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Mixed Fractions
A mixed fraction is a type of fraction in which there is a whole number part and a fractional part. For example, \(3\dfrac{1}{7}\) is a mixed fraction. It is also referred to as a mixed number.
What Are Mixed Fractions?
A mixed fraction is defined as a fraction formed by combining a whole number and a fraction. For example, if 8 is a whole number and \(\dfrac{1}{2}\) is a fraction, then 8\(\dfrac{1}{2}\) is a mixed fraction.
Converting an Improper Fraction to a Mixed Fraction
An improper fraction is a fraction that has a numerator greater than or equal to the denominator and can not be simplified further. For example, 13/5 is an improper fraction. Let us learn how to convert this improper fraction to a mixed fraction.
 Step 1: Divide the numerator with the denominator.
 Step 2: Find the remainder.
 Step 3: Arrange the numbers in the following way, quotient followed by a fraction of remainder/divisor.
Converting a Mixed Fraction to an Improper Fraction
A mixed fraction can also be converted to an improper fraction. To do that, follow the steps given below. Let us understand this by taking an example of a mixed fraction 2\(\dfrac{4}{5}\). Here 2 is the whole number, 4 is the numerator and 5 is the denominator.
 Step 1: Multiply the denominator of the mixed fraction with the whole number part.
 Step 2: Add the numerator to the product obtained from step 1.
 Step 3: Write the improper fraction with the sum obtained from step 2 in the numerator/denominator form.
Operations on Mixed Fractions
Like we add, subtract, multiply and divide numbers, in the same way, we can apply arithmetic operations on mixed fractions also.
Addition of Mixed Fractions
To add mixed fractions, follow the steps given below:
 Step 1: Convert the mixed fractions to improper fractions.
 Step 2: Check whether the denominators are the same or not.
 Step 3: If yes, add the numerators of the fractions and write down the result.
 Step 4: If the denominators are not the same, then find out the LCM of the denominators to make them the same.
 Step 5: Now add the numerators to get the result of the addition.
Example: Let us add \(1\dfrac{1}{2}\) and \(2\dfrac{1}{2}\).
Converting the fractions to improper fractions we get, 3/2 and 5/2. On adding 3/2 and 5/2, we get 8/2. Further simplifying 8/2, we get 4.
Subtraction of Mixed Fractions
To subtract mixed fractions, follow the steps given below:
 Step 1: Convert the mixed fractions to improper fractions.
 Step 2: Check whether the denominators are the same or not.
 Step 3: If yes, subtract the numerators of the fractions and write down the result.
 Step 4: If the denominators are not the same, then find out the LCM of the denominators to make them the same.
 Step 5: Now subtract the numerators to get the result of the subtraction.
Example: Let us subtract \(2\frac{1}{3}\) from \(3\frac{2}{3}\).
Converting the fractions to improper fractions we get, 11/3 and 7/3. On subtracting 11/3 and 7/3, we get 4/3. Converting 4/3 to mixed fraction, we get \(1\frac{1}{3}\).
Multiplying Mixed Fractions
To multiply mixed fractions, follow the steps given below:
 Step 1: Convert the mixed fractions to improper fractions.
 Step 2: Multiply the numerator with numerator and denominators and write down the result.
 Step 3: The result can be simplified to its lowest form or left as an improper or converted to mixed fraction form.
Example: Let us multiply \(2\frac{2}{5}\) and \(3\frac{1}{5}\).
Converting the fractions to improper fractions we get, 12/5 and 16/5. On multiplying 12/5 and 16/5, we get 192/25. Converting 192/25 to mixed fraction, we get \(7\frac{17}{25}\).
Division of Mixed Fractions
To divide mixed fractions, follow the steps given below:
 Step 1: Convert the mixed fractions to improper fractions.
 Step 2: Multiply the first fraction with the multiplicative inverse of the second fraction.
 Step 3: The result can be simplified to its lowest form or left as an improper or mixed fraction.
Example: Let us divide \(1\frac{1}{5}\) by \(3\frac{4}{5}\).
Converting the fractions to improper fractions we get, 6/5 and 19/5. On dividing 6/5 and 19/5, we get (6/5) × (5/19), which is equal to 6/19.
Mixed Equivalent Fractions
Two fractions are said to be equivalent when they both are equal when reduced to their simplest forms. For example, 1/3 and 2/6 are equivalent fractions. Similarly, the fractions 7/2 and 14/4, when converted to mixed fractions are equivalent. When 7/2 is converted to a mixed fraction, we get \(3\frac{1}{2}\) and when we convert 14/4, we get \(3\frac{2}{4}\). Here \(3\frac{1}{2}\) and \(3\frac{2}{4}\) are called mixed equivalent fractions since, in fraction \(3\frac{2}{4}\), the fractional part 2/4 can be simplified to 1/2.
Related Topics
Check these interesting articles related to the concept of mixed fractions.
Mixed Fractions Examples

Example 1: Convert the following improper fractions to mixed fractions.
a) 16/5 b) 17/7
Solution:
Follow the steps below, to convert an improper fraction to a mixed fraction.
 Step 1: Divide the numerator with the denominator.
 Step 2: Find the remainder.
 Step 3: Arrange the numbers in the following way, quotient followed by a fraction of remainder/divisor.
a) Converting 16/5 to a mixed fraction, we get \(3\frac{1}{5}\).
b) Converting 17/7 to a mixed fraction, we get \(2\frac{3}{7}\). 
Example 2: Convert the following mixed fractions to improper fractions.
a) \(4\frac{1}{3}\) b) \(5\frac{2}{7}\)Solution:
Follow the steps below to convert a mixed fraction to an improper fraction.
 Step 1: Multiply the denominator with the whole number.
 Step 2: Add the numerator to the product obtained from step 1.
 Step 3: Write the mixed fraction with the sum obtained from step 2 as the numerator and the denominator of the original fractional part of the mixed fraction.
a) Converting \(4\frac{1}{3}\) to an improper fraction, we get 13/3.
b) Converting \(5\frac{2}{7}\) to an improper fraction, we get 37/7.

