How to Add Fractions Without a Common Denominator
Learning to add fractions can be difficult. But once you learn the parts of a fraction and how to add them together, it gets easier. The top number in a fraction is called a numerator. The bottom number in a fraction is called a denominator. To add fractions together, the denominators must be the same. For example, adding 1/4 and 1/4 would equal 2/4. The bottom denominators are the same. If you are presented with two fractions that have different denominators, it is still possible to add them, but you must multiply them first to come up with a common denominator.
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Instructions
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Find the Common Denominator
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Select a method to find a common denominator. Use multiplication to find the least common multiple. This method is best used for a few fractions with small denominators. You can do this for any equation, but the more fractions you have or the larger the numbers are, the more time it will take. Try to find a common denominator using prime numbers for larger fractions.
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Find the least common multiple by finding multiples of your denominators. For example, if you were adding the fractions 2/5 + 1/3 + 5/6, you would find the multiples for 5, 3 and 6. Multiples of 5 include 5, 10, 15, 20, 25, 30 and 35. The multiples of 3 are 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, and 33. Multiples of 6 include 6, 12, 18, 24, 30, and 36. Look at the list of multiples to find the lowest number that appears in all 3 lists. The least common multiple for 5, 3 and 6 is 30. This will be your common denominator.
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Use prime numbers to find the common denominator for a fraction. Prime numbers are numbers that can only be divided by 1 and themselves. For example, some smaller prime numbers are 2, 3, 5, 7 and 11. Use the fraction 2/5 + 2/9 + 3/8 as an example. The prime number multiplied to equal 5, is simply 5, because it is itself a prime number. The prime numbers multiplied to equal 9 are 3 x 3. The prime numbers multiplied to equal 8 are 2 x 2 x 2. Review the prime numbers to find how many times the prime numbers occur in one sequence. The 5 is mentioned once, the 3's are mentioned twice, and the 2's are mentioned three times. Multiply the instances of these prime numbers together. For example, multiply 5 x 3 x 3 x 2 x 2 x 2 to get a product of 360. This will be your common denominator.
Finish your Fraction
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Multiply your fractions to create the common denominator. Make 2/5 have a denominator of 30 by multiplying the numerator and the denominator by 6. Multiply each part of the fraction by the same number. Your fractions from step 2, above, should appear as 12/30 + 10/30 + 25/30. The fraction from step 3, above, should appear as 144/360 + 80/360 + 135/360.
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Add your fraction as you normally would now that they have common denominators. The solution to the first fraction is 47/30. The solution to the second fraction is 359/360.
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Simplify your fraction as necessary. Use basic division to determine the simplified mixed number to represent the fraction. A mixed number is a whole number and a fraction. Divide the numerator by the denominator. For example, 47 divided by 30 equals 1, with a remainder of 17. Show this as a whole number, written as 1 17/30. The second fraction cannot be simplified.
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