Addition of Mixed Fractions

We will learn how to solve addition of mixed fractions or addition of mixed numbers. There are two methods to add the mixed fractions.

For example, add 2 3/5 and 1 3/10.

We can use the two methods to add the mixed numbers.

Method 1:

Method 2:

Now let us consider some of the examples on addition of mixed numbers using Method 1.

1. Add 1 1/6 , 2 1/8 and 3 ¼

Solution:

1 1/6 + 2 1/8 + 3 ¼

= (1 + 2 + 3) + (1/6 + 1/8 + ¼)

= 6 + 1/6 + 1/8 + ¼

= 6 + 1 × 4/6 × 4 + 1 × 3/8 × 3 + 1 × 6 /4 × 6, (Since, the L.C.M. of 6, 8 and 4 = 24)

= 6 + 4/24 + 3/24 + 6/24

= 6 + (4 + 3 + 6)/24

= 6 + 13/24

= 6 13/24

2. Add 5 1/9, 2 1/12 and ¾

Solution:

5 1/9, 2 1/12 + ¾

= (5 + 2 +0) + (1/9 + 1/12 + ¾)

= 7 + 1/9 + 1/12 + ¾

= 7 + 1 × 4/9 × 4 + 1 × 3/12 × 3 + 3 × 9/4 × 9, (Since the L.C.M. of 9, 12 and 4 = 36)

= 7 + 4/36 + 3/36 + 27/36

= 7 + (4 + 3 + 27)/36

= 7 + 34/36

= 7 + 17/18,

= 7 17/18.

3. Add 5/6, 2 ½ and 3 ¼

Solution:

5/6 + 2 ½ + 3 ¼

= (0 + 2 + 3) + 5/6 + ½ + ¼

= 5 + 5/6 + ½ + ¼

= 5 + 5 × 2/6 × 2 + 1 × 6/2 × 6 + 1 × 3/4 × 3, (Since, the L.C.M. of 6, 2 and 4 = 12)

= 5 + 10/12 + 6/12 + 3/12

= 5 + (10 + 6 +3)/12

= 5 + 19/12 (Here, fraction 19/12 can write as mixed number.)

= 5 + 1 7/12

= 5 + 1 + 7/12

= 6 7/12

Now let us consider some of the examples on addition of mixed numbers using Method 2.

1. Add 2 3/9, 1 1/6 and 2 2/3

Solution:

2 3/9 + 1 1/6 + 2 2/3

= (9 × 2) + 3/9 + (6 × 1) + /6 + (3 × 2) + 2/3

= 21/9 + 7/6 + 8/3, (L.C.M. of 9, 6 and 3 = 18)

= 21 × 2/9 × 2 + 7 × 3/6 × 3 + 8 × 6/3 × 6

= 42/18 + 21/18 + 48/18

= 42 + 21 + 48/18

= 111/18

= 37/6

= 6 1/6

2. Add 2 ½, 3 1/3 and 4 ¼

Solution:

2 ½ + 3 1/3 + 4 ¼

= (2 × 2) + ½ + (3 × 3) + 1/3 + (4 × 4) + ¼

= 5/2 + 10/3 + 17/4, (L.C.M. of 2, 3 and 4 = 12)

= 5 × 6/2 × 6 + 10 × 4/3 × 4 + 17 × 3/4 × 3, (Since, L.C.M. of 2, 3 and 4 = 12)

= 30/12 + 40/12 + 51/12

= 30 + 40 + 51/12

= 121/12

= 10 1/12

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Related Concept

● Fraction of a Whole Numbers

● Representation of a Fraction

● Equivalent Fractions

● Properties of Equivalent Fractions

● Like and Unlike Fractions

● Comparison of Like Fractions

● Comparison of Fractions having the same Numerator

● Types of Fractions

● Changing Fractions

● Conversion of Fractions into Fractions having Same Denominator

● Conversion of a Fraction into its Smallest and Simplest Form

● Addition of Fractions having the Same Denominator

● Subtraction of Fractions having the Same Denominator

● Addition and Subtraction of Fractions on the Fraction Number Line

4th Grade Math Activities

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