# Subtract fractions, online calculator: subtracting simple (common, ordinary) equal (like) or different (unlike) denominators math fractions, explanations

## The latest subtracted fractions

 7/102 + 5 = ? Jan 26 14:56 UTC (GMT) 7/2 - 7/4 = ? Jan 26 14:56 UTC (GMT) 10/84 + 8 = ? Jan 26 14:55 UTC (GMT) 3/59 + 25 = ? Jan 26 14:55 UTC (GMT) 3/59 + 25 = ? Jan 26 14:55 UTC (GMT) - 15/3 - 411/76 = ? Jan 26 14:53 UTC (GMT) 7/11 - 9/8 = ? Jan 26 14:53 UTC (GMT) - 33/1,533 - 33/1,533 = ? Jan 26 14:53 UTC (GMT) 4/11 - 7/9 = ? Jan 26 14:53 UTC (GMT) 18 - 20/26 = ? Jan 26 14:52 UTC (GMT) 7/8 - 3/64 = ? Jan 26 14:52 UTC (GMT) 8/716 + 8 = ? Jan 26 14:52 UTC (GMT) 18/6 + 8/14 + 16/6 - 7/11 + 10/7 - 8/15 = ? Jan 26 14:51 UTC (GMT) see more... subtracted fractions

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

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

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

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

• Simply subtract 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 subtracting ordinary fractions that have like denominators, with explanations

• #### 3/18 + 4/18 - 5/18 = (3 + 4 - 5)/18 = 2/18;

• We simply subtracted the numerators of the fractions: 3 + 4 - 5 = 2;
• The denominator of the resulting fraction is: 18;

### B. To subtract 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 (simplify them).

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

• Calculate GCF, the greatest common factor of the numerator and of the denominator of each fraction.
• GCF is the product of all the unique common prime factors of the numerator and of the denominator, multiplied by the lowest exponents.
• #### Calculate the greatest common factor, GCF, online.

• Divide the numerator and the denominator of each fraction by their 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, also called the lowest common denominator (the least common denominator).
• 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, multiplied 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 the denominator of each fraction, in order to calculate each fraction's expanding number.
• #### 4. Expand each fraction:

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

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

### An example of subtracting fractions that have different denominators (unlike denominators), step by step explanations

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

• Factor all the denominators, break them down to their prime factors, then multiply all these prime factors, uniquely, by the largest exponents.

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

• Divide the least common multiple, LCM, by the denominator of each fraction.

• #### 4. Expand each fraction:

• Multiply both the numerator and the denominator of each fraction by their expanding number.

• #### 5. Subtract the fractions:

• Simply subtract the numerators of the fractions. The denominator = LCM.