# 16/38 + 18/56 = ? Adding Ordinary (Simple, Common) Math Fractions Calculator, Addition Explained Step by Step

## Add ordinary fractions, online calculator

 16/38 + 18/56 = ? Jun 29 21:55 UTC (GMT) 31/41 + 19/28 = ? Jun 29 21:55 UTC (GMT) - 44/14 + 39/474 = ? Jun 29 21:55 UTC (GMT) - 43/5,542 + 5,140/53,153 - 49/7 = ? Jun 29 21:55 UTC (GMT) 58/11 - 11/14 - 22/40 - 19/14 + 118/117 = ? Jun 29 21:55 UTC (GMT) 6/37 + 10 = ? Jun 29 21:55 UTC (GMT) 42/46 - 32/54 = ? Jun 29 21:55 UTC (GMT) - 40/3,750 - 50,070/19 = ? Jun 29 21:55 UTC (GMT) 15/31 + 10/31 - 15/17 - 7/17 = ? Jun 29 21:55 UTC (GMT) 3/32 + 20/128 = ? Jun 29 21:55 UTC (GMT) 91/147 + 33/55 = ? Jun 29 21:55 UTC (GMT) - 15/19 + 17/772 = ? Jun 29 21:55 UTC (GMT) 286/229 - 92/52 = ? Jun 29 21:54 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.