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Grade 6Mixed Fractions - Addition and Subtraction
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(1) Simplif y the f ollowing f ractions:
A) 21
139
323 - 6
10
17 =
B) 6
55
234 - 2
7
18 =
C) 26
105
323 - 4
10
17 =
D) 6
73
306 - 2
5
17 =
E) 22
106
165 - 4
10
11 =
F) 22
278
285 - 3
2
15 =
G) 38
41
176 - 7
6
11 =
H) 19
149
266 - 2
12
19 =
I) 17
159
272 - 4
11
17 =
J) 16
1
4 - 7
5
16 =
(2) Add the f ollowing f ractions:
A) 17
25
26 + 5
6
13 =
B) 14
23
28 + 1
22
35 =
C) 19
19
21 + 2
29
47 =
D) 13
14
19 + 7
2
5 =
E) 11
14
19 + 3
10
17 =
F) 17
21
25 + 3
29
31 =
G) 10
9
11 + 6
20
37 =
H) 19
9
14 + 1
11
19 =
I) 9
14
15 + 1
29
52 =
ID : ww-6-Mixed-Fractions-Addition-and-Subtraction [1]
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J) 9
29
32 + 7
22
35 =
K) 10
29
31 + 1
11
31 =
L) 18
27
28 + 1
21
22 =
M) 12
22
25 + 7
27
40 =
N) 8
24
29 + 2
21
37 =
O) 19
29
30 + 2
23
38 =
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AnswersID : ww-6-Mixed-Fractions-Addition-and-Subtraction [3]
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(1) A) 21
139
323 - 6
10
17 = 14
16
19
Step 1
Let us f irst convert the given mixed f ractions into improper f ractions. In order to
convert the mixed f raction 21139
323 into an improper f raction, we will need to
multiply the denominator 323 by 21 and add the numerator 139 to the result. Theresulting number will be the numerator of the improper f raction and thedenominator will remain the same:
21139
323 =
21 × 323 + 139
323 =
6922
323
Similarly, the mixed f raction 610
17 can be converted into an improper f raction
as:
610
17 =
6 × 17 + 10
17 =
112
17
Step 2
We now need to subtract the f ollowing unlike f ractions: 6922
323 and
112
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 323 and 17.The LCM of 323 and 17 is 323.
Step 4
What should we multiply with the denominator 323 to get the LCM 323?
It is 323
323 = 1.
So, the f irst f raction can be written as:
6922 × 1
323 × 1 =
6922
323
Step 5
Similarly, the second f raction can be written as:
112 × 19
17 × 19 =
2128
323
Step 6
Let us now subtract the two like f ractions:
6922
323 -
2128
323
ID : ww-6-Mixed-Fractions-Addition-and-Subtraction [4]
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= 6922 - 2128
323
= 4794
323
= 4794 ÷ 17
323 ÷ 17 ...[ Dividing both numerator and denominator by their HCF to
bring ]
= 282
19
= 1416
19
Step 7
Thus, the simplif ied value of the given f ractions is 1416
19 .
ID : ww-6-Mixed-Fractions-Addition-and-Subtraction [5]
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B) 6
55
234 - 2
7
18 = 3
11
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 655
234 into an improper f raction, we will need to
multiply the denominator 234 by 6 and add the numerator 55 to the result. Theresulting number will be the numerator of the improper f raction and thedenominator will remain the same:
655
234 =
6 × 234 + 55
234 =
1459
234
Similarly, the mixed f raction 27
18 can be converted into an improper f raction
as:
27
18 =
2 × 18 + 7
18 =
43
18
Step 2
We now need to subtract the f ollowing unlike f ractions: 1459
234 and
43
18 .
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 234 and 18.The LCM of 234 and 18 is 234.
Step 4
What should we multiply with the denominator 234 to get the LCM 234?
It is 234
234 = 1.
So, the f irst f raction can be written as:
1459 × 1
234 × 1 =
1459
234
Step 5
Similarly, the second f raction can be written as:
43 × 13
18 × 13 =
559
234
Step 6
Let us now subtract the two like f ractions:
1459
234 -
559
234
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= 1459 - 559
234
= 900
234
= 900 ÷ 18
234 ÷ 18 ...[ Dividing both numerator and denominator by their HCF to bring ]
= 50
13
= 311
13
Step 7
Thus, the simplif ied value of the given f ractions is 311
13 .
