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:
2 3/5 + 1 3/10
= (2 + 1) + 3/5 + 3/10 = 3 + 3/5 + 3/10 = 3 + 3 × 2/5 × 5 + 3 × 1/10 × 1, = 3 + 6/10 + 3/10 = 3 + 9/10 = 3 9/10 
Step I: We add the whole numbers, separately.
Step II: To add fractions, we take L.C.M. of the denominators and change the fractions into like fractions. Step III: We find the sum of the whole numbers and the fractions in the simplest form. 
Method 2:
2 3/5 + 1 3/10
= (5 × 2) + 3/5 + (10 × 1) + 3/10 = 13/5 + 13/10 = 13 × 2/5 × 2 + 13 × 1/10 × 1, [L.C.M. of 5 and 10 = 10] = 26/10 + 13/10 = 26 + 13/10 = 39/10 = 3 9/10 
Step I: We change the mixed fractions into improper fractions.
Step II: We take L.C.M. of the denominators and change the fractions into like fractions. Step III: We add the like fractions and express the sum to its simplest form. 
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
Related Concept
● Representation of a Fraction
● Properties of Equivalent Fractions
● Comparison of Like Fractions
● Comparison of Fractions having the same Numerator
● 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
From Addition of Mixed Fractions to HOME PAGE
Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.

New! Comments
Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.