# 20/217 + 30 = ? Adding Ordinary (Simple, Common) Math Fractions Calculator, Addition Explained Step by Step

## Add ordinary fractions, online calculator

 20/217 + 30 = ? Dec 01 05:15 UTC (GMT) 21/15 - 8/15 = ? Dec 01 05:15 UTC (GMT) 27/14 - 44/14 = ? Dec 01 05:15 UTC (GMT) - 16/33 + 10/29 = ? Dec 01 05:15 UTC (GMT) 8/102,047 - 111/3 = ? Dec 01 05:15 UTC (GMT) 40/5,466 + 542,627 = ? Dec 01 05:15 UTC (GMT) - 24/6,431 + 657/43 = ? Dec 01 05:15 UTC (GMT) - 7/77 - 6/63 = ? Dec 01 05:15 UTC (GMT) - 14/30 + 19/42 + 18/30 = ? Dec 01 05:15 UTC (GMT) 8/137 - 9/20 = ? Dec 01 05:15 UTC (GMT) - 18/31 - 28/57 = ? Dec 01 05:15 UTC (GMT) - 52/92 + 41/27 = ? Dec 01 05:15 UTC (GMT) 27/50 - 11/45 = ? Dec 01 05:15 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.