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C) 26
105
323 - 4
10
17 = 21
14
19
Step 1
Let us f irst convert the given mixed f ractions into improper f ractions. In order to
convert the mixed f raction 26105
323 into an improper f raction, we will need to
multiply the denominator 323 by 26 and add the numerator 105 to the result. Theresulting number will be the numerator of the improper f raction and thedenominator will remain the same:
26105
323 =
26 × 323 + 105
323 =
8503
323
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: 8503
323 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 323 and 17.The LCM of 323 and 17 is 323.
Step 4
What should we multiply with the denominator 323 to get the LCM 323?
It is 323
323 = 1.
So, the f irst f raction can be written as:
8503 × 1
323 × 1 =
8503
323
Step 5
Similarly, the second f raction can be written as:
78 × 19
17 × 19 =
1482
323
Step 6
Let us now subtract the two like f ractions:
8503
323 -
1482
323
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= 8503 - 1482
323
= 7021
323
= 7021 ÷ 17
323 ÷ 17 ...[ Dividing both numerator and denominator by their HCF to bring
]
= 413
19
= 2114
19
Step 7
Thus, the simplif ied value of the given f ractions is 2114
19 .
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D) 6
73
306 - 2
5
17 = 3
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 673
306 into an improper f raction, we will need to
multiply the denominator 306 by 6 and add the numerator 73 to the result. Theresulting number will be the numerator of the improper f raction and thedenominator will remain the same:
673
306 =
6 × 306 + 73
306 =
1909
306
Similarly, the mixed f raction 25
17 can be converted into an improper f raction
as:
25
17 =
2 × 17 + 5
17 =
39
17
Step 2
We now need to subtract the f ollowing unlike f ractions: 1909
306 and
39
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 306 and 17.The LCM of 306 and 17 is 306.
Step 4
What should we multiply with the denominator 306 to get the LCM 306?
It is 306
306 = 1.
So, the f irst f raction can be written as:
1909 × 1
306 × 1 =
1909
306
Step 5
Similarly, the second f raction can be written as:
39 × 18
17 × 18 =
702
306
Step 6
Let us now subtract the two like f ractions:
1909
306 -
702
306
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= 1909 - 702
306
= 1207
306
= 1207 ÷ 17
306 ÷ 17 ...[ Dividing both numerator and denominator by their HCF to bring
]
= 71
18
= 317
18
Step 7
Thus, the simplif ied value of the given f ractions is 317
18 .
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E) 22
106
165 - 4
10
11 = 17
11
15
Step 1
Let us f irst convert the given mixed f ractions into improper f ractions. In order to
convert the mixed f raction 22106
165 into an improper f raction, we will need to
multiply the denominator 165 by 22 and add the numerator 106 to the result. Theresulting number will be the numerator of the improper f raction and thedenominator will remain the same:
22106
165 =
22 × 165 + 106
165 =
3736
165
Similarly, the mixed f raction 410
11 can be converted into an improper f raction
as:
410
11 =
4 × 11 + 10
11 =
54
11
Step 2
We now need to subtract the f ollowing unlike f ractions: 3736
165 and
54
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 165 and 11.The LCM of 165 and 11 is 165.
Step 4
What should we multiply with the denominator 165 to get the LCM 165?
It is 165
165 = 1.
So, the f irst f raction can be written as:
3736 × 1
165 × 1 =
3736
165
Step 5
Similarly, the second f raction can be written as:
54 × 15
11 × 15 =
810
165
Step 6
Let us now subtract the two like f ractions:
3736
165 -
810
165
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= 3736 - 810
165
= 2926
165
= 2926 ÷ 11
165 ÷ 11 ...[ Dividing both numerator and denominator by their HCF to bring
]
= 266
15
= 1711
15
Step 7
Thus, the simplif ied value of the given f ractions is 1711
15 .
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F) 22
278
285 - 3
2
15 = 19
16
19
Step 1
Let us f irst convert the given mixed f ractions into improper f ractions. In order to
convert the mixed f raction 22278
285 into an improper f raction, we will need to
multiply the denominator 285 by 22 and add the numerator 278 to the result. Theresulting number will be the numerator of the improper f raction and thedenominator will remain the same:
22278
285 =
22 × 285 + 278
285 =
6548
285
Similarly, the mixed f raction 32
15 can be converted into an improper f raction
as:
32
15 =
3 × 15 + 2
15 =
47
15
Step 2
We now need to subtract the f ollowing unlike f ractions: 6548
285 and
47
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 285 and 15.The LCM of 285 and 15 is 285.
Step 4
What should we multiply with the denominator 285 to get the LCM 285?
It is 285
285 = 1.
