Class 6Mixed Fractions - Addition and Subtraction

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(1) Simplif y the f ollowing f ractions:

A) 31

89

198 - 7

8

11 =

B) 30

37

84 - 6

11

21 =

C) 19

63

136 - 4

10

17 =

D) 24

1

6 - 2

4

15 =

E) 21

59

140 - 3

4

7 =

F) 10

161

240 - 1

11

15 =

G) 26

35

99 - 2

9

22 =

H) 25

31

180 - 3

9

20 =

I) 33

41

220 - 7

11

20 =

J) 18

218

221 - 1

5

17 =

(2) Add the f ollowing f ractions:

A) 8

17

21 + 6

29

52 =

B) 9

19

20 + 2

19

29 =

C) 10

23

24 + 3

26

49 =

D) 20

14

17 + 1

18

29 =

E) 14

11

15 + 4

14

33 =

F) 23

29

30 + 1

27

52 =

G) 8

11

14 + 5

5

6 =

H) 11

24

25 + 3

18

29 =

I) 9

21

25 + 6

24

41 =

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J) 11

19

22 + 4

4

15 =

K) 9

16

19 + 2

18

31 =

L) 11

23

24 + 2

17

31 =

M) 20

8

11 + 4

10

23 =

N) 17

17

18 + 4

26

31 =

O) 12

9

10 + 1

17

31 =

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(1) A) 31

89

198 - 7

8

11 = 23

13

18

Step 1

Let us f irst convert the given mixed f ractions into improper f ractions. In order to

convert the mixed f raction 3189

198 into an improper f raction, we will need to

multiply the denominator 198 by 31 and add the numerator 89 to the result. Theresulting number will be the numerator of the improper f raction and thedenominator will remain the same:

3189

198 =

31 × 198 + 89

198 =

6227

198

Similarly, the mixed f raction 78

11 can be converted into an improper f raction

as:

78

11 =

7 × 11 + 8

11 =

85

11

Step 2

We now need to subtract the f ollowing unlike f ractions: 6227

198 and

85

11 .

Bef ore we subtract, let us f irst convert them to like f ractions.

Step 3

Let us f ind the LCM of the denominators 198 and 11.The LCM of 198 and 11 is 198.

Step 4

What should we multiply with the denominator 198 to get the LCM 198?

It is 198

198 = 1.

So, the f irst f raction can be written as:

6227 × 1

198 × 1 =

6227

198

Step 5

Similarly, the second f raction can be written as:

85 × 18

11 × 18 =

1530

198

Step 6

Let us now subtract the two like f ractions:

6227

198 -

1530

198

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= 6227 - 1530

198

= 4697

198

= 4697 ÷ 11

198 ÷ 11 ...[ Dividing both numerator and denominator by their HCF to bring

]

= 427

18

= 2313

18

Step 7

Thus, the simplif ied value of the given f ractions is 2313

18 .

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B) 30

37

84 - 6

11

21 = 23

11

12

Step 1

Let us f irst convert the given mixed f ractions into improper f ractions. In order to

convert the mixed f raction 3037

84 into an improper f raction, we will need to

multiply the denominator 84 by 30 and add the numerator 37 to the result. Theresulting number will be the numerator of the improper f raction and thedenominator will remain the same:

3037

84 =

30 × 84 + 37

84 =

2557

84

Similarly, the mixed f raction 611

21 can be converted into an improper f raction

as:

611

21 =

6 × 21 + 11

21 =

137

21

Step 2

We now need to subtract the f ollowing unlike f ractions: 2557

84 and

137

21 .

Bef ore we subtract, let us f irst convert them to like f ractions.

Step 3

Let us f ind the LCM of the denominators 84 and 21.The LCM of 84 and 21 is 84.

Step 4

What should we multiply with the denominator 84 to get the LCM 84?

It is 84

84 = 1.

So, the f irst f raction can be written as:

2557 × 1

84 × 1 =

2557

84

Step 5

Similarly, the second f raction can be written as:

137 × 4

21 × 4 =

548

84

Step 6

Let us now subtract the two like f ractions:

2557

84 -

548

84

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= 2557 - 548

84

= 2009

84

= 2009 ÷ 7

84 ÷ 7 ...[ Dividing both numerator and denominator by their HCF to bring ]

= 287

12

= 2311

12

Step 7

Thus, the simplif ied value of the given f ractions is 2311

12 .

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C) 19

63

136 - 4

10

17 = 14

7

8

Step 1

Let us f irst convert the given mixed f ractions into improper f ractions. In order to

convert the mixed f raction 1963

136 into an improper f raction, we will need to

multiply the denominator 136 by 19 and add the numerator 63 to the result. Theresulting number will be the numerator of the improper f raction and thedenominator will remain the same:

1963

136 =

19 × 136 + 63

136 =

2647

136

Similarly, the mixed f raction 410

17 can be converted into an improper f raction

as:

410

17 =

4 × 17 + 10

17 =

78

17

Step 2

We now need to subtract the f ollowing unlike f ractions: 2647

136 and

78

17 .

Bef ore we subtract, let us f irst convert them to like f ractions.

