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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