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Addition of Unlike Fractions

We will learn how to solve addition of unlike fractions.

In order to add unlike fractions, first we convert them as like fractions with same denominator in each fraction with the help of method explained earlier and then we add the fractions.

Let us consider some of the examples of adding unlike fractions:

1. Add 1223 and 47.

Solution:

Let us find the LCM of the denominators 2, 3 and 7. 

The LCM of 2, 3 and 7 is 42.

12 = 1×212×21 = 2142

23 = 2×143×14 = 2842

47 = 4×67×6 = 2442

Therefore, we get the like fractions 1223 and 47.

Now, 2142 + 2842 + 2442

       = 21+28+2442

       = 7342


2. Add 78 and 910

Solution:

The L.C.M. of the denominators 8 and 10 is 40.

 787×58×5 =  3540, (because 40 ÷ 8 = 5)

 789×410×4 = 3640, (because 40 ÷ 10 = 4)

Thus, 78 + 910

      = 3540 + 3640

      = 35+3640

      = 7140

      = 13140



3. Add 16 and 512

Solution:

Let L.C.M. of the denominators 6 and 12 is 12.

161×26×2 = 212, (because 12 ÷ 6 = 2)

5125×112×1 = 512, (because 12 ÷ 12 = 1)

Thus, 16 + 512

      = 212 + 512

      = 2+512

      = 712




4. 
Add 23, 115 and 56

Solution:

The L.C.M. of the denominators 3, 15 and 6 is 30.


23 = 2×103×10 = 2030, (because 30 ÷ 3 = 10)

115 = 1×215×2 = 230, (because 30 ÷ 15 = 2)

56  = 5×56×5 = 2530, (because 30 ÷ 6 = 5)

Thus, 23 + 115 + 56


      = 2030 + 230 + 2530

      = 20+2+2530

      = 4730

      = 11730




More examples on Addition of Unlike Fractions (Fractions having Different Denominators)

5. Add 16 + 34

Solution:

First Method:

Step I: Find the L.C.M. of the denominators 6 and 4.

L.C.M. of 6 and 4 = 2 × 3 × 2 =12

LCM of 6 and 4

Step II:Write the equivalent fractions of 16 and 34 with denominator 12.


1×26×2212

3×34×3912

Step III:Add the equivalent fractions

16 + 34

212 + 912

= 2+912

= 1112

Add 16 + 34



Second Method:

16 + 34


L.C.M. of 6 and 4 is 12

(12÷6)×1+(12÷4)×312

= (2×1)+(3×312

= 2+912

= 1112

Steps:

Divide 12 by I denominator. Multiply the quotient with I numerator.

Divide 12 by II denominator. Multiply the quotient with II numerator.

6. Add 38 + 24 + 616

Solution:

L.C.M. of 8, 4, 16 = 2 × 2 × 2 × 2 = 16

38 + 24 + 616

= (16÷8)×3+(16÷4)×2+(16÷16)×616

= (2×3)+(4×2)+(1×6)16

= 6+8+616

= 2016

= 54

= 114

L.C.M. of 8, 4 and 16

Addition of Mixed Numbers

7. Add 226 + 513 + 145

Solution:

First Method:

Separate the whole numbers and proper fractions.

226 + 513 + 145 = (2 + 5 + 1) + 26 + 13 + 45

= 8 + 26 + 13 + 45

L.C.M. of 6, 3 and 5 is 30.

= 8 + (30÷6)×2+(30÷3)×1+(30÷5)×430

= 8 + (5×2)+(10×1)+(6×4)30

= 8 + 10+10+2430

= 8 + 4430

= 8 + 2215

= 8 + 1715


Second Method:

Add 226 + 513 + 145

Convert the mixed number into improper fractions and find the sum

226 = (2×6)+26 = 146

513 = (5×3)+13 = 163

145 = (1×5)+45 = 95

Therefore, 226 + 513 + 145 = 146 + 163 + 95

                          = 14×56×5 + 16×103×10 + 9×65×6

                          = 7030 + 16030 + 5430

                          = 70+160+5430

                          = 28430

                          = 14215

                          = 9715


8. Add 26, 4 and 712

Solution:

4 = 41

26 + 4 + 712

= 26 + 41 + 712

           L.C.M. of 6, 1, 12 is 12


= (12÷6)×2+(12÷1)×4+(12÷12)×712

= (2×2)+(12×4)+(1×7)12

= 4+48+712

= 5912

= 41112

L.C.M. of 6, 1 and 12
Addition of Unlike Fractions

To add unlike fractions, we first convert them into like fractions. In order to make a common denominator we find the LCM of all different denominators of the given fractions and then make them equivalent fractions with a common denominator.


Word Problems on Addition of Unlike Fractions:

1. On Monday Michael read 516 of the book. On Wednesday he reads 48 of the book. What fraction of the book has Michael read?

Solution:

On Monday Michael read 516 of the book.

On Wednesday he reads 48 of the book.

Now add the two fractions

51648

Let us find the LCM of the denominators 16 and 8. 

The LCM of 16 and 8 is 16.

516 = 5×116×1 = 516

48 = 4×28×2 = 816

Therefore, we get the like fractions 516 and 816.

Now, 516 + 816

       = 5+816

       = 1316

Therefore, Michael read in two days 1316 of the book.


2. Sarah ate 13 part of the pizza and her sister ate 12 of the pizza. What fraction of the pizza was eaten by both sisters?

Solution:

Sarah ate 13 part of the pizza.

Her sister ate 12 of the pizza.

Now add the two fractions

1312

Let us find the LCM of the denominators 3 and 2. 

The LCM of 3 and 2 is 6.

13 = 1×23×2 = 26

12 = 1×32×3 = 36

Therefore, we get the like fractions 26 and 36.

Now, 26 + 36

       = 2+36

       = 56

Therefore, 56 of the pizza was eaten by both sisters.


3. Catherine is preparing for her final exam. She study 922 hours on Wednesday and 511 hours on Sunday. How many hours she studied in two days?

Solution:

Catherine study 922 hours on Wednesday.

Again, she study 511 hours on Sunday.

Now add the two fractions

922511

Let us find the LCM of the denominators 22 and 11. 

The LCM of 22 and 11 is 22.

922 = 9×122×1 = 922

511 = 5×211×2 = 1022

Therefore, we get the like fractions 922 and 1022.

Now, 922 + 1022

       = 9+1022

       = 1922

Therefore, Catherine studied a total 922 hours in two days.


Questions and Answers Addition of Unlike Fractions:

1. Add the following Unlike Fractions:

(i) 34 + 56

(ii) 17 + 23 + 67

(iii) 78 + 56 + 410

(iv) 37 + 25 + 611

(v) 358 + 416 + 4712


Answer:

1. (i) 1712

(ii) 123 

(iii) 213120

(iv) 1144385 

(v) 1238

Related Concept





4th Grade Math Activities

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