Step 3

Let us f ind the LCM of the denominators 136 and 17.The LCM of 136 and 17 is 136.

Step 4

What should we multiply with the denominator 136 to get the LCM 136?

It is 136

136 = 1.

So, the f irst f raction can be written as:

2647 × 1

136 × 1 =

2647

136

Step 5

Similarly, the second f raction can be written as:

78 × 8

17 × 8 =

624

136

Step 6

Let us now subtract the two like f ractions:

2647

136 -

624

136

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= 2647 - 624

136

= 2023

136

= 2023 ÷ 17

136 ÷ 17 ...[ Dividing both numerator and denominator by their HCF to bring

]

= 119

8

= 147

8

Step 7

Thus, the simplif ied value of the given f ractions is 147

8 .

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D) 24

1

6 - 2

4

15 = 21

9

10

Step 1

Let us f irst convert the given mixed f ractions into improper f ractions. In order to

convert the mixed f raction 241

6 into an improper f raction, we will need to

multiply the denominator 6 by 24 and add the numerator 1 to the result. Theresulting number will be the numerator of the improper f raction and thedenominator will remain the same:

241

6 =

24 × 6 + 1

6 =

145

6

Similarly, the mixed f raction 24

15 can be converted into an improper f raction

as:

24

15 =

2 × 15 + 4

15 =

34

15

Step 2

We now need to subtract the f ollowing unlike f ractions: 145

6 and

34

15 .

Bef ore we subtract, let us f irst convert them to like f ractions.

Step 3

Let us f ind the LCM of the denominators 6 and 15.The LCM of 6 and 15 is 30.

Step 4

What should we multiply with the denominator 6 to get the LCM 30?

It is 30

6 = 5.

So, the f irst f raction can be written as:

145 × 5

6 × 5 =

725

30

Step 5

Similarly, the second f raction can be written as:

34 × 2

15 × 2 =

68

30

Step 6

Let us now subtract the two like f ractions:

725

30 -

68

30

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= 725 - 68

30

= 657

30

= 657 ÷ 3

30 ÷ 3 ...[ Dividing both numerator and denominator by their HCF to bring ]

= 219

10

= 219

10

Step 7

Thus, the simplif ied value of the given f ractions is 219

10 .

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E) 21

59

140 - 3

4

7 = 17

17

20

Step 1

Let us f irst convert the given mixed f ractions into improper f ractions. In order to

convert the mixed f raction 2159

140 into an improper f raction, we will need to

multiply the denominator 140 by 21 and add the numerator 59 to the result. Theresulting number will be the numerator of the improper f raction and thedenominator will remain the same:

2159

140 =

21 × 140 + 59

140 =

2999

140

Similarly, the mixed f raction 34

7 can be converted into an improper f raction as:

34

7 =

3 × 7 + 4

7 =

25

7

Step 2

We now need to subtract the f ollowing unlike f ractions: 2999

140 and

25

7 .

Bef ore we subtract, let us f irst convert them to like f ractions.

Step 3

Let us f ind the LCM of the denominators 140 and 7.The LCM of 140 and 7 is 140.

Step 4

What should we multiply with the denominator 140 to get the LCM 140?

It is 140

140 = 1.

So, the f irst f raction can be written as:

2999 × 1

140 × 1 =

2999

140

Step 5

Similarly, the second f raction can be written as:

25 × 20

7 × 20 =

500

140

Step 6

Let us now subtract the two like f ractions:

2999

140 -

500

140

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= 2999 - 500

140

= 2499

140

= 2499 ÷ 7

140 ÷ 7 ...[ Dividing both numerator and denominator by their HCF to bring ]

= 357

20

= 1717

20

Step 7

Thus, the simplif ied value of the given f ractions is 1717

20 .

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F) 10

161

240 - 1

11

15 = 8

15

16

Step 1

Let us f irst convert the given mixed f ractions into improper f ractions. In order to

convert the mixed f raction 10161

240 into an improper f raction, we will need to

multiply the denominator 240 by 10 and add the numerator 161 to the result. Theresulting number will be the numerator of the improper f raction and thedenominator will remain the same:

10161

240 =

10 × 240 + 161

240 =

2561

240

Similarly, the mixed f raction 111

15 can be converted into an improper f raction

as:

111

15 =

1 × 15 + 11

15 =

26

15

Step 2

We now need to subtract the f ollowing unlike f ractions: 2561

240 and

26

15 .

Bef ore we subtract, let us f irst convert them to like f ractions.

Step 3

Let us f ind the LCM of the denominators 240 and 15.The LCM of 240 and 15 is 240.

Step 4

What should we multiply with the denominator 240 to get the LCM 240?

It is 240

240 = 1.

So, the f irst f raction can be written as:

2561 × 1

240 × 1 =

2561

240

Step 5

Similarly, the second f raction can be written as:

26 × 16

15 × 16 =

416

240

Step 6

Let us now subtract the two like f ractions:

2561

240 -

416

240

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= 2561 - 416

240

= 2145

240

= 2145 ÷ 15

240 ÷ 15 ...[ Dividing both numerator and denominator by their HCF to bring

]

= 143

16

= 815

16

Step 7

Thus, the simplif ied value of the given f ractions is 815

16 .