So, the f irst f raction can be written as:
6548 × 1
285 × 1 =
6548
285
Step 5
Similarly, the second f raction can be written as:
47 × 19
15 × 19 =
893
285
Step 6
Let us now subtract the two like f ractions:
6548
285 -
893
285
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= 6548 - 893
285
= 5655
285
= 5655 ÷ 15
285 ÷ 15 ...[ Dividing both numerator and denominator by their HCF to bring
]
= 377
19
= 1916
19
Step 7
Thus, the simplif ied value of the given f ractions is 1916
19 .
ID : ww-6-Mixed-Fractions-Addition-and-Subtraction [15]
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G) 38
41
176 - 7
6
11 = 30
11
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 3841
176 into an improper f raction, we will need to
multiply the denominator 176 by 38 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:
3841
176 =
38 × 176 + 41
176 =
6729
176
Similarly, the mixed f raction 76
11 can be converted into an improper f raction
as:
76
11 =
7 × 11 + 6
11 =
83
11
Step 2
We now need to subtract the f ollowing unlike f ractions: 6729
176 and
83
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 176 and 11.The LCM of 176 and 11 is 176.
Step 4
What should we multiply with the denominator 176 to get the LCM 176?
It is 176
176 = 1.
So, the f irst f raction can be written as:
6729 × 1
176 × 1 =
6729
176
Step 5
Similarly, the second f raction can be written as:
83 × 16
11 × 16 =
1328
176
Step 6
Let us now subtract the two like f ractions:
6729
176 -
1328
176
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= 6729 - 1328
176
= 5401
176
= 5401 ÷ 11
176 ÷ 11 ...[ Dividing both numerator and denominator by their HCF to bring
]
= 491
16
= 3011
16
Step 7
Thus, the simplif ied value of the given f ractions is 3011
16 .
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H) 19
149
266 - 2
12
19 = 16
13
14
Step 1
Let us f irst convert the given mixed f ractions into improper f ractions. In order to
convert the mixed f raction 19149
266 into an improper f raction, we will need to
multiply the denominator 266 by 19 and add the numerator 149 to the result. Theresulting number will be the numerator of the improper f raction and thedenominator will remain the same:
19149
266 =
19 × 266 + 149
266 =
5203
266
Similarly, the mixed f raction 212
19 can be converted into an improper f raction
as:
212
19 =
2 × 19 + 12
19 =
50
19
Step 2
We now need to subtract the f ollowing unlike f ractions: 5203
266 and
50
19 .
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 266 and 19.The LCM of 266 and 19 is 266.
Step 4
What should we multiply with the denominator 266 to get the LCM 266?
It is 266
266 = 1.
So, the f irst f raction can be written as:
5203 × 1
266 × 1 =
5203
266
Step 5
Similarly, the second f raction can be written as:
50 × 14
19 × 14 =
700
266
Step 6
Let us now subtract the two like f ractions:
5203
266 -
700
266
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= 5203 - 700
266
= 4503
266
= 4503 ÷ 19
266 ÷ 19 ...[ Dividing both numerator and denominator by their HCF to bring
]
= 237
14
= 1613
14
Step 7
Thus, the simplif ied value of the given f ractions is 1613
14 .
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I) 17
159
272 - 4
11
17 = 12
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 17159
272 into an improper f raction, we will need to
multiply the denominator 272 by 17 and add the numerator 159 to the result. Theresulting number will be the numerator of the improper f raction and thedenominator will remain the same:
17159
272 =
17 × 272 + 159
272 =
4783
272
Similarly, the mixed f raction 411
17 can be converted into an improper f raction
as:
411
17 =
4 × 17 + 11
17 =
79
17
Step 2
We now need to subtract the f ollowing unlike f ractions: 4783
272 and
79
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 272 and 17.The LCM of 272 and 17 is 272.
Step 4
What should we multiply with the denominator 272 to get the LCM 272?
It is 272
272 = 1.
So, the f irst f raction can be written as:
4783 × 1
272 × 1 =
4783
272
Step 5
Similarly, the second f raction can be written as:
79 × 16
17 × 16 =
1264
272
Step 6
Let us now subtract the two like f ractions:
4783
272 -
1264
272
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= 4783 - 1264
272
= 3519
272
= 3519 ÷ 17
272 ÷ 17 ...[ Dividing both numerator and denominator by their HCF to bring
]
= 207
16
= 1215
16
Step 7
Thus, the simplif ied value of the given f ractions is 1215
16 .
