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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 235 and 1310.

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

Method 1:

235 + 1310

= (2 + 1) + 35 + 310

 = 3 + 35 + 310

= 3 + 3×25×2 + 3×110×1

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

= 3 + 610 + 310

= 3 + 6+310 

= 3 + 910

= 3910



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:

235 + 1310

= (5 × 2) + 35 + (10 × 1) + 310

= 135 + 1310

13×25×2 + 13×110×1, [L.C.M. of 5 and 10 = 10]

= 2610 + 1310

26+1310

3910

= 3910


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 116 , 218 and 314

Solution:

116 + 218 + 314

Let us add whole numbers and fraction parts separately.

= (1 + 2 + 3) + (16 + 18 + 14)

= 6 + (16 + 18 + 14)

= 6 + 1×46×41×38×31×64×6; [Since, the L.C.M. of 6, 8 and 4 = 24]

= 6 + 424 + 324 + 624

= 6 + 4+3+624

= 6 + 1324

= 61324


2. Add 519, 2112 and 34.

Solution:

519 + 2112 + 34

Let us add whole numbers and fraction parts separately.

= (5 + 2 + 0) + (19 + 112 + 34)

= 7 + 19 + 112 + 34

= 7 + 1×49×41×312×33×94×9, [Since the L.C.M. of 9, 12 and 4 = 36]

= 7 + 436 + 336 + 2736

= 7 + 4+3+2736

= 7 + 3436

= 7 + 1718,

= 71718.


3. Add 56, 212 and 314

Solution:

56 + 212 + 314

Let us add whole numbers and fraction parts separately.

= (0 + 2 + 3) + 56 + 12 + 14

= 5 + 56 + 12 + 14

= 5 + 5×26×21×62×61×34×3, [Since, the L.C.M. of 6, 2 and 4 = 12]

= 5 + 1012 + 612 + 312

= 5 + 10+6+312

= 5 + 1912; [Here, fraction 1912 can write as mixed number.]

= 5 + 1712

= 5 + 1 + 712

= 6712


4. Add 358 and 223.

Solution:

Let us add whole numbers and fraction parts separately.

358 + 223

= (3 + 2) + (58 + 23)

5 + (58 + 23)

L.C.M. of denominator 8 and 3 = 24.

= 5 + 5×38×32×83×8, (Since, L.C.M. of 8 and 3 = 24)

= 5 + 1524 + 1624

= 5 + 15+1624

= 5 + 3124

= 5 + 1724.

= 6724.


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

1. Add 239, 116 and 223

Solution:

239 + 116 + 223

(9×2)+39(6×1)+16(3×2)+23

= 219 + 76 + 83, (L.C.M. of 9, 6 and 3 = 18)

21×29×27×36×38×63×6

= 4218 + 2118 + 4818

= 42+21+4818

= 11118

= 376

= 616


2. Add212, 313 and 414.

Solution:

212 + 313 + 414

(2×2)+12(3×3)+13(4×4)+13

= 52 + 103 + 174, (L.C.M. of 2, 3 and 4 = 12)

5×62×610×43×417×34×3, (Since, L.C.M. of 2, 3 and 4 = 12)

= 3012 + 4012 + 5112

= 30+40+5112

= 12112

= 10112


3. Add 358 and 223.

Solution:

358 + 223

Let us convert the mixed fractions into improper fractions.

(8×3)+58(3×2)+23

= 298 + 83,

L.C.M. of denominator 8 and 3 = 24.

29×38×38×83×8, (Since, L.C.M. of 8 and 3 = 24)

= 8724 + 6424

= 87+6424

= 15124

= 6724.

Addition of Mixed Fractions


Word Problem on Addition of Mixed Fraction:

The doctor advises every child to drink 312 litres of water in morning, 414 litres in the after noon and 12 litre before going to bed. How much water should a child drink every day?

Solution:

312414 + 12

Let us add whole numbers and fraction parts separately.

= (3 + 4 + 0) + (12 + 14 + 12)

7 + (12 + 1412)

L.C.M. of denominators 2, 4 and 2 = 4.

= 7 + 1×22×21×14×11×22×2, [Since, the L.C.M. of 2, 4 and 2 = 4.]

= 7 + 24 + 14 + 24

= 7 + 2+1+24

= 7 + 54

[Here, the fraction 54 can write as mixed number.]

= 7 + 114

= 814

Therefore, 814 litres of water should a child drink every day.

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