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Adding fractions can seem daunting, especially when the fractions have different denominators. However, understanding the concept and following a few simple steps can make this task much more manageable. In this article, we will explore how to add multiple fractions with different denominators. We will discuss finding a common denominator, converting the fractions, and adding them together to get the final result. By the end, you will have a solid understanding of how to add fractions with different denominators and be able to apply this knowledge to various arithmetic problems.
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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
- 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.
- 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.
- 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.
- For example: 63 + 70 = 133. This result is the numerator and the final answer is 133/35.
- 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
- For example, 6 3/8 + 9 1/24 would become 51/8 + 217/24.
- 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.
- 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.
- 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.
- For example: 153/24 + 217/24 = 370/24.
- 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.
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.
In conclusion, adding multiple fractions with different denominators can be a challenging task, but with a clear understanding of the process and some practice, it becomes easier to handle. By finding a common denominator and converting each fraction to its equivalent form, we are able to add the fractions together accurately. It is important to simplify the result by reducing the fraction to its simplest form, if possible. Additionally, it is vital to pay attention to the signs and ensure they are distributed correctly throughout the calculation. Overall, by following the steps outlined in this guide and carrying out the necessary operations, anyone can successfully add multiple fractions with different denominators, making complex arithmetic problems more manageable.
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