# - 31/314,945 + 36/10 = ? Adding Ordinary (Simple, Common) Math Fractions Calculator, Addition Explained Step by Step

## The latest added fractions

 - 31/314,945 + 36/10 = ? Sep 26 20:10 UTC (GMT) 79/26 - 51/139 = ? Sep 26 20:10 UTC (GMT) - 14/25 + 13/25 = ? Sep 26 20:10 UTC (GMT) - 41/74 - 139/306 = ? Sep 26 20:10 UTC (GMT) - 17/8,268 + 22/14 = ? Sep 26 20:09 UTC (GMT) 7/11 + 3/9 = ? Sep 26 20:09 UTC (GMT) 1/8 + 2/16 = ? Sep 26 20:09 UTC (GMT) 326/22,565 + 20 - 705/39 - 29/1,757 + 21 - 989/40 = ? Sep 26 20:09 UTC (GMT) 14/15 + 16/39 = ? Sep 26 20:09 UTC (GMT) 39/174 + 90/32 = ? Sep 26 20:09 UTC (GMT) 21/36 - 3/40 = ? Sep 26 20:09 UTC (GMT) 4/13 - 10/15 + 12/23 = ? Sep 26 20:09 UTC (GMT) 26/13 - 18/22 - 92/115 = ? Sep 26 20:09 UTC (GMT) see more... added fractions

## How to: Adding ordinary (simple, common) math fractions. Steps.

There are two cases regarding the denominators when we add ordinary fractions:

• A. the fractions have like denominators;
• B. the fractions have unlike denominators.

### A. How to add ordinary fractions that have like denominators?

• Simply add the numerators of the fractions.
• The denominator of the resulting fraction will be the common denominator of the fractions.
• Reduce the resulting fraction.

### An example of adding ordinary fractions that have like denominators, with explanations

• #### 3/18 + 4/18 + 5/18 = (3 + 4 + 5)/18 = 12/18;

• We simply added the numerators of the fractions: 3 + 4 + 5 = 12;
• The denominator of the resulting fraction is: 18;

### B. To add fractions with different denominators (unlike denominators), build up the fractions to the same denominator. How is it done?

• #### 1. Reduce the fractions to the lowest terms (simplifying).

• Factor the numerator and the denominator of each fraction down to prime factors (prime factorization).
• #### Factor numbers online down to their prime factors.

• Calculate GCF, the greatest common factor (also called GCD, greatest common divisor, HCF, greatest common factor) of each fraction's numerator and denominator.
• GCF is the product of all the unique common prime factors of the numerator and the denominator, taken by the lowest exponents.
• #### Calculate online the greatest common factor, GCF.

• Divide the numerator and the denominator of each fraction by their greatest common factor, GCF - after this operation the fraction is reduced to its lowest terms equivalent.

• #### 2. Calculate the least common multiple, LCM, of all the fractions' new denominators:

• LCM is going to be the common denominator of the added fractions.
• Factor all the new denominators of the reduced fractions (run the prime factorization).
• The least common multiple, LCM, is the product of all the unique prime factors of the denominators, taken by the largest exponents.

• #### 3. Calculate each fraction's expanding number:

• The expanding number is the non-zero number that will be used to multiply both the numerator and the denominator of each fraction, in order to build all the fractions up to the same common denominator.
• Divide the least common multiple, LCM, calculated above, by each fraction's denominator, in order to calculate each fraction's expanding number.
• #### 4. Expand each fraction:

• Multiply each fraction's both numerator and denominator by expanding number.
• At this point, fractions are built up to the same denominator.
• #### 5. Add the fractions:

• In order to add all the fractions simply add all the fractions' numerators.
• The end fraction will have as a denominator the least common multiple, LCM, calculated above.