Example 3: Add the following mixed fractions.
a) \(1\frac{2}{3}\) and \(2\frac{4}{3}\) b) \(1\frac{3}{4}\) and \(2\frac{5}{6}\)
Solution:
a) \(1\frac{2}{3}\) and \(2\frac{4}{3}\)
 Step 1: Convert the mixed fractions to improper fractions. We get, 5/3 and 10/3.
 Step 2: Since the denominators are the same, we add the numerators. 5/3 + 10/3 = 15/3.
 Step 3: On simplification, we get 5.
b) \(1\frac{3}{4}\) and \(2\frac{5}{6}\)
 Step 1: Convert the mixed fractions to improper fractions. We get, 7/4 and 17/6.
 Step 2: Since the denominators are not the same, we find the LCM of the denominators. The LCM of 4 and 6 is 12.
 Step 3: By converting them to like fractions, we get, 21/12 + 34/12.
 Step 4: Since the denominators are the same now, we can add the numerators.
 Step 5: The sum is 55/12 = \(4\frac{7}{12}\).

Example 4: Subtract the following mixed fractions.
a) \(4\frac{3}{8}\) and \(3\frac{1}{8}\) b) \(5\frac{3}{5}\) and \(3\frac{2}{3}\)
Solution:
a) \(4\frac{3}{8}\) and \(3\frac{1}{8}\)
 Step 1: Convert the mixed fractions to improper fractions. We get, 35/8 and 25/8.
 Step 2: Since the denominators are the same, we can subtract the numerators. This gives us 10/8.
 Step 3: On simplification, we get 5/4.
b) \(5\frac{3}{5}\) and \(3\frac{2}{3}\)
 Step 1: Convert the mixed fractions to improper fractions. We get, 28/5 and 11/3.
 Step 2: Since the denominators are not the same, we find the LCM of the denominators. The LCM of 5 and 3 is 15.
 Step 3: By converting them to like fractions, we get, 84/15  55/15.
 Step 4: Since the denominators are the same now, we can subtract the numerators.
 Step 5: The sum is 29/15.

Example 5: Multiply the following mixed fractions.
3\(\frac{4}{7}\) and \(4\frac{5}{9}\)
Solution:
 Step 1: Convert the given mixed fractions to improper fractions. After conversion, the fractions become 25/7 and 41/9.
 Step 2: Multiply the numerators and denominators. It can be expressed as 25/7 × 41/9.
 Step 3: On multiplying, we get 1025/63 or \(16\frac{17}{63}\).
FAQs on Mixed Fractions
What Is a Mixed Fraction?
A whole number along with a fractional part makes a mixed fraction. They are also called 'Mixed numbers'. For example, if 2 is a whole number and 1/5 is a fraction, then 2\(\dfrac{1}{5}\) is a mixed fraction.
What Is an Improper Fraction?
An improper fraction is a type of fraction in which the numerator is equal to or greater than the denominator. For example 13/5.
How to Convert Improper Fraction To Mixed Fraction?
To convert an improper fraction to a mixed fraction, we divide the numerator by the denominator and express it in the form of 'Quotient \(\dfrac{Remainder}{Denominator}\).
How to Convert Mixed Fraction To Improper Fraction?
To convert a mixed fraction to an improper fraction, we multiply the denominator and the whole number and then add the product to the numerator and write the sum as the numerator with the denominator. For example, converting \(3\frac{2}{3}\) to an improper fraction, we get 11/3.
How to Add Mixed Fractions?
To add mixed fractions with the same denominators, we first convert them to improper fractions and then write the sum of the numerators over the common denominator. If the denominators are not equal then we find the LCM of the denominators and make them common. Then we add the numerators with the denominator being the same. For example, \(2\frac{1}{2}\) and \(3\frac{1}{2}\). Firstly, convert the fractions to improper fractions we get, 5/2 and 7/2. On adding 5/2 and 7/2, we get 12/2. Then, on further simplifying 12/2 we get 6. Therefore, \(2\frac{1}{2}\) + \(3\frac{1}{2}\) = 6.
How to Subtract Mixed Fractions?
To subtract mixed fractions with the same denominators, we first convert them to improper fractions and then subtract the numerators. If the denominators are not equal then we find the LCM of the denominators and make them common. Then we subtract the numerators with the denominator being the same. For example, to subtract \(3\frac{1}{3}\) from \(4\frac{2}{3}\), convert the fractions to improper fractions we get, 10/3 from 14/3. On subtracting 10/3 from 14/3, we get 4/3. Then, converting 4/3 to mixed fraction, we get \(1\frac{1}{3}\).
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