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J) 16
1
4 - 7
5
16 = 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 161
4 into an improper f raction, we will need to
multiply the denominator 4 by 16 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:
161
4 =
16 × 4 + 1
4 =
65
4
Similarly, the mixed f raction 75
16 can be converted into an improper f raction
as:
75
16 =
7 × 16 + 5
16 =
117
16
Step 2
We now need to subtract the f ollowing unlike f ractions: 65
4 and
117
16 .
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 4 and 16.The LCM of 4 and 16 is 16.
Step 4
What should we multiply with the denominator 4 to get the LCM 16?
It is 16
4 = 4.
So, the f irst f raction can be written as:
65 × 4
4 × 4 =
260
16
Step 5
Similarly, the second f raction can be written as:
117 × 1
16 × 1 =
117
16
Step 6
Let us now subtract the two like f ractions:
260
16 -
117
16
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= 260 - 117
16
= 143
16
= 815
16
Step 7
Thus, the simplif ied value of the given f ractions is 815
16 .
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(2) A) 17
25
26 + 5
6
13 = 23
11
26
Step 1
Let us f irst convert the given mixed f ractions into improper f ractions. In order to
convert the mixed f raction 1725
26 into an improper f raction, we will need to
multiply the denominator 26 by 17 and add the numerator 25 to the result. Theresulting number will be the numerator of the improper f raction and thedenominator will remain the same:
1725
26 =
17 × 26 + 25
26 =
467
26
Similarly, the mixed f raction 56
13 can be converted to an improper f raction as:
56
13 =
5 × 13 + 6
13 =
71
13
Step 2
We now need to add the f ollowing unlike f ractions: 467
26 and
71
13 .
Let us f irst convert them to like f ractions.
Step 3
Let us f ind the LCM of the denominators 26 and 13.The LCM of 26 and 13 is 26.
Step 4
What should we multiply with the denominator 26 to get the LCM 26?
It is 26
26 = 1.
So, the f irst f raction can be written as:
467 × 1
26 =
467
26
Step 5
Similarly, the second f raction can be written as:
71 × 2
26 =
142
26
Step 6
Let us now add the two like f ractions:
467
26 +
142
26
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= 467 + 142
26
= 609
26
= 2311
26
Step 7
Thus, the sum of the f ractions 1725
26 and 5
6
13 is 23
11
26 .
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B) 14
23
28 + 1
22
35 = 16
9
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 1423
28 into an improper f raction, we will need to
multiply the denominator 28 by 14 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:
1423
28 =
14 × 28 + 23
28 =
415
28
Similarly, the mixed f raction 122
35 can be converted to an improper f raction as:
122
35 =
1 × 35 + 22
35 =
57
35
Step 2
We now need to add the f ollowing unlike f ractions: 415
28 and
57
35 .
Let us f irst convert them to like f ractions.
Step 3
Let us f ind the LCM of the denominators 28 and 35.The LCM of 28 and 35 is 140.
Step 4
What should we multiply with the denominator 28 to get the LCM 140?
It is 140
28 = 5.
So, the f irst f raction can be written as:
415 × 5
140 =
2075
140
Step 5
Similarly, the second f raction can be written as:
57 × 4
140 =
228
140
Step 6
Let us now add the two like f ractions:
2075
140 +
228
140
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= 2075 + 228
140
= 2303
140
= 169
20
Step 7
Thus, the sum of the f ractions 1423
28 and 1
22
35 is 16
9
20 .
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C) 19
19
21 + 2
29
47 = 22
515
987
Step 1
Let us f irst convert the given mixed f ractions into improper f ractions. In order to
convert the mixed f raction 1919
21 into an improper f raction, we will need to
multiply the denominator 21 by 19 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:
1919
21 =
19 × 21 + 19
21 =
418
21
Similarly, the mixed f raction 229
47 can be converted to an improper f raction as:
229
47 =
2 × 47 + 29
47 =
123
47
Step 2
We now need to add the f ollowing unlike f ractions: 418
21 and
123
47 .
Let us f irst convert them to like f ractions.
Step 3
Let us f ind the LCM of the denominators 21 and 47.The LCM of 21 and 47 is 987.
Step 4
What should we multiply with the denominator 21 to get the LCM 987?
It is 987
21 = 47.
So, the f irst f raction can be written as:
418 × 47
987 =
19646
987
Step 5
Similarly, the second f raction can be written as:
123 × 21
987 =
2583
987
Step 6
Let us now add the two like f ractions:
19646
987 +
2583
987
ID : ww-6-Mixed-Fractions-Addition-and-Subtraction [28]
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= 19646 + 2583
987
= 22229
987
= 22515
987
Step 7
Thus, the sum of the f ractions 1919
21 and 2
29
47 is 22
515
987 .
