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Subtracting mixed fractions with different denominators

How to subtract mixed fractions with different denominators?

Examples of subtracting mixed fractions with different denominators

Problem: Subtract mixed fractions with different denominators

83 - 31
511

Solution.

1. Subtract the whole numbers of the mixed fractions

8 - 3 = 5

2. Subtract the fractions

3 - 1
511

The denominators are 5 and 11.

The least common multiple of 5 and 11:

lcm(5, 11) = 55

See least common multiple 11 and 5.

The least common multiple is the lowest common denominator of the fractions.

So, the lowest common denominator of the fractions is 55.

Change the first fraction to the lowest common denominator

3 * 11 = 33
5 * 1155

Change the second fraction to the lowest common denominator

1 * 5 = 5
11 * 555

Subtract the fractions

33 - 5 = 28
555555

3. Combine the whole and fraction parts

5 + 28 = 528
5555

Answer

83 - 31 = 528
51155