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G) 26

35

99 - 2

9

22 = 23

17

18

Step 1

Let us f irst convert the given mixed f ractions into improper f ractions. In order to

convert the mixed f raction 2635

99 into an improper f raction, we will need to

multiply the denominator 99 by 26 and add the numerator 35 to the result. Theresulting number will be the numerator of the improper f raction and thedenominator will remain the same:

2635

99 =

26 × 99 + 35

99 =

2609

99

Similarly, the mixed f raction 29

22 can be converted into an improper f raction

as:

29

22 =

2 × 22 + 9

22 =

53

22

Step 2

We now need to subtract the f ollowing unlike f ractions: 2609

99 and

53

22 .

Bef ore we subtract, let us f irst convert them to like f ractions.

Step 3

Let us f ind the LCM of the denominators 99 and 22.The LCM of 99 and 22 is 198.

Step 4

What should we multiply with the denominator 99 to get the LCM 198?

It is 198

99 = 2.

So, the f irst f raction can be written as:

2609 × 2

99 × 2 =

5218

198

Step 5

Similarly, the second f raction can be written as:

53 × 9

22 × 9 =

477

198

Step 6

Let us now subtract the two like f ractions:

5218

198 -

477

198

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= 5218 - 477

198

= 4741

198

= 4741 ÷ 11

198 ÷ 11 ...[ Dividing both numerator and denominator by their HCF to bring

]

= 431

18

= 2317

18

Step 7

Thus, the simplif ied value of the given f ractions is 2317

18 .

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H) 25

31

180 - 3

9

20 = 21

13

18

Step 1

Let us f irst convert the given mixed f ractions into improper f ractions. In order to

convert the mixed f raction 2531

180 into an improper f raction, we will need to

multiply the denominator 180 by 25 and add the numerator 31 to the result. Theresulting number will be the numerator of the improper f raction and thedenominator will remain the same:

2531

180 =

25 × 180 + 31

180 =

4531

180

Similarly, the mixed f raction 39

20 can be converted into an improper f raction

as:

39

20 =

3 × 20 + 9

20 =

69

20

Step 2

We now need to subtract the f ollowing unlike f ractions: 4531

180 and

69

20 .

Bef ore we subtract, let us f irst convert them to like f ractions.

Step 3

Let us f ind the LCM of the denominators 180 and 20.The LCM of 180 and 20 is 180.

Step 4

What should we multiply with the denominator 180 to get the LCM 180?

It is 180

180 = 1.

So, the f irst f raction can be written as:

4531 × 1

180 × 1 =

4531

180

Step 5

Similarly, the second f raction can be written as:

69 × 9

20 × 9 =

621

180

Step 6

Let us now subtract the two like f ractions:

4531

180 -

621

180

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= 4531 - 621

180

= 3910

180

= 3910 ÷ 10

180 ÷ 10 ...[ Dividing both numerator and denominator by their HCF to bring

]

= 391

18

= 2113

18

Step 7

Thus, the simplif ied value of the given f ractions is 2113

18 .

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I) 33

41

220 - 7

11

20 = 25

7

11

Step 1

Let us f irst convert the given mixed f ractions into improper f ractions. In order to

convert the mixed f raction 3341

220 into an improper f raction, we will need to

multiply the denominator 220 by 33 and add the numerator 41 to the result. Theresulting number will be the numerator of the improper f raction and thedenominator will remain the same:

3341

220 =

33 × 220 + 41

220 =

7301

220

Similarly, the mixed f raction 711

20 can be converted into an improper f raction

as:

711

20 =

7 × 20 + 11

20 =

151

20

Step 2

We now need to subtract the f ollowing unlike f ractions: 7301

220 and

151

20 .

Bef ore we subtract, let us f irst convert them to like f ractions.

Step 3

Let us f ind the LCM of the denominators 220 and 20.The LCM of 220 and 20 is 220.

Step 4

What should we multiply with the denominator 220 to get the LCM 220?

It is 220

220 = 1.

So, the f irst f raction can be written as:

7301 × 1

220 × 1 =

7301

220

Step 5

Similarly, the second f raction can be written as:

151 × 11

20 × 11 =

1661

220

Step 6

Let us now subtract the two like f ractions:

7301

220 -

1661

220

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= 7301 - 1661

220

= 5640

220

= 5640 ÷ 20

220 ÷ 20 ...[ Dividing both numerator and denominator by their HCF to bring

]

= 282

11

= 257

11

Step 7

Thus, the simplif ied value of the given f ractions is 257

11 .

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J) 18

218

221 - 1

5

17 = 17

9

13

Step 1

Let us f irst convert the given mixed f ractions into improper f ractions. In order to

convert the mixed f raction 18218

221 into an improper f raction, we will need to

multiply the denominator 221 by 18 and add the numerator 218 to the result. Theresulting number will be the numerator of the improper f raction and thedenominator will remain the same:

18218

221 =

18 × 221 + 218

221 =

4196

221

Similarly, the mixed f raction 15

17 can be converted into an improper f raction

as:

15

17 =

1 × 17 + 5

17 =

22

17

Step 2

We now need to subtract the f ollowing unlike f ractions: 4196

221 and

22

17 .

