two operands that are 3 ½. After converting 3 ½ into an improper fraction, the result becomes 7/2.
  2. The denominators of the two fractions are 2 and 4. LCM of 2 and 4 is 4.
  3. The result of the LCM is 4. Divide the LCM with the denominator ¼, so 4 is divided by the denominator of 4. The result is 1, which you'd multiply with the numerator, 1, resulting in a sum of 1.

Similarly, the same step needs to be performed in the second fraction. The sum would be 14. Finally, you can add the sum of the product and place the LCM in the denominator.

  • ([Numerator of fraction 1 *(LCM/denominator of fraction 1)]+ [Numerator of fraction 2 *(LCM/denominator of fraction 2)]) /LCM
  • = ([1 * (4/4)]+[7*(4/2)])/4
  • = (1+14)/4 =15/4

After adding, the result would be 15/4, which is an improper fraction. However, it could be converted to a mixed fraction. The steps to convert an improper fraction to mixed fractions are described above.


Fractions are very important not only for mathematics but also in our daily life. Calculation using fractions is required in almost every field, so understanding how to convert mixed and improper fractions will save you time and help keep your results accurate.

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