Adding mixed fractions means finding the sum of mixed fractions. A mixed fraction is a combination of a whole number and a proper fraction. Combining two or more mixed fractions is known as adding mixed fractions. Let us learn more about adding mixed fractions in this article. Show
Adding Mixed Numbers with Like DenominatorsAdding mixed numbers with like denominators means adding those mixed fractions that have the same denominator. For example, \(2\dfrac{2}{3}\), \(1\dfrac{1}{3}\) are mixed fractions with like denominators. These mixed fractions can be added using the usual rules of addition of fractions. However, we need to note a few facts about mixed fractions that would help us solve these questions easily. Here is a list of a few points that need to be kept in mind while adding mixed fractions in a better way:
Let us take an example to understand the steps for adding mixed fractions with like denominators. Example: Add the mixed fractions \(2\dfrac{2}{3}\) + \(1\dfrac{1}{3}\) This can be solved using 2 methods. Method 1
Hence, the result is \(2\dfrac{2}{3}\) + \(1\dfrac{1}{3}\) = 4 Method 2 Now, let us solve this question using the second method which is the basic method of addition of fractions. Example: Add the mixed fractions \(2\dfrac{2}{3}\) + \(1\dfrac{1}{3}\) Solution: Let us convert the mixed fractions to improper fractions.
Adding Mixed Numbers with Unlike DenominatorsMixed fractions with unlike denominators are a group of those mixed fractions that do not have the same denominator. Let us learn how to add mixed fractions with unlike denominators using an example with the help of the following steps. Example: Add the mixed fractions with unlike denominators: \(3\dfrac{1}{4}\) + \(6\dfrac{1}{2}\) Solution:
Hence, the result of \(3\dfrac{1}{4}\) + \(6\dfrac{1}{2}\) = \(9\dfrac{3}{4}\) Another way for adding mixed fractions with unlike denominators is to first add the whole number parts of the given fractions and then add the proper fractions. For example, \(3\dfrac{1}{4}\) + \(6\dfrac{1}{2}\) = (3 + 6) + (1/4 + 1/2). It can be solved as follows. = 9 + (1/4 + 2/4) (as the LCM of 2 and 4 is 4) = 9 + 3/4 = \(9\dfrac{3}{4}\) Therefore, any of the above two methods can be used to add mixed fractions. Adding Mixed Fractions and Proper FractionsThe addition of mixed fractions and proper fractions involves the same procedure except for a few changes. Let us understand this using the following examples. Case 1: Mixed fraction and the proper fraction having the same denominator. Example: Add the mixed fraction and the proper fraction \(3\dfrac{2}{5}\) + 1/5 Note that, \(3\dfrac{2}{5}\) = 3 + (2/5). Therefore, \(3\dfrac{2}{5}\) + (1/5) = 3 + (2/5) + (1/5) = 3 + (3/5) = \(3\dfrac{3}{5}\) Therefore, \(3\dfrac{2}{5}\) + (1/5) = \(3\dfrac{3}{5}\) Case 2: Mixed fraction and the proper fraction having different denominators. Example: Add the mixed fraction and the proper fraction \(5\dfrac{1}{2}\) + 2/3 \(5\dfrac{1}{2}\) + 2/3 = (11/2) + (2/3) [We have converted \(5\dfrac{1}{2}\) to an improper fraction, 11/2] = [(11 × 3) / (2 × 3)] + [(2 × 2) / (3 × 2)] [Since the LCM of 2 and 3 is 6] = (33/6) + (4/6) = 37/6 = \(6\dfrac{1}{6}\) Therefore, \(5\dfrac{1}{2}\) + 2/3 = \(6\dfrac{1}{6}\). FAQs on Adding Mixed FractionsHow to Add Mixed Numbers?Mixed fractions can be added in different ways. If the mixed fractions have like denominators then the whole number part and the fractional part can be added separately and combined to get the result. For mixed fractions with unlike denominators, they are first converted into improper fractions. After this we need to make the denominators the same, so we find their LCM, convert them into respective equivalent fractions and then add the numerators. How to Add Mixed Fractions with Whole Numbers?To add mixed fractions with whole numbers, we add the whole number part of the mixed fraction with the given whole number and finally combine it with the fractional part to get the result. This can also be solved by converting the mixed number to an improper fraction and then the fractions can be added using the usual method of addition of fractions. What are the Steps in Adding Fractions and Mixed Fractions?The steps to add fractions and mixed fractions can be understood with the help of the following example. For example, let us add \(5\dfrac{4}{7}\) + (1/7)
How to Add Mixed Fractions with Proper Fractions?Mixed fractions can be added with proper fractions easily. We just need to convert the mixed fractions into improper fractions and then add them using the same rules. For example, let us add \(2\dfrac{2}{5}\) + 3/5 using the following steps:
What are the Steps of Adding Mixed Fractions with Same Denominators?Addition of mixed fractions with the same denominator can be easily done by combining the whole numbers separately and the fractional parts separately. Then, they are added and combined to get the final answer. For example,
let us add \(6\dfrac{1}{6}\) + \(2\dfrac{4}{6}\) How to Add Mixed Fractions with Different Denominators?The addition of mixed fractions with different denominators is done by first converting the mixed fractions to improper fractions. Then, we find their LCM, convert them into equivalent fractions and then add the numerators. Finally, the sum is converted back to a mixed fraction. For example, let us add
\(4\dfrac{5}{8}\) + \(3\dfrac{1}{2}\) How to Add and Subtract Mixed Fractions?The addition and subtraction of mixed fractions is done in a similar way. The mixed fractions are converted to improper fractions and then added or subtracted as per the usual rules. How do you add 3 fractions with different denominators?Step 1: Find LCM of denominators. Step 2: Divide the LCM by the denominator of each number which are to be added. Step 3: Multiply the numerator with the quotient ( found in the above step). Step 4: Add the numerators we get after multiplying with quotients like simple addition.
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