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# Math: Basic Tutorials : Subtracting Fractions

## Subtracting Fractions

To subtract fractions, you have to start with a common denominator. This section goes through the process of finding the common denominator and subtracting fractions.

## Examples

### Examples

Click on the titles below to view each example.

Line 1: Subtract 5 over 8 minus 5 over twelve.

Line 2: Determine the lowest common denominator of 8 and 12 is 24.

Line 3: Change the fractions into equivalent fractions with a denominator of 24. Multiply the numerator and denominator of the first fraction by 3, so the numerator is 5 times 3 and the denominator is 8 times 3. Multiply the numerator and denominator of the second fraction by 2, so the numerator is 5 times 2 and the denominator is 12 times 2.

Line 4: Simplify the numerators and denominators of each fraction so the problem becomes 15 over 24 minus 10 over 24.

Line 5: Subtract the numerators and keep the denominator the same, so the answer is 5 over 24.

Line 6: Remember to always check if the answer can be simplified. Since 5 and 24 have no common factors 5 over 24 can not be reduced.

### Method 1: Add 2 and 2 over 3 plus 1 and 1 over 4

Line 1: Method 1 for adding mixed numbers.

Line 2: Convert the mixed numbers to improper numbers. In the first fraction, the numerator becomes 2 times 3 plus 2 and the denominator stays as 3. In the second fraction, the numerator becomes 1 times 4 plus 1 and the denominator stays as 4.

Line 3: Simplify the numerators so the problem becomes 8 over 3 plus 5 over 4.

Line 4: Determine the lowest common denominator of 3 and 4 is 12. Change the fractions into equivalent fractions with a denominator of 12. Multiply the numerator and denominator of the first fraction by 4, so the numerator is 8 times 4 and the denominator is 3 times 4. Multiply the numerator and denominator of the second fraction by 3, so the numerator is 5 times 3 and the denominator is 4 times 3.

Line 4: Simplify the numerators and denominators of each fraction so the problem becomes 32 over 12 plus 15 over 12.

Line 5: Add the numerators together and keep the denominator the same, so the answer is 47 over 12.

Line 6: If necessary, convert 47 over 12 to the mixed number 3 and 11 over 12.

Line 7: Remember to always check the fraction is simplified. There are no common factors between 11 and 12, so the fraction 11 over 12 is simplified.

### Method 2: Add 2 and 2 over 3 plus 1 and 1 over 4

Line 1: Method 2 for adding mixed numbers.

Line 2: Add the whole numbers of the mixed numbers together. 2 plus 1 equals 3.

Line 3: Add the fractions part of the mixed numbers together. 2 over 3 plus 1 over 4.

Line 4: Determine the lowest common denominator of 3 and 4 is 12. Change the fractions into equivalent fractions with a denominator of 12. Multiply the numerator and denominator of the first fraction by 4, so the numerator is 2 times 4 and the denominator is 3 times 4. Multiply the numerator and denominator of the second fraction by 3, so the numerator is 1 times 3 and the denominator is 4 times 3.

Line 5: Simplify the numerators and denominators of each fraction so the problem becomes 8 over 12 plus 3 over 12.

Line 6: Add the numerators together and keep the denominator the same, so the fraction is 11 over 12.

Line 7: Place the whole number from Line 2 in front of the fraction so the answer is 3 and 11 over 12.

Line 8: Remember to always check the fraction is simplified. There are no common factors between 11 and 12, so the fraction 11 over 12 is simplified.

### Activity

Try this activity to test your skills. If you have trouble, check out the information in the module for help.