Bef ore we subtract, let us f irst convert them to like f ractions.

Step 3

Let us f ind the LCM of the denominators 221 and 17.The LCM of 221 and 17 is 221.

Step 4

What should we multiply with the denominator 221 to get the LCM 221?

It is 221

221 = 1.

So, the f irst f raction can be written as:

4196 × 1

221 × 1 =

4196

221

Step 5

Similarly, the second f raction can be written as:

22 × 13

17 × 13 =

286

221

Step 6

Let us now subtract the two like f ractions:

4196

221 -

286

221

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= 4196 - 286

221

= 3910

221

= 3910 ÷ 17

221 ÷ 17 ...[ Dividing both numerator and denominator by their HCF to bring

]

= 230

13

= 179

13

Step 7

Thus, the simplif ied value of the given f ractions is 179

13 .

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(2) A) 8

17

21 + 6

29

52 = 15

401

1092

Step 1

Let us f irst convert the given mixed f ractions into improper f ractions. In order to

convert the mixed f raction 817

21 into an improper f raction, we will need to

multiply the denominator 21 by 8 and add the numerator 17 to the result. Theresulting number will be the numerator of the improper f raction and thedenominator will remain the same:

817

21 =

8 × 21 + 17

21 =

185

21

Similarly, the mixed f raction 629

52 can be converted to an improper f raction as:

629

52 =

6 × 52 + 29

52 =

341

52

Step 2

We now need to add the f ollowing unlike f ractions: 185

21 and

341

52 .

Let us f irst convert them to like f ractions.

Step 3

Let us f ind the LCM of the denominators 21 and 52.The LCM of 21 and 52 is 1092.

Step 4

What should we multiply with the denominator 21 to get the LCM 1092?

It is 1092

21 = 52.

So, the f irst f raction can be written as:

185 × 52

1092 =

9620

1092

Step 5

Similarly, the second f raction can be written as:

341 × 21

1092 =

7161

1092

Step 6

Let us now add the two like f ractions:

9620

1092 +

7161

1092

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= 9620 + 7161

1092

= 16781

1092

= 15401

1092

Step 7

Thus, the sum of the f ractions 817

21 and 6

29

52 is 15

401

1092 .

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B) 9

19

20 + 2

19

29 = 12

351

580

Step 1

Let us f irst convert the given mixed f ractions into improper f ractions. In order to

convert the mixed f raction 919

20 into an improper f raction, we will need to

multiply the denominator 20 by 9 and add the numerator 19 to the result. Theresulting number will be the numerator of the improper f raction and thedenominator will remain the same:

919

20 =

9 × 20 + 19

20 =

199

20

Similarly, the mixed f raction 219

29 can be converted to an improper f raction as:

219

29 =

2 × 29 + 19

29 =

77

29

Step 2

We now need to add the f ollowing unlike f ractions: 199

20 and

77

29 .

Let us f irst convert them to like f ractions.

Step 3

Let us f ind the LCM of the denominators 20 and 29.The LCM of 20 and 29 is 580.

Step 4

What should we multiply with the denominator 20 to get the LCM 580?

It is 580

20 = 29.

So, the f irst f raction can be written as:

199 × 29

580 =

5771

580

Step 5

Similarly, the second f raction can be written as:

77 × 20

580 =

1540

580

Step 6

Let us now add the two like f ractions:

5771

580 +

1540

580

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= 5771 + 1540

580

= 7311

580

= 12351

580

Step 7

Thus, the sum of the f ractions 919

20 and 2

19

29 is 12

351

580 .

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C) 10

23

24 + 3

26

49 = 14

575

1176

Step 1

Let us f irst convert the given mixed f ractions into improper f ractions. In order to

convert the mixed f raction 1023

24 into an improper f raction, we will need to

multiply the denominator 24 by 10 and add the numerator 23 to the result. Theresulting number will be the numerator of the improper f raction and thedenominator will remain the same:

1023

24 =

10 × 24 + 23

24 =

263

24

Similarly, the mixed f raction 326

49 can be converted to an improper f raction as:

326

49 =

3 × 49 + 26

49 =

173

49

Step 2

We now need to add the f ollowing unlike f ractions: 263

24 and

173

49 .

Let us f irst convert them to like f ractions.

Step 3

Let us f ind the LCM of the denominators 24 and 49.The LCM of 24 and 49 is 1176.

Step 4

What should we multiply with the denominator 24 to get the LCM 1176?

It is 1176

24 = 49.

So, the f irst f raction can be written as:

263 × 49

1176 =

12887

1176

Step 5

Similarly, the second f raction can be written as:

173 × 24

1176 =

4152

1176

Step 6

Let us now add the two like f ractions:

12887

1176 +

4152

1176

ID : in-6-Mixed-Fractions-Addition-and-Subtraction [28]

(C) 2016 Edugain (www.Edugain.com) Personal use only, commercial use is strictly prohibited

= 12887 + 4152

1176

= 17039

1176

= 14575

1176

Step 7

Thus, the sum of the f ractions 1023

24 and 3

26

49 is 14

575

1176 .