ID : ww-6-Mixed-Fractions-Addition-and-Subtraction [29]
(C) 2016 Edugain (www.Edugain.com) Personal use only, commercial use is strictly prohibited
D) 13
14
19 + 7
2
5 = 21
13
95
Step 1
Let us f irst convert the given mixed f ractions into improper f ractions. In order to
convert the mixed f raction 1314
19 into an improper f raction, we will need to
multiply the denominator 19 by 13 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:
1314
19 =
13 × 19 + 14
19 =
261
19
Similarly, the mixed f raction 72
5 can be converted to an improper f raction as:
72
5 =
7 × 5 + 2
5 =
37
5
Step 2
We now need to add the f ollowing unlike f ractions: 261
19 and
37
5 .
Let us f irst convert them to like f ractions.
Step 3
Let us f ind the LCM of the denominators 19 and 5.The LCM of 19 and 5 is 95.
Step 4
What should we multiply with the denominator 19 to get the LCM 95?
It is 95
19 = 5.
So, the f irst f raction can be written as:
261 × 5
95 =
1305
95
Step 5
Similarly, the second f raction can be written as:
37 × 19
95 =
703
95
Step 6
Let us now add the two like f ractions:
1305
95 +
703
95
ID : ww-6-Mixed-Fractions-Addition-and-Subtraction [30]
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= 1305 + 703
95
= 2008
95
= 2113
95
Step 7
Thus, the sum of the f ractions 1314
19 and 7
2
5 is 21
13
95 .
ID : ww-6-Mixed-Fractions-Addition-and-Subtraction [31]
(C) 2016 Edugain (www.Edugain.com) Personal use only, commercial use is strictly prohibited
E) 11
14
19 + 3
10
17 = 15
105
323
Step 1
Let us f irst convert the given mixed f ractions into improper f ractions. In order to
convert the mixed f raction 1114
19 into an improper f raction, we will need to
multiply the denominator 19 by 11 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:
1114
19 =
11 × 19 + 14
19 =
223
19
Similarly, the mixed f raction 310
17 can be converted to an improper f raction as:
310
17 =
3 × 17 + 10
17 =
61
17
Step 2
We now need to add the f ollowing unlike f ractions: 223
19 and
61
17 .
Let us f irst convert them to like f ractions.
Step 3
Let us f ind the LCM of the denominators 19 and 17.The LCM of 19 and 17 is 323.
Step 4
What should we multiply with the denominator 19 to get the LCM 323?
It is 323
19 = 17.
So, the f irst f raction can be written as:
223 × 17
323 =
3791
323
Step 5
Similarly, the second f raction can be written as:
61 × 19
323 =
1159
323
Step 6
Let us now add the two like f ractions:
3791
323 +
1159
323
ID : ww-6-Mixed-Fractions-Addition-and-Subtraction [32]
(C) 2016 Edugain (www.Edugain.com) Personal use only, commercial use is strictly prohibited
= 3791 + 1159
323
= 4950
323
= 15105
323
Step 7
Thus, the sum of the f ractions 1114
19 and 3
10
17 is 15
105
323 .
ID : ww-6-Mixed-Fractions-Addition-and-Subtraction [33]
(C) 2016 Edugain (www.Edugain.com) Personal use only, commercial use is strictly prohibited
F) 17
21
25 + 3
29
31 = 21
601
775
Step 1
Let us f irst convert the given mixed f ractions into improper f ractions. In order to
convert the mixed f raction 1721
25 into an improper f raction, we will need to
multiply the denominator 25 by 17 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:
1721
25 =
17 × 25 + 21
25 =
446
25
Similarly, the mixed f raction 329
31 can be converted to an improper f raction as:
329
31 =
3 × 31 + 29
31 =
122
31
Step 2
We now need to add the f ollowing unlike f ractions: 446
25 and
122
31 .
Let us f irst convert them to like f ractions.
Step 3
Let us f ind the LCM of the denominators 25 and 31.The LCM of 25 and 31 is 775.
Step 4
What should we multiply with the denominator 25 to get the LCM 775?
It is 775
25 = 31.
So, the f irst f raction can be written as:
446 × 31
775 =
13826
775
Step 5
Similarly, the second f raction can be written as:
122 × 25
775 =
3050
775
Step 6
Let us now add the two like f ractions:
13826
775 +
3050
775
ID : ww-6-Mixed-Fractions-Addition-and-Subtraction [34]
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= 13826 + 3050
775
= 16876
775
= 21601
775
Step 7
Thus, the sum of the f ractions 1721
25 and 3
29
31 is 21
601
775 .
