Mixed Numbers

Mixed Numbers 

A mixed number consists of a whole number and a fraction that is not improperly formed. Mixed numbers are also known as mixed fractions because they simplify our understanding of a quantity. In this tutorial, we will learn more about mixed numbers, adding mixed numbers, and converting mixed numbers.

Definition of Fraction

The ratio of the two numbers is referred to as a fraction.

15/7 is a fraction in which 15 is the numerator and 7 is the denominator. The number of components that the entire number divides into is seven.

A fraction represents a portion of the whole.

What are Mixed Numbers?

Mixed numbers consist of a whole number and a fraction that is in the correct format. For example, \(2\frac{1}{4}\) is a mixed number consisting of the whole number 2 and the correct fraction 1/4. It should be emphasized that once mixed integers are transformed to improper fractions, they can be readily added, subtracted, multiplied, and divided.

Converting Improper Fractions to Mixed Numbers  

Most of the time, we change improper fractions to Mixed Numbers to get a better idea of how much something is. For example,  \(9\frac{2}{3}\) liters of milk is easier to understand than 29/3 liters of milk. Follow these steps to change an improper fraction into a mixed number. Let’s get a mixed number from 43/9.

• Step 1: Divide the numerator by the denominator to find the quotient and the remainder. In this case, the quotient is 4, and the remainder is 7.
• Step 2: This quotient (4) becomes the part of the mixed number that is a whole number. The rest, which is seven, goes into the numerator. The denominator stays the same.
• Step 3: Therefore, the improper fraction, 43/9 changes to a mixed number and is written as \(4\frac{7}{9}\), which means 43/9 = \(4\frac{7}{9}\)

Adding Mixed Numbers  

If the given fractions are changed to an improper fraction, adding mixed numbers is easy. Let’s take a look at an example to see what it mean.

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

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

• Step 1: First, let us convert them to improper fractions. So, \(5\frac{1}{3}\) = 16/3, and \(7\frac{1}{3}\) = 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 with the same denominator, we only need to add the numerators. (We change fractions with different denominators into fractions with the same number of parts. We find a common denominator by taking the least common multiple of the denominators, 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 = \(12\frac{2}{3}\)

Subtracting Mixed Numbers 

Here’s how to subtract an improper fraction with the same or different denominators, step by step.

Subtracting with the same Denominators. Example: 6/4 – 5/4	Subtracting with the different Denominator 12/8 – 8/6
Step 1: Keep the denominator ‘4’ same.	Step 1: Find the LCM between the denominators, i.e. the LCM of 8 and 6 is 24
Step 2: Subtract the numerators ‘6’ -’5’ =1.	Step 2: Multiply both Denominators and Numerators of both fractions with a number such that they have the LCM as their new Denominator.Multiply the numerator and Denominator of  8/6 with 4 and 12/8 with 3.
Step 3: If the answer is in improper form, Convert it into a mixed fraction. i.e. 1/4	Step 3: Subtract the Numerator and keep the Denominators same.36 / 24 – 32/24 = 4/24
So, We have 1/4 wholes.	Step 4: If the answer is in Improper form, convert it into Mixed Fraction. 4/24 = 1/6

Multiplying Mixed Numbers 

Example: 2(⅚)  × 3 (½)

Solution:

Step 1: Convert the mixed into an improper fraction. 17/6  × 7/2

Step 2: Multiply the numerators of both the fractions together and denominators of both the fractions together. {17 ×  7} {6 × 2}

Step 3: You can convert the denominators into the simplest form or Mixed one = 119 / 12 or 9 (11/12)

Converting Mixed Numbers  to Decimals

Some things are the same for mixed numbers and decimals. A decimal number is made up of a whole number and a fractional part that is separated by a decimal point. A mixed number is also made up of a whole number and a fraction, but there is no decimal point between them. In the decimal number 2.25, for example, 2 is the whole number and.25 is the fractional part. The same number can be written as \(2\frac{1}{4}\) as a mixed number, but here the fractional part is written as a proper fraction. Let’s look at two ways to change a mixed number to a decimal.

• Method 1: Turn the mixed number into an improper fraction, then divide the numerator by the denominator.

• Method 2: Set aside the part of the fraction that is a whole number, and change the part that is a fraction to a decimal. After that, the part with the decimal point is just added to the part with the whole number.

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

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

Example 2 (using method 2): Convert \(3\frac{1}{4}\) 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

To convert a mixed number into an improper fraction, we multiply the denominator by the whole number, then add the result to the numerator.

Example: Convert the mixed number, \(5\frac{1}{8}\) 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, \(5\frac{1}{8}\) is converted to an improper fraction and is expressed as 41/8.

Mixed Equivalent Fractions

How do we find mixed fractions that are the same? Let’s find out here what the answer is.

Two fractions are said to be equivalent if their values are equal after simplification. Suppose ½ and 2/4 are two equivalent fractions since 2/4 = ½.  

Now, if two mixed fractions are the same, that means they are the same in nature. So, if we want to turn two fractions that are the same into a mixed fraction, we should divide the numerator by the denominator and get the same number.

For example :  5/2 and 10/4 are two equivalent fractions.

5/2: when we divide 5 by 2 we get quotient equal to 2 and remainder equal to 1. So 5/2 could be written in the form of a mixed fraction as 21/2.

Similarly, the fraction 10/4 when we divide 10 by 4 we get quotient equal to 2 and remainder equal to 2. Therefore, 10/4 = 22/4.

Hence, for both mixed fractions 21/2 and 22/4, the quotient value equal to 2.

Mixed Numbers Examples

Example 1: Add the given mixed numbers: \(7\frac{1}{8}\) + \(5\frac{3}{8}\)

Solution: After converting the given numbers to improper fractions, we get \(7\frac{1}{8}\) = 57/8; and \(5\frac{3}{8}\) = 43/8.

Since these are like fractions, we will just add the numerators. This means, 57/8 + 43/8 = (57 + 43)/8 = 100/8. This can be reduced to 25/2 and then converted to a mixed number which makes it 25/2 = \(12\frac{1}{2}\)

Example 2: Convert the mixed number to an improper fraction: \(6\frac{1}{7}\)

Solution: In order to convert the given mixed number into an improper fraction we will multiply the denominator with the whole number and add the product with the numerator. Here, 7 × 6 = 42, and after adding this product to the numerator we get 42 + 1 = 43. This becomes the numerator and the denominator remains the same. Hence, \(6\frac{1}{7}\) changes to 43/7.

Example 3: There are 5/4 liters of plain juice in the refrigerator. Convert the given quantity into a mixed number.

Solution: To convert the given improper fraction 5/4 to a mixed number, we have to divide 5 by 4. By dividing, we will get 1 as the quotient, and 1 as the remainder. Therefore, the answer is \(1\frac{1}{4}\).

FAQs – Frequently Asked Questions