ID : in-6-Mixed-Fractions-Addition-and-Subtraction [29]

(C) 2016 Edugain (www.Edugain.com) Personal use only, commercial use is strictly prohibited

D) 20

14

17 + 1

18

29 = 22

219

493

Step 1

Let us f irst convert the given mixed f ractions into improper f ractions. In order to

convert the mixed f raction 2014

17 into an improper f raction, we will need to

multiply the denominator 17 by 20 and add the numerator 14 to the result. Theresulting number will be the numerator of the improper f raction and thedenominator will remain the same:

2014

17 =

20 × 17 + 14

17 =

354

17

Similarly, the mixed f raction 118

29 can be converted to an improper f raction as:

118

29 =

1 × 29 + 18

29 =

47

29

Step 2

We now need to add the f ollowing unlike f ractions: 354

17 and

47

29 .

Let us f irst convert them to like f ractions.

Step 3

Let us f ind the LCM of the denominators 17 and 29.The LCM of 17 and 29 is 493.

Step 4

What should we multiply with the denominator 17 to get the LCM 493?

It is 493

17 = 29.

So, the f irst f raction can be written as:

354 × 29

493 =

10266

493

Step 5

Similarly, the second f raction can be written as:

47 × 17

493 =

799

493

Step 6

Let us now add the two like f ractions:

10266

493 +

799

493

ID : in-6-Mixed-Fractions-Addition-and-Subtraction [30]

(C) 2016 Edugain (www.Edugain.com) Personal use only, commercial use is strictly prohibited

= 10266 + 799

493

= 11065

493

= 22219

493

Step 7

Thus, the sum of the f ractions 2014

17 and 1

18

29 is 22

219

493 .

ID : in-6-Mixed-Fractions-Addition-and-Subtraction [31]

(C) 2016 Edugain (www.Edugain.com) Personal use only, commercial use is strictly prohibited

E) 14

11

15 + 4

14

33 = 19

26

165

Step 1

Let us f irst convert the given mixed f ractions into improper f ractions. In order to

convert the mixed f raction 1411

15 into an improper f raction, we will need to

multiply the denominator 15 by 14 and add the numerator 11 to the result. Theresulting number will be the numerator of the improper f raction and thedenominator will remain the same:

1411

15 =

14 × 15 + 11

15 =

221

15

Similarly, the mixed f raction 414

33 can be converted to an improper f raction as:

414

33 =

4 × 33 + 14

33 =

146

33

Step 2

We now need to add the f ollowing unlike f ractions: 221

15 and

146

33 .

Let us f irst convert them to like f ractions.

Step 3

Let us f ind the LCM of the denominators 15 and 33.The LCM of 15 and 33 is 165.

Step 4

What should we multiply with the denominator 15 to get the LCM 165?

It is 165

15 = 11.

So, the f irst f raction can be written as:

221 × 11

165 =

2431

165

Step 5

Similarly, the second f raction can be written as:

146 × 5

165 =

730

165

Step 6

Let us now add the two like f ractions:

2431

165 +

730

165

ID : in-6-Mixed-Fractions-Addition-and-Subtraction [32]

(C) 2016 Edugain (www.Edugain.com) Personal use only, commercial use is strictly prohibited

= 2431 + 730

165

= 3161

165

= 1926

165

Step 7

Thus, the sum of the f ractions 1411

15 and 4

14

33 is 19

26

165 .

ID : in-6-Mixed-Fractions-Addition-and-Subtraction [33]

(C) 2016 Edugain (www.Edugain.com) Personal use only, commercial use is strictly prohibited

F) 23

29

30 + 1

27

52 = 25

379

780

Step 1

Let us f irst convert the given mixed f ractions into improper f ractions. In order to

convert the mixed f raction 2329

30 into an improper f raction, we will need to

multiply the denominator 30 by 23 and add the numerator 29 to the result. Theresulting number will be the numerator of the improper f raction and thedenominator will remain the same:

2329

30 =

23 × 30 + 29

30 =

719

30

Similarly, the mixed f raction 127

52 can be converted to an improper f raction as:

127

52 =

1 × 52 + 27

52 =

79

52

Step 2

We now need to add the f ollowing unlike f ractions: 719

30 and

79

52 .

Let us f irst convert them to like f ractions.

Step 3

Let us f ind the LCM of the denominators 30 and 52.The LCM of 30 and 52 is 780.

Step 4

What should we multiply with the denominator 30 to get the LCM 780?

It is 780

30 = 26.

So, the f irst f raction can be written as:

719 × 26

780 =

18694

780

Step 5

Similarly, the second f raction can be written as:

79 × 15

780 =

1185

780

Step 6

Let us now add the two like f ractions:

18694

780 +

1185

780

ID : in-6-Mixed-Fractions-Addition-and-Subtraction [34]

(C) 2016 Edugain (www.Edugain.com) Personal use only, commercial use is strictly prohibited

= 18694 + 1185

780

= 19879

780

= 25379

780

Step 7

Thus, the sum of the f ractions 2329

30 and 1

27

52 is 25

379

780 .