ID : ww-6-Mixed-Fractions-Addition-and-Subtraction [35]
(C) 2016 Edugain (www.Edugain.com) Personal use only, commercial use is strictly prohibited
G) 10
9
11 + 6
20
37 = 17
146
407
Step 1
Let us f irst convert the given mixed f ractions into improper f ractions. In order to
convert the mixed f raction 109
11 into an improper f raction, we will need to
multiply the denominator 11 by 10 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:
109
11 =
10 × 11 + 9
11 =
119
11
Similarly, the mixed f raction 620
37 can be converted to an improper f raction as:
620
37 =
6 × 37 + 20
37 =
242
37
Step 2
We now need to add the f ollowing unlike f ractions: 119
11 and
242
37 .
Let us f irst convert them to like f ractions.
Step 3
Let us f ind the LCM of the denominators 11 and 37.The LCM of 11 and 37 is 407.
Step 4
What should we multiply with the denominator 11 to get the LCM 407?
It is 407
11 = 37.
So, the f irst f raction can be written as:
119 × 37
407 =
4403
407
Step 5
Similarly, the second f raction can be written as:
242 × 11
407 =
2662
407
Step 6
Let us now add the two like f ractions:
4403
407 +
2662
407
ID : ww-6-Mixed-Fractions-Addition-and-Subtraction [36]
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= 4403 + 2662
407
= 7065
407
= 17146
407
Step 7
Thus, the sum of the f ractions 109
11 and 6
20
37 is 17
146
407 .
ID : ww-6-Mixed-Fractions-Addition-and-Subtraction [37]
(C) 2016 Edugain (www.Edugain.com) Personal use only, commercial use is strictly prohibited
H) 19
9
14 + 1
11
19 = 21
59
266
Step 1
Let us f irst convert the given mixed f ractions into improper f ractions. In order to
convert the mixed f raction 199
14 into an improper f raction, we will need to
multiply the denominator 14 by 19 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:
199
14 =
19 × 14 + 9
14 =
275
14
Similarly, the mixed f raction 111
19 can be converted to an improper f raction as:
111
19 =
1 × 19 + 11
19 =
30
19
Step 2
We now need to add the f ollowing unlike f ractions: 275
14 and
30
19 .
Let us f irst convert them to like f ractions.
Step 3
Let us f ind the LCM of the denominators 14 and 19.The LCM of 14 and 19 is 266.
Step 4
What should we multiply with the denominator 14 to get the LCM 266?
It is 266
14 = 19.
So, the f irst f raction can be written as:
275 × 19
266 =
5225
266
Step 5
Similarly, the second f raction can be written as:
30 × 14
266 =
420
266
Step 6
Let us now add the two like f ractions:
5225
266 +
420
266
ID : ww-6-Mixed-Fractions-Addition-and-Subtraction [38]
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= 5225 + 420
266
= 5645
266
= 2159
266
Step 7
Thus, the sum of the f ractions 199
14 and 1
11
19 is 21
59
266 .
ID : ww-6-Mixed-Fractions-Addition-and-Subtraction [39]
(C) 2016 Edugain (www.Edugain.com) Personal use only, commercial use is strictly prohibited
I) 9
14
15 + 1
29
52 = 11
383
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 914
15 into an improper f raction, we will need to
multiply the denominator 15 by 9 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:
914
15 =
9 × 15 + 14
15 =
149
15
Similarly, the mixed f raction 129
52 can be converted to an improper f raction as:
129
52 =
1 × 52 + 29
52 =
81
52
Step 2
We now need to add the f ollowing unlike f ractions: 149
15 and
81
52 .
Let us f irst convert them to like f ractions.
Step 3
Let us f ind the LCM of the denominators 15 and 52.The LCM of 15 and 52 is 780.
Step 4
What should we multiply with the denominator 15 to get the LCM 780?
It is 780
15 = 52.
So, the f irst f raction can be written as:
149 × 52
780 =
7748
780
Step 5
Similarly, the second f raction can be written as:
81 × 15
780 =
1215
780
Step 6
Let us now add the two like f ractions:
7748
780 +
1215
780
ID : ww-6-Mixed-Fractions-Addition-and-Subtraction [40]
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= 7748 + 1215
780
= 8963
780
= 11383
780
Step 7
Thus, the sum of the f ractions 914
15 and 1
29
52 is 11
383
780 .
