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Mixed Fraction Addition

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Introduction to Mixed Fractions

A fraction, which derives from the Latin word fractus, which means "broken," is a portion of a whole or, more broadly, any number of equal pieces. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many components of a particular size there are when stated in ordinary English. The mixed fraction is the combination of a whole number or integer and a fraction. To find out the addition of the mixed fraction, you should convert the mixed fraction into simplified regular fractions. Example: \[4\dfrac{7}{2}\] In the given mixed fraction 4 is the whole number or integer and \[\dfrac{7}{2}\]is the fraction.


How To Add Mixed Fractions

The addition of a mixed fraction is like finding the sum or the total of two or more mixed fractions. There are two types of methods by which we can find out the sum of various mixed fractions: one is by separating the whole number, and another is by converting the mixed fraction into a simpler form. Before applying any arithmetic operations such as addition, subtraction, multiplication, etc., we need to change the mixed fractions to improper fractions.


Mixed Fraction Addition Method Explanation

We will now learn different methods of adding mixed fractions


Method 1. Separating the Whole Number

Mixed Fraction Example:

Add \[1\dfrac{1}{2}\] and \[2\dfrac{1}{2}\].

Solution:

Step 1: Find the whole or integer number from a mixed fraction.

The whole number of \[1\dfrac{1}{2}\] is 1. And for \[2\dfrac{1}{2}\] is 2.

Step 2: Separate the whole number and add it.

Now we separate the whole number from the fraction and add it separately

\[ = (1 + 2) + \dfrac{1}{2} + \dfrac{1}{2}\]

\[ = 3 + \dfrac{1}{2} + \dfrac{1}{2}\]

Step 3: Taking LCM as 2

\[ = \dfrac{{3 \times 2}}{{1 \times 2}} + \dfrac{1}{2} + \dfrac{1}{2}\]

\[ = \dfrac{{6 + 1 + 1}}{2}\]

\[ = \dfrac{8}{2}\]

\[ = 4.\]

Hence, the answer is 4.


Method 2. Converting into a Simpler Fraction

Mixed Fraction Example:

Add \[1\dfrac{1}{2}\] and \[2\dfrac{1}{2}\].

Solution:

\[ = 1\dfrac{1}{2} + 2\dfrac{1}{2}\]

Step 1. Convert mixed fractions into improper fractions.

( In this we have multiplied the denominator with the whole number and added it to the numerator we have converted the mixed fraction into a simpler fraction)

\[ = \dfrac{{2 \times 1 + 1}}{2} + \dfrac{{2 \times 2 + 1}}{2}\]


Step 2. Taking LCM as 2

\[ = \dfrac{3}{2} + \dfrac{5}{2}\]

\[ = \dfrac{8}{2}\]

\[ = 4.\]

Hence, the answer is 4.


Mixed Fraction Questions (Solved)

Question 1.

Add the fraction \[7\dfrac{1}{4}\] and \[4\dfrac{2}{4}\]

Solution: \[7\dfrac{1}{4} + 4\dfrac{2}{4}\]

\[ = (7 + 4) + \dfrac{1}{4} + \dfrac{2}{4}\]

\[ = 11 + \dfrac{1}{4} + \dfrac{2}{4}\]

\[ = \dfrac{{11 \times 4}}{{1 \times 4}} + \dfrac{1}{4} + \dfrac{2}{4}\]

\[ = \dfrac{{44}}{4} + \dfrac{1}{4} + \dfrac{2}{4}\]

\[ = \dfrac{{44 + 1 + 2}}{4}\]

\[ = \dfrac{{47}}{4}\]

Hence, The fraction is \[ = \dfrac{{47}}{4}\]


Question 2.

Add \[4\dfrac{1}{2}\] and \[2\dfrac{1}{4}\]

Solution: \[4\dfrac{1}{2} + 2\dfrac{1}{4}\]

\[ = \dfrac{{2 \times 4 + 1}}{2} + \dfrac{{4 \times 2 + 1}}{4}\]

\[ = \dfrac{9}{2} + \dfrac{9}{4}\]

\[ = \dfrac{{9 \times 2}}{{2 \times 2}} + \dfrac{9}{4}\]

\[ = \dfrac{{18}}{4} + \dfrac{9}{4}\]

\[ = \dfrac{{27}}{4}\]

Hence, The fraction is \[ = \dfrac{{27}}{4}\].


Summary

As we have solved the above example using both methods of adding mixed fractions. Now, we can see that the addition of mixed fractions can be done by two methods. This topic has covered two methods: separating the whole number and converting the mixed fraction into a simpler form. The answer obtained from both methods will be the same.

Last updated date: 18th Sep 2023
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FAQs on Mixed Fraction Addition

1. What is the Definition of a Fraction?

A fraction is a mathematical number that illustrates the components of a whole.

2. What is meant by the whole number?

All positive integers from 0 to infinity are included in the group of numbers known as whole numbers.

3. Can a proper number be written as a mixed number?

No, a proper number cannot be written as a mixed number, only improper numbers can be written as mixed numbers.