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Subtracting fractions and mixed numbers

How to subtract fractions and mixed numbers?

Rules for subtracting fractions and mixed numbers:

1. Convert the mixed number to improper fraction;
2. Subtract these two fractions;
3. Convert the result to a mixed fraction.

Example of subtracting fractions and mixed numbers

Subtract a fraction and a mixed number:

7 - 21
1117

1. The mixed number is equal to the improper fraction:

21 = 35
1717

2. We subtract the fractions:

7 - 35
1117

The denominators are 17 and 11.

The least common multiple of 17 and 11:

lcm(17, 11) = 187

See least common multiple 17 and 11.

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

So, the lowest common denominator of the fractions is 187.

Change the first fraction to the lowest common denominator

7 * 17 = 119
11 * 17187

Change the second fraction to the lowest common denominator

35 * 11 = 385
17 * 11187

Subtract the fractions

119 - 385 = - 266
187187187

3. Convert the result to a mixed fraction

266 = -179
187187

Answer

7 - 21 = -179
1117187