ID : in-6-Mixed-Fractions-Addition-and-Subtraction [35]

(C) 2016 Edugain (www.Edugain.com) Personal use only, commercial use is strictly prohibited

G) 8

11

14 + 5

5

6 = 14

13

21

Step 1

Let us f irst convert the given mixed f ractions into improper f ractions. In order to

convert the mixed f raction 811

14 into an improper f raction, we will need to

multiply the denominator 14 by 8 and add the numerator 11 to the result. Theresulting number will be the numerator of the improper f raction and thedenominator will remain the same:

811

14 =

8 × 14 + 11

14 =

123

14

Similarly, the mixed f raction 55

6 can be converted to an improper f raction as:

55

6 =

5 × 6 + 5

6 =

35

6

Step 2

We now need to add the f ollowing unlike f ractions: 123

14 and

35

6 .

Let us f irst convert them to like f ractions.

Step 3

Let us f ind the LCM of the denominators 14 and 6.The LCM of 14 and 6 is 42.

Step 4

What should we multiply with the denominator 14 to get the LCM 42?

It is 42

14 = 3.

So, the f irst f raction can be written as:

123 × 3

42 =

369

42

Step 5

Similarly, the second f raction can be written as:

35 × 7

42 =

245

42

Step 6

Let us now add the two like f ractions:

369

42 +

245

42

ID : in-6-Mixed-Fractions-Addition-and-Subtraction [36]

(C) 2016 Edugain (www.Edugain.com) Personal use only, commercial use is strictly prohibited

= 369 + 245

42

= 614

42

= 1413

21

Step 7

Thus, the sum of the f ractions 811

14 and 5

5

6 is 14

13

21 .

ID : in-6-Mixed-Fractions-Addition-and-Subtraction [37]

(C) 2016 Edugain (www.Edugain.com) Personal use only, commercial use is strictly prohibited

H) 11

24

25 + 3

18

29 = 15

421

725

Step 1

Let us f irst convert the given mixed f ractions into improper f ractions. In order to

convert the mixed f raction 1124

25 into an improper f raction, we will need to

multiply the denominator 25 by 11 and add the numerator 24 to the result. Theresulting number will be the numerator of the improper f raction and thedenominator will remain the same:

1124

25 =

11 × 25 + 24

25 =

299

25

Similarly, the mixed f raction 318

29 can be converted to an improper f raction as:

318

29 =

3 × 29 + 18

29 =

105

29

Step 2

We now need to add the f ollowing unlike f ractions: 299

25 and

105

29 .

Let us f irst convert them to like f ractions.

Step 3

Let us f ind the LCM of the denominators 25 and 29.The LCM of 25 and 29 is 725.

Step 4

What should we multiply with the denominator 25 to get the LCM 725?

It is 725

25 = 29.

So, the f irst f raction can be written as:

299 × 29

725 =

8671

725

Step 5

Similarly, the second f raction can be written as:

105 × 25

725 =

2625

725

Step 6

Let us now add the two like f ractions:

8671

725 +

2625

725

ID : in-6-Mixed-Fractions-Addition-and-Subtraction [38]

(C) 2016 Edugain (www.Edugain.com) Personal use only, commercial use is strictly prohibited

= 8671 + 2625

725

= 11296

725

= 15421

725

Step 7

Thus, the sum of the f ractions 1124

25 and 3

18

29 is 15

421

725 .

ID : in-6-Mixed-Fractions-Addition-and-Subtraction [39]

(C) 2016 Edugain (www.Edugain.com) Personal use only, commercial use is strictly prohibited

I) 9

21

25 + 6

24

41 = 16

436

1025

Step 1

Let us f irst convert the given mixed f ractions into improper f ractions. In order to

convert the mixed f raction 921

25 into an improper f raction, we will need to

multiply the denominator 25 by 9 and add the numerator 21 to the result. Theresulting number will be the numerator of the improper f raction and thedenominator will remain the same:

921

25 =

9 × 25 + 21

25 =

246

25

Similarly, the mixed f raction 624

41 can be converted to an improper f raction as:

624

41 =

6 × 41 + 24

41 =

270

41

Step 2

We now need to add the f ollowing unlike f ractions: 246

25 and

270

41 .

Let us f irst convert them to like f ractions.

Step 3

Let us f ind the LCM of the denominators 25 and 41.The LCM of 25 and 41 is 1025.

Step 4

What should we multiply with the denominator 25 to get the LCM 1025?

It is 1025

25 = 41.

So, the f irst f raction can be written as:

246 × 41

1025 =

10086

1025

Step 5

Similarly, the second f raction can be written as:

270 × 25

1025 =

6750

1025

Step 6

Let us now add the two like f ractions:

10086

1025 +

6750

1025

ID : in-6-Mixed-Fractions-Addition-and-Subtraction [40]

(C) 2016 Edugain (www.Edugain.com) Personal use only, commercial use is strictly prohibited

= 10086 + 6750

1025

= 16836

1025

= 16436

1025

Step 7

Thus, the sum of the f ractions 921

25 and 6

24

41 is 16

436

1025 .