ID : ww-6-Mixed-Fractions-Addition-and-Subtraction [41]
(C) 2016 Edugain (www.Edugain.com) Personal use only, commercial use is strictly prohibited
J) 9
29
32 + 7
22
35 = 17
599
1120
Step 1
Let us f irst convert the given mixed f ractions into improper f ractions. In order to
convert the mixed f raction 929
32 into an improper f raction, we will need to
multiply the denominator 32 by 9 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:
929
32 =
9 × 32 + 29
32 =
317
32
Similarly, the mixed f raction 722
35 can be converted to an improper f raction as:
722
35 =
7 × 35 + 22
35 =
267
35
Step 2
We now need to add the f ollowing unlike f ractions: 317
32 and
267
35 .
Let us f irst convert them to like f ractions.
Step 3
Let us f ind the LCM of the denominators 32 and 35.The LCM of 32 and 35 is 1120.
Step 4
What should we multiply with the denominator 32 to get the LCM 1120?
It is 1120
32 = 35.
So, the f irst f raction can be written as:
317 × 35
1120 =
11095
1120
Step 5
Similarly, the second f raction can be written as:
267 × 32
1120 =
8544
1120
Step 6
Let us now add the two like f ractions:
11095
1120 +
8544
1120
ID : ww-6-Mixed-Fractions-Addition-and-Subtraction [42]
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= 11095 + 8544
1120
= 19639
1120
= 17599
1120
Step 7
Thus, the sum of the f ractions 929
32 and 7
22
35 is 17
599
1120 .
ID : ww-6-Mixed-Fractions-Addition-and-Subtraction [43]
(C) 2016 Edugain (www.Edugain.com) Personal use only, commercial use is strictly prohibited
K) 10
29
31 + 1
11
31 = 12
9
31
Step 1
Let us f irst convert the given mixed f ractions into improper f ractions. In order to
convert the mixed f raction 1029
31 into an improper f raction, we will need to
multiply the denominator 31 by 10 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:
1029
31 =
10 × 31 + 29
31 =
339
31
Similarly, the mixed f raction 111
31 can be converted to an improper f raction as:
111
31 =
1 × 31 + 11
31 =
42
31
Step 2
We now need to add the f ollowing like f ractions: 339
31 and
42
31 .
Step 3
Let us add the two like f ractions:
339
31 +
42
31
= 339 + 42
31
= 381
31
= 129
31
Step 4
Thus, the sum of the f ractions 1029
31 and 1
11
31 is 12
9
31 .
ID : ww-6-Mixed-Fractions-Addition-and-Subtraction [44]
(C) 2016 Edugain (www.Edugain.com) Personal use only, commercial use is strictly prohibited
L) 18
27
28 + 1
21
22 = 20
283
308
Step 1
Let us f irst convert the given mixed f ractions into improper f ractions. In order to
convert the mixed f raction 1827
28 into an improper f raction, we will need to
multiply the denominator 28 by 18 and add the numerator 27 to the result. Theresulting number will be the numerator of the improper f raction and thedenominator will remain the same:
1827
28 =
18 × 28 + 27
28 =
531
28
Similarly, the mixed f raction 121
22 can be converted to an improper f raction as:
121
22 =
1 × 22 + 21
22 =
43
22
Step 2
We now need to add the f ollowing unlike f ractions: 531
28 and
43
22 .
Let us f irst convert them to like f ractions.
Step 3
Let us f ind the LCM of the denominators 28 and 22.The LCM of 28 and 22 is 308.
Step 4
What should we multiply with the denominator 28 to get the LCM 308?
It is 308
28 = 11.
So, the f irst f raction can be written as:
531 × 11
308 =
5841
308
Step 5
Similarly, the second f raction can be written as:
43 × 14
308 =
602
308
Step 6
Let us now add the two like f ractions:
5841
308 +
602
308
ID : ww-6-Mixed-Fractions-Addition-and-Subtraction [45]
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= 5841 + 602
308
= 6443
308
= 20283
308
Step 7
Thus, the sum of the f ractions 1827
28 and 1
21
22 is 20
283
308 .
ID : ww-6-Mixed-Fractions-Addition-and-Subtraction [46]
(C) 2016 Edugain (www.Edugain.com) Personal use only, commercial use is strictly prohibited
M) 12
22
25 + 7
27
40 = 20
111
200
Step 1
Let us f irst convert the given mixed f ractions into improper f ractions. In order to
convert the mixed f raction 1222
25 into an improper f raction, we will need to
multiply the denominator 25 by 12 and add the numerator 22 to the result. Theresulting number will be the numerator of the improper f raction and thedenominator will remain the same:
1222
25 =
12 × 25 + 22
25 =
322
25
Similarly, the mixed f raction 727
40 can be converted to an improper f raction as:
727
40 =
7 × 40 + 27
40 =
307
40
Step 2
We now need to add the f ollowing unlike f ractions: 322
25 and
307
40 .
