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. A mixed fraction is also referred to as a mixed number.

A mixed fraction is a fraction formed by combining a whole number and a proper fraction.

Mixed Fraction Definition

A mixed fraction is defined as a fraction that is formed by the combination of a whole number and a fraction.

For example, 8\(\dfrac{1}{2}\) is a mixed fraction.

An improper fraction is a fraction in which the numerator is greater than or equal to the denominator. 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 by the denominator.
• Step 2: Find the quotient and the remainder.
• Step 3: Arrange these results using the formula, Mixed fraction = Quotient \(\dfrac{Remainder}{Divisor}\) This arrangement is also known as the Mixed fraction formula. Let us understand this formula now.

Mixed Fraction Formula

The mixed fraction formula is the way in which we express a mixed fraction in which there is a whole number and a proper fraction and it is expressed as, Mixed fraction = Quotient \(\dfrac{Remainder}{Divisor}\). This mixed fraction formula is explained in the following points. Let us understand this using the same example where we are converting 13/5 to a mixed fraction. Observe the calculation shown below to relate to the steps.

• We divide the numerator by the denominator. This means 13 ÷ 5.
• The quotient that we get is written as the whole number part. In this case, 2 is the quotient.
• The remainder is written as the numerator of the proper fraction. In this case, the remainder is 3.
• The divisor is written as the denominator of the proper fraction. In this case, the divisor is 5.
• Therefore, the mixed fraction is now written as, 2\(\dfrac{3}{5}\)

A mixed fraction can also be converted to an improper fraction. 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. Let us convert this mixed fraction to an improper fraction using the following steps and the explanation given below.

• Step 1: Multiply the denominator of the mixed fraction with the whole number part. In this case, 5 × 2 = 10
• Step 2: Add the numerator to the product obtained from step 1. Here, 4 + 10 = 14.
• Step 3: Write the improper fraction with the sum obtained from step 2 in the numerator/denominator form. Here, it will be 14/5

We can apply arithmetic operations on mixed fractions in the same way as we add, subtract, multiply and divide numbers.

Addition of Mixed Fractions

To add mixed fractions, we 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 convert them to like fractions, find out the Least Common Multiple (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 \(2\dfrac{1}{2}\).
Solution: After we convert the fractions to improper fractions we get, 3/2 and 5/2. On adding 3/2 and 5/2, we get 8/2. After simplifying 8/2, we get 4.

Subtraction of Mixed Fractions

To subtract mixed fractions, we 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 \(3\frac{2}{3}\).
Solution: After we convert 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, we 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 \(3\frac{1}{5}\).
Solution: After we convert 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, we follow the steps given below:

• Step 1: Convert the mixed fractions to improper fractions.
• Step 2: Multiply the first fraction with the reciprocal 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 \(3\frac{4}{5}\)
Solution: After we convert 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.

• Fractions
• Improper Fractions
• Subtracting Mixed Fractions Calculator
• Mixed Number to Improper Fraction
• Improper Fraction to Mixed Number

What is a Mixed Fraction?

A whole number along with a fractional part makes a mixed fraction. Mixed fractions are also called 'Mixed numbers' in which there is a whole number and a proper fraction. For example, 2\(\dfrac{1}{5}\) is a mixed fraction.

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 use the formula: Quotient \(\dfrac{Remainder}{Divisor}\). Let us understand it using the following steps using an example where we will convert 14/3 to a mixed fraction.

• We divide the numerator by the denominator. This means 14 ÷ 3.
• The quotient that we get is written as the whole number part. In this case, 4 is the quotient.
• The remainder is written as the numerator of the proper fraction. In this case, the remainder is 2.
• The divisor is written as the denominator of the proper fraction. In this case, the divisor is 3.
• Therefore, the mixed fraction is now written as, 4\(\dfrac{2}{3}\)

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 \(3\frac{1}{2}\). First, we 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 \(1\frac{1}{3}\).

How to Solve a Mixed Fraction?

In order to solve a mixed fraction, we first need to convert the mixed fraction to an improper fraction and then proceed with the given operation. In order to convert a mixed fraction to an improper fraction, we multiply the denominator and the whole number. Then, add the product to the numerator and write the sum as the numerator and use the same denominator. For example, converting \(3\frac{2}{3}\) to an improper fraction, we get 11/3.

What is the Mixed Fraction Formula?

The mixed fraction formula can be expressed as, Quotient \(\dfrac{Remainder}{Divisor}\). This is a way in which we convert the improper fraction to a mixed fraction. Let us understand it using the following steps using an example where we will convert 24/7 to a mixed fraction.

• We divide the numerator by the denominator. This means 24 ÷ 7.
• The quotient that we get is written as the whole number part. In this case, 3 is the quotient.
• The remainder is written as the numerator of the proper fraction. In this case, the remainder is 3.
• The divisor is written as the denominator of the proper fraction. In this case, the divisor is 7.
• Therefore, the mixed fraction is now written as, 3\(\dfrac{3}{7}\)

How to Write Mixed Fractions?

We know that mixed fractions are those fractions that have a whole number part and a proper fraction in it. For example, 3\(\dfrac{1}{7}\) is a mixed fraction. In order to convert an improper fraction to a mixed fraction, we use the following steps.

• For example, if we need to convert 17/3 to a mixed fraction, we first divide the numerator by the denominator. Here, 17 ÷ 3
• The quotient that we get is written as the whole number part. In this case, 5 is the quotient.
• The remainder is written as the numerator of the proper fraction. In this case, the remainder is 2.
• The divisor is written as the denominator of the proper fraction. In this case, the divisor is 3.
• Therefore, the mixed fraction is now written as, 5\(\dfrac{2}{3}\)