ID : in-6-Mixed-Fractions-Addition-and-Subtraction [41]

(C) 2016 Edugain (www.Edugain.com) Personal use only, commercial use is strictly prohibited

J) 11

19

22 + 4

4

15 = 16

43

330

Step 1

Let us f irst convert the given mixed f ractions into improper f ractions. In order to

convert the mixed f raction 1119

22 into an improper f raction, we will need to

multiply the denominator 22 by 11 and add the numerator 19 to the result. Theresulting number will be the numerator of the improper f raction and thedenominator will remain the same:

1119

22 =

11 × 22 + 19

22 =

261

22

Similarly, the mixed f raction 44

15 can be converted to an improper f raction as:

44

15 =

4 × 15 + 4

15 =

64

15

Step 2

We now need to add the f ollowing unlike f ractions: 261

22 and

64

15 .

Let us f irst convert them to like f ractions.

Step 3

Let us f ind the LCM of the denominators 22 and 15.The LCM of 22 and 15 is 330.

Step 4

What should we multiply with the denominator 22 to get the LCM 330?

It is 330

22 = 15.

So, the f irst f raction can be written as:

261 × 15

330 =

3915

330

Step 5

Similarly, the second f raction can be written as:

64 × 22

330 =

1408

330

Step 6

Let us now add the two like f ractions:

3915

330 +

1408

330

ID : in-6-Mixed-Fractions-Addition-and-Subtraction [42]

(C) 2016 Edugain (www.Edugain.com) Personal use only, commercial use is strictly prohibited

= 3915 + 1408

330

= 5323

330

= 1643

330

Step 7

Thus, the sum of the f ractions 1119

22 and 4

4

15 is 16

43

330 .

ID : in-6-Mixed-Fractions-Addition-and-Subtraction [43]

(C) 2016 Edugain (www.Edugain.com) Personal use only, commercial use is strictly prohibited

K) 9

16

19 + 2

18

31 = 12

249

589

Step 1

Let us f irst convert the given mixed f ractions into improper f ractions. In order to

convert the mixed f raction 916

19 into an improper f raction, we will need to

multiply the denominator 19 by 9 and add the numerator 16 to the result. Theresulting number will be the numerator of the improper f raction and thedenominator will remain the same:

916

19 =

9 × 19 + 16

19 =

187

19

Similarly, the mixed f raction 218

31 can be converted to an improper f raction as:

218

31 =

2 × 31 + 18

31 =

80

31

Step 2

We now need to add the f ollowing unlike f ractions: 187

19 and

80

31 .

Let us f irst convert them to like f ractions.

Step 3

Let us f ind the LCM of the denominators 19 and 31.The LCM of 19 and 31 is 589.

Step 4

What should we multiply with the denominator 19 to get the LCM 589?

It is 589

19 = 31.

So, the f irst f raction can be written as:

187 × 31

589 =

5797

589

Step 5

Similarly, the second f raction can be written as:

80 × 19

589 =

1520

589

Step 6

Let us now add the two like f ractions:

5797

589 +

1520

589

ID : in-6-Mixed-Fractions-Addition-and-Subtraction [44]

(C) 2016 Edugain (www.Edugain.com) Personal use only, commercial use is strictly prohibited

= 5797 + 1520

589

= 7317

589

= 12249

589

Step 7

Thus, the sum of the f ractions 916

19 and 2

18

31 is 12

249

589 .

ID : in-6-Mixed-Fractions-Addition-and-Subtraction [45]

(C) 2016 Edugain (www.Edugain.com) Personal use only, commercial use is strictly prohibited

L) 11

23

24 + 2

17

31 = 14

377

744

Step 1

Let us f irst convert the given mixed f ractions into improper f ractions. In order to

convert the mixed f raction 1123

24 into an improper f raction, we will need to

multiply the denominator 24 by 11 and add the numerator 23 to the result. Theresulting number will be the numerator of the improper f raction and thedenominator will remain the same:

1123

24 =

11 × 24 + 23

24 =

287

24

Similarly, the mixed f raction 217

31 can be converted to an improper f raction as:

217

31 =

2 × 31 + 17

31 =

79

31

Step 2

We now need to add the f ollowing unlike f ractions: 287

24 and

79

31 .

Let us f irst convert them to like f ractions.

Step 3

Let us f ind the LCM of the denominators 24 and 31.The LCM of 24 and 31 is 744.

Step 4

What should we multiply with the denominator 24 to get the LCM 744?

It is 744

24 = 31.

So, the f irst f raction can be written as:

287 × 31

744 =

8897

744

Step 5

Similarly, the second f raction can be written as:

79 × 24

744 =

1896

744

Step 6

Let us now add the two like f ractions:

8897

744 +

1896

744

ID : in-6-Mixed-Fractions-Addition-and-Subtraction [46]

(C) 2016 Edugain (www.Edugain.com) Personal use only, commercial use is strictly prohibited

= 8897 + 1896

744

= 10793

744

= 14377

744

Step 7

Thus, the sum of the f ractions 1123

24 and 2

17

31 is 14

377

744 .

