# 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:

 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, [L.C.M. of 5 and 10 = 10] = 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

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