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Adding fractions with different denominators may seem difficult, but once you find a common denominator, the calculation is as easy as turning the back of your hand. If you have to add fractions that aren’t really – whose numerator is greater than the denominator, find the common denominator, then add the numerators together. If you want to perform an addition between mixed numbers, you would convert them to real fractions and find a common denominator. As such, you can add fractions easily.
Steps
Add fractions that are not real
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Find the least common multiple of the denominators. To get a common denominator before adding the fractions, you need to find their common multiple, then choose the least common multiple. [1] X Research Source
- For example, with the calculation 9/5 + 14/7, multiples of 5 are 5, 10, 15, 20, 25, 30 and 35, and multiples of 7 are 7, 14, 21, 28 and 35. So 35 is least common multiple.
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Multiply the numerator and denominator by a number to get a common denominator. You need to multiply the whole fraction so that the denominator becomes the least common multiple. [2] X Research Source
- For example, multiply 9/5 by 7 to get the denominator 35. You also need to multiply the numerator by 7 for the fraction to become 63/35.
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Convert the remaining fraction so that it has a common denominator. Note, when you convert one fraction in a calculation, you must also convert the other fraction to get the same denominator. [3] X Research Sources
- For example, if you converted 9/5 to 63/35, multiply 14/7 by 5 to get the fraction 70/35. Your initial calculation will become 63/35 + 70/35.
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Add the numerator and keep the denominator the same. When all the denominators in the calculation are the same, you simply add the numerators. Write the answer you just found on the denominator. [4] X Research Sources
- For example: 63 + 70 = 133. This result is the numerator and the final answer is 133/35.
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Shorten or simplify the answer if necessary. If the answer is a real fraction, you will convert the fraction to a mixed number. To do this, you simply divide the numerator by the denominator to get an integer. Next, write the balance on the denominator. All that remains is to reduce the fraction as much as possible. [5] X Research Sources
- For example, 133/35 can be reduced to 3 28/35. The fraction will be further reduced to 4/5 to get the final answer of 3 4/5.
Add mixed numbers
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Convert mixed numbers to real fractions. If you have fractions with whole numbers, converting to fractions doesn’t really make the calculation easier. The numerator of the fraction will not actually be larger than the denominator. [6] X Research Source
- For example, 6 3/8 + 9 1/24 would become 51/8 + 217/24.
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Find the least common denominator if necessary. If the calculation has different denominators, you need to list the multiples of each denominator to find the common multiple. For example, with the calculation 51/8 + 217/24, you would list multiples of 8 and 24 to get a common denominator of 24. [7] X Research Source
- Since multiples of 8 include 8, 16, 24, 32, and 48, and multiples of 24 are 24, 48, and 72, the least common multiple is 24.
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Convert so that the fraction has a common denominator if you need to change the denominator. The denominators must all become the least common multiple you just found. Multiply the whole fraction by some number so that the denominator becomes the least common multiple. [8] X Research Sources
- For example, to turn the denominator of 51/8 into 24, you would multiply the fraction by 3. Thus, the original fraction becomes 153/24.
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Convert fractions in calculations to get a common denominator. If the fractions in the calculation have different denominators, you must multiply them by another number to get a common denominator. If the fraction already has a denominator to convert, keep the denominator. [9] X Research Source
- For the fraction 217/24, for example, you don’t need to make any further adjustments because the denominator is the same as the common denominator.
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Add the numerator and keep the denominator the same. You can add the numerator when the denominator has been converted to a common denominator, or if the denominator is already the same from the start. After adding the denominator, you just need to write your answer on the denominator. No need to add denominators. [10] X Research Source
- For example: 153/24 + 217/24 = 370/24.
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Shorten the answer . If the answer has a numerator greater than the denominator, you must divide to get an integer. To convert your answer to a mixed number, you would rewrite the remainder. This remainder is the numerator, and the denominator remains the same. Continue reducing fractions until you can’t. [11] X Research Source
- For example, 370/24 would become 15 10/24 because 370 divided by 24 equals 15 and leaves a remainder of 10. Next, 10/24 can be reduced to 5/12 to get a final answer of 15 5/12.
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This article is co-authored by a team of editors and trained researchers who confirm the accuracy and completeness of the article.
The wikiHow Content Management team carefully monitors the work of editors to ensure that every article is up to a high standard of quality.
This article has been viewed 137,090 times.
Adding fractions with different denominators may seem difficult, but once you find a common denominator, the calculation is as easy as turning the back of your hand. If you have to add fractions that aren’t really – whose numerator is greater than the denominator, find the common denominator, then add the numerators together. If you want to do an addition between mixed numbers, you would convert them to real fractions and find a common denominator. As such, you can add fractions easily.
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