Let us f irst convert them to like f ractions.
Step 3
Let us f ind the LCM of the denominators 25 and 40.The LCM of 25 and 40 is 200.
Step 4
What should we multiply with the denominator 25 to get the LCM 200?
It is 200
25 = 8.
So, the f irst f raction can be written as:
322 × 8
200 =
2576
200
Step 5
Similarly, the second f raction can be written as:
307 × 5
200 =
1535
200
Step 6
Let us now add the two like f ractions:
2576
200 +
1535
200
ID : ww-6-Mixed-Fractions-Addition-and-Subtraction [47]
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= 2576 + 1535
200
= 4111
200
= 20111
200
Step 7
Thus, the sum of the f ractions 1222
25 and 7
27
40 is 20
111
200 .
ID : ww-6-Mixed-Fractions-Addition-and-Subtraction [48]
(C) 2016 Edugain (www.Edugain.com) Personal use only, commercial use is strictly prohibited
N) 8
24
29 + 2
21
37 = 11
424
1073
Step 1
Let us f irst convert the given mixed f ractions into improper f ractions. In order to
convert the mixed f raction 824
29 into an improper f raction, we will need to
multiply the denominator 29 by 8 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:
824
29 =
8 × 29 + 24
29 =
256
29
Similarly, the mixed f raction 221
37 can be converted to an improper f raction as:
221
37 =
2 × 37 + 21
37 =
95
37
Step 2
We now need to add the f ollowing unlike f ractions: 256
29 and
95
37 .
Let us f irst convert them to like f ractions.
Step 3
Let us f ind the LCM of the denominators 29 and 37.The LCM of 29 and 37 is 1073.
Step 4
What should we multiply with the denominator 29 to get the LCM 1073?
It is 1073
29 = 37.
So, the f irst f raction can be written as:
256 × 37
1073 =
9472
1073
Step 5
Similarly, the second f raction can be written as:
95 × 29
1073 =
2755
1073
Step 6
Let us now add the two like f ractions:
9472
1073 +
2755
1073
ID : ww-6-Mixed-Fractions-Addition-and-Subtraction [49]
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= 9472 + 2755
1073
= 12227
1073
= 11424
1073
Step 7
Thus, the sum of the f ractions 824
29 and 2
21
37 is 11
424
1073 .
ID : ww-6-Mixed-Fractions-Addition-and-Subtraction [50]
(C) 2016 Edugain (www.Edugain.com) Personal use only, commercial use is strictly prohibited
O) 19
29
30 + 2
23
38 = 22
163
285
Step 1
Let us f irst convert the given mixed f ractions into improper f ractions. In order to
convert the mixed f raction 1929
30 into an improper f raction, we will need to
multiply the denominator 30 by 19 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:
1929
30 =
19 × 30 + 29
30 =
599
30
Similarly, the mixed f raction 223
38 can be converted to an improper f raction as:
223
38 =
2 × 38 + 23
38 =
99
38
Step 2
We now need to add the f ollowing unlike f ractions: 599
30 and
99
38 .
Let us f irst convert them to like f ractions.
Step 3
Let us f ind the LCM of the denominators 30 and 38.The LCM of 30 and 38 is 570.
Step 4
What should we multiply with the denominator 30 to get the LCM 570?
It is 570
30 = 19.
So, the f irst f raction can be written as:
599 × 19
570 =
11381
570
Step 5
Similarly, the second f raction can be written as:
99 × 15
570 =
1485
570
Step 6
Let us now add the two like f ractions:
11381
570 +
1485
570
ID : ww-6-Mixed-Fractions-Addition-and-Subtraction [51]
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= 11381 + 1485
570
= 12866
570
= 22163
285
Step 7
Thus, the sum of the f ractions 1929
30 and 2
23
38 is 22
163
285 .
ID : ww-6-Mixed-Fractions-Addition-and-Subtraction [52]
(C) 2016 Edugain (www.Edugain.com) Personal use only, commercial use is strictly prohibited
![Mixed Fractions - Addition and Subtraction Class 6...Thus, the simplified value of the given fractions is 14 7 8. ID : in-6-Mixed-Fractions-Addition-and-Subtraction [9] (C) 2016 Edugain](https://img.dokumen.tips/doc/110x75/5f59799aafa4520ae1630d35/mixed-fractions-addition-and-subtraction-class-6-thus-the-simplified-value.jpg)
