Mixed Numbers

A mixed number is a combination of a whole number and a proper fraction. Mixed numbers are also known as mixed fractions and they help us to understand a quantity in a simpler way. Let us learn more about mixed numbers, adding mixed numbers, and conversion of mixed numbers in this article.

Mixed numbers consist of a whole number and a proper fraction. For example, \(2\dfrac{1}{4}\) is a mixed number in which 2 is the whole number part and 1/4 is the proper fraction. It should be noted that mixed numbers can be added, subtracted, multiplied, and divided easily once they are converted to an improper fraction.

Converting Improper Fractions to Mixed Numbers

We usually convert improper fractions to mixed fractions because it helps us have a better idea of a quantity. For example, it is easy to understand \(9\dfrac{2}{3}\) liters of milk rather than 29/3 liters of milk. In order to convert improper fractions to mixed numbers, we use the following steps. Let us convert 43/9 to a mixed number.

• Step 1: The first step is to divide the numerator by the denominator and get the remainder and the quotient. In this case, 43 ÷ 9 gives 4 as the quotient and 7 as the remainder.
• Step 2: This quotient (4) becomes the whole number part of the mixed number. The remainder (7) becomes the numerator part while the denominator remains the same.
• Step 3: Therefore, the improper fraction, 43/9 changes to a mixed number and is written as \(4\dfrac{7}{9}\), which means 43/9 = \(4\dfrac{7}{9}\)

Adding mixed numbers becomes easy if the given fractions are converted to an improper fraction. Let us understand this with the help of the following example.

Example: Add \(5\dfrac{1}{3}\) and \(7\dfrac{1}{3}\)

Solution: In order to add the mixed numbers, we use the following steps:

• Step 1: First, let us convert them to improper fractions. So, \(5\dfrac{1}{3}\) = 16/3, and \(7\dfrac{1}{3}\) = 22/3
• Step 2: Now, we will add the fractions using the rules for the addition of fractions.
• Step 3: Since these are like fractions that have the same denominator, we just need to add the numerators. (In the case of unlike fractions, which have different denominators, we convert them to equivalent fractions. We take the LCM of the denominators to get a common denominator and then we add the fractions).
• Step 4: After adding the numerators, we get, (16 + 22)/3. This becomes 38/3. Then, we convert the improper fraction to a mixed fraction. So, 38/3 = \(12\dfrac{2}{3}\)

Converting Mixed Numbers to Decimals

Mixed numbers and decimals have a few things that are common. A decimal number consists of a whole number and a fractional part which is separated by a decimal point. A mixed number also consists of a whole number and a proper fraction but it is not separated by a decimal point. For example, 2.25 is a decimal number in which 2 is the whole number and .25 is the fractional part. The same number can be expressed as a mixed number as \(2\dfrac{1}{4}\), but here the fractional part is expressed in the form of a proper fraction. Let us see how to convert mixed numbers to decimals using two methods.

• Method 1: Change the mixed number to an improper fraction and then divide the numerator by the denominator.
• Method 2: Keep the whole number part of the fraction aside, and convert the fractional part to a decimal. After this, the decimal part is simply added to the whole number part.

Example 1 (using method 1): Convert \(3\dfrac{1}{4}\) to an improper fraction.

Solution: After converting the mixed number to an improper fraction, we get \(3\dfrac{1}{4}\) = 13/4. Now, we divide 13 by 4 which gives us 13 ÷ 4 = 3.25

Example 2 (using method 2): Convert \(3\dfrac{1}{4}\) to an improper fraction.

Solution: Keeping the whole number part (3) aside, we will convert only the fractional part to a decimal by dividing 1 by 4. This gives 1 ÷ 4 = 0.25. Then, we add 0.25 to the whole number part 3 which makes it 3 + 0.25 = 3.25.

Converting Mixed Numbers to Improper Fractions

In order to convert a mixed number into an improper fraction, we multiply the denominator with the whole number then add the resultant product with the numerator.

Example: Convert the mixed number, \(5\dfrac{1}{8}\) to an improper fraction.

Solution: We will multiply the denominator (8) by 5 and the product is 8 × 5 = 40. This product is added to the numerator (1), which makes it 40 + 1 = 41. So, 41 will become the new numerator while 8 will remain as the denominator. Therefore, \(5\dfrac{1}{8}\) is converted to an improper fraction and is expressed as 41/8.

☛Related Topics

Check out the following pages related to mixed numbers.

• Numbers
• Proper fraction
• Improper Fractions

What are Mixed Numbers in Math?

Mixed numbers are also known as mixed fractions which consist of a whole number and a proper fraction. For example, \(3\dfrac{1}{7}\) and \(8\dfrac{1}{4}\) are a few examples of mixed numbers. In the first example, 3 is the whole number part and 1/7 is the proper fraction. In the second example, 8 is the whole number part and 1/4 is the proper fraction.

How to Add Mixed Numbers?

Adding mixed numbers becomes easy once the mixed numbers are converted to improper fractions. After this step, they can be easily added using the rules of addition of fractions. For example, to add \(3\dfrac{1}{7}\) and \(8\dfrac{1}{7}\), we convert them to improper fractions which means, \(3\dfrac{1}{7}\) = 22/7; and \(8\dfrac{1}{7}\) = 57/7. Since these are like fractions, we just need to add the numerators. This means, (22 + 57)/7 = 79/7 = \(11\dfrac{2}{7}\).

How to Multiply Mixed Numbers?

In order to multiply mixed numbers, we first need to convert them to improper fractions. After this step we multiply them as we multiply regular fractions. In other words, after the conversion, we just need to multiply the numerators first, then the denominators are multiplied. After this, they are reduced to the lowest terms, if needed. The resultant fraction is the product of the given fractions. For example, to multiply \(2\dfrac{1}{3}\) and \(4\dfrac{1}{2}\), we will convert them to improper fractions, which means, 7/3 × 9/2 = 63/6 = 21/2 = \(10\dfrac{1}{2}\)

How to Convert Improper Fractions to Mixed Numbers?

In order to convert improper fractions to mixed numbers, we divide the numerator by the denominator to get the remainder and the quotient. The quotient becomes the whole number part of the mixed number, the remainder becomes the numerator part and the denominator remains the same. For example, to change 56/3 to a mixed number, 56 ÷ 3 gives 18 as the quotient and 2 as the remainder. The quotient (18) becomes the whole number, the remainder (2) becomes the new numerator and the denominator (3) remains the same. Therefore, the improper fraction, 56/3 changes to a mixed number and is written as \(18\dfrac{2}{3}\).

What are Mixed Numbers Examples?

A few examples of mixed numbers are \(18\dfrac{2}{3}\), \(1\dfrac{2}{3}\) and \(4\dfrac{5}{6}\). It should be noted that all these have a whole number and a proper fraction.

How to Divide Fractions with Mixed Numbers?

Mixed numbers are divided easily once they get converted to improper fractions. After this step, they are divided in the same way as the fractions are divided. For example, to divide \(3\dfrac{1}{2}\) ÷ \(1\dfrac{1}{4}\), let us first convert them to improper fractions. this makes them 7/2 ÷ 5/4. This means 7/2 × 4/5 = 28/10 = 14/5 = \(2\dfrac{4}{5}\)