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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.
is simplified.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.
Summary and Worksheet
- Summary: Subtracting Fractions - PDF - Opens in a new windowThis document contains a short (1 – 2 page) summary of this topic as well as detailed examples to illustrate key concepts. Use this summary to review this topic.
- Worksheet: Subtracting Fractions - PDF - Opens in a new windowThis document contains practice questions on this topic. Use the worksheet to test your knowledge and practice the skills learned in this module. The answers to the practice questions are provided at the end.
Attribution
Examples Source: "Prealgebra - opens in a new window" by Lynn Marecek & Mary Anne Anthony-Smith is licensed under CC BY 4.0 - opens in a new window / A derivative from the original work - opens in a new window