ID : in-6-Mixed-Fractions-Addition-and-Subtraction [47]

(C) 2016 Edugain (www.Edugain.com) Personal use only, commercial use is strictly prohibited

M) 20

8

11 + 4

10

23 = 25

41

253

Step 1

Let us f irst convert the given mixed f ractions into improper f ractions. In order to

convert the mixed f raction 208

11 into an improper f raction, we will need to

multiply the denominator 11 by 20 and add the numerator 8 to the result. Theresulting number will be the numerator of the improper f raction and thedenominator will remain the same:

208

11 =

20 × 11 + 8

11 =

228

11

Similarly, the mixed f raction 410

23 can be converted to an improper f raction as:

410

23 =

4 × 23 + 10

23 =

102

23

Step 2

We now need to add the f ollowing unlike f ractions: 228

11 and

102

23 .

Let us f irst convert them to like f ractions.

Step 3

Let us f ind the LCM of the denominators 11 and 23.The LCM of 11 and 23 is 253.

Step 4

What should we multiply with the denominator 11 to get the LCM 253?

It is 253

11 = 23.

So, the f irst f raction can be written as:

228 × 23

253 =

5244

253

Step 5

Similarly, the second f raction can be written as:

102 × 11

253 =

1122

253

Step 6

Let us now add the two like f ractions:

5244

253 +

1122

253

ID : in-6-Mixed-Fractions-Addition-and-Subtraction [48]

(C) 2016 Edugain (www.Edugain.com) Personal use only, commercial use is strictly prohibited

= 5244 + 1122

253

= 6366

253

= 2541

253

Step 7

Thus, the sum of the f ractions 208

11 and 4

10

23 is 25

41

253 .

ID : in-6-Mixed-Fractions-Addition-and-Subtraction [49]

(C) 2016 Edugain (www.Edugain.com) Personal use only, commercial use is strictly prohibited

N) 17

17

18 + 4

26

31 = 22

437

558

Step 1

Let us f irst convert the given mixed f ractions into improper f ractions. In order to

convert the mixed f raction 1717

18 into an improper f raction, we will need to

multiply the denominator 18 by 17 and add the numerator 17 to the result. Theresulting number will be the numerator of the improper f raction and thedenominator will remain the same:

1717

18 =

17 × 18 + 17

18 =

323

18

Similarly, the mixed f raction 426

31 can be converted to an improper f raction as:

426

31 =

4 × 31 + 26

31 =

150

31

Step 2

We now need to add the f ollowing unlike f ractions: 323

18 and

150

31 .

Let us f irst convert them to like f ractions.

Step 3

Let us f ind the LCM of the denominators 18 and 31.The LCM of 18 and 31 is 558.

Step 4

What should we multiply with the denominator 18 to get the LCM 558?

It is 558

18 = 31.

So, the f irst f raction can be written as:

323 × 31

558 =

10013

558

Step 5

Similarly, the second f raction can be written as:

150 × 18

558 =

2700

558

Step 6

Let us now add the two like f ractions:

10013

558 +

2700

558

ID : in-6-Mixed-Fractions-Addition-and-Subtraction [50]

(C) 2016 Edugain (www.Edugain.com) Personal use only, commercial use is strictly prohibited

= 10013 + 2700

558

= 12713

558

= 22437

558

Step 7

Thus, the sum of the f ractions 1717

18 and 4

26

31 is 22

437

558 .

ID : in-6-Mixed-Fractions-Addition-and-Subtraction [51]

(C) 2016 Edugain (www.Edugain.com) Personal use only, commercial use is strictly prohibited

O) 12

9

10 + 1

17

31 = 14

139

310

Step 1

Let us f irst convert the given mixed f ractions into improper f ractions. In order to

convert the mixed f raction 129

10 into an improper f raction, we will need to

multiply the denominator 10 by 12 and add the numerator 9 to the result. Theresulting number will be the numerator of the improper f raction and thedenominator will remain the same:

129

10 =

12 × 10 + 9

10 =

129

10

Similarly, the mixed f raction 117

31 can be converted to an improper f raction as:

117

31 =

1 × 31 + 17

31 =

48

31

Step 2

We now need to add the f ollowing unlike f ractions: 129

10 and

48

31 .

Let us f irst convert them to like f ractions.

Step 3

Let us f ind the LCM of the denominators 10 and 31.The LCM of 10 and 31 is 310.

Step 4

What should we multiply with the denominator 10 to get the LCM 310?

It is 310

10 = 31.

So, the f irst f raction can be written as:

129 × 31

310 =

3999

310

Step 5

Similarly, the second f raction can be written as:

48 × 10

310 =

480

310

Step 6

Let us now add the two like f ractions:

3999

310 +

480

310

ID : in-6-Mixed-Fractions-Addition-and-Subtraction [52]

(C) 2016 Edugain (www.Edugain.com) Personal use only, commercial use is strictly prohibited

= 3999 + 480

310

= 4479

310

= 14139

310

Step 7

Thus, the sum of the f ractions 129

10 and 1

17

31 is 14

139

310 .

ID : in-6-Mixed-Fractions-Addition-and-Subtraction [53]

(C) 2016 Edugain (www.Edugain.com) Personal use only, commercial use is strictly prohibited