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Grade 6Mixed Fractions - Addition and Subtraction
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(1) Add the f ollowing f ractions:
A) 22
13
17 + 7
11
21 =
B) 20
11
12 + 4
22
39 =
C) 21
29
30 + 1
3
17 =
D) 13
27
28 + 1
7
16 =
E) 17
7
8 + 6
22
35 =
F) 14
21
23 + 4
11
25 =
G) 20
7
8 + 7
12
37 =
H) 20
28
33 + 2
4
9 =
I) 20
16
17 + 4
4
11 =
J) 15
24
29 + 7
6
29 =
K) 10
21
25 + 5
8
13 =
L) 15
15
16 + 4
18
23 =
M) 19
15
16 + 4
18
29 =
N) 23
19
23 + 6
23
32 =
O) 20
29
33 + 1
16
39 =
(2) Simplif y the f ollowing f ractions:
A) 29
35
99 - 5
9
22 =
B) 27
47
119 - 4
4
7 =
C) 21
83
114 - 7
5
6 =
D) 28
167
234 - 4
10
13 =
ID : ae-6-Mixed-Fractions-Addition-and-Subtraction [1]
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E) 21
113
182 - 4
9
13 =
F) 6
246
247 - 2
2
13 =
G) 28
23
198 - 5
7
18 =
H) 11
0
1 - 2
3
14 =
I) 30
161
285 - 5
12
19 =
J) 27
49
240 - 4
4
15 =
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ID : ae-6-Mixed-Fractions-Addition-and-Subtraction [2]
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AnswersID : ae-6-Mixed-Fractions-Addition-and-Subtraction [3]
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(1) A) 22
13
17 + 7
11
21 = 30
103
357
Step 1
Let us f irst convert the given mixed f ractions into improper f ractions. In order to
convert the mixed f raction 2213
17 into an improper f raction, we will need to
multiply the denominator 17 by 22 and add the numerator 13 to the result. Theresulting number will be the numerator of the improper f raction and thedenominator will remain the same:
2213
17 =
22 × 17 + 13
17 =
387
17
Similarly, the mixed f raction 711
21 can be converted to an improper f raction as:
711
21 =
7 × 21 + 11
21 =
158
21
Step 2
We now need to add the f ollowing unlike f ractions: 387
17 and
158
21 .
Let us f irst convert them to like f ractions.
Step 3
Let us f ind the LCM of the denominators 17 and 21.The LCM of 17 and 21 is 357.
Step 4
What should we multiply with the denominator 17 to get the LCM 357?
It is 357
17 = 21.
So, the f irst f raction can be written as:
387 × 21
357 =
8127
357
Step 5
Similarly, the second f raction can be written as:
158 × 17
357 =
2686
357
Step 6
Let us now add the two like f ractions:
8127
357 +
2686
357
ID : ae-6-Mixed-Fractions-Addition-and-Subtraction [4]
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= 8127 + 2686
357
= 10813
357
= 30103
357
Step 7
Thus, the sum of the f ractions 2213
17 and 7
11
21 is 30
103
357 .
ID : ae-6-Mixed-Fractions-Addition-and-Subtraction [5]
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B) 20
11
12 + 4
22
39 = 25
25
52
Step 1
Let us f irst convert the given mixed f ractions into improper f ractions. In order to
convert the mixed f raction 2011
12 into an improper f raction, we will need to
multiply the denominator 12 by 20 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:
2011
12 =
20 × 12 + 11
12 =
251
12
Similarly, the mixed f raction 422
39 can be converted to an improper f raction as:
422
39 =
4 × 39 + 22
39 =
178
39
Step 2
We now need to add the f ollowing unlike f ractions: 251
12 and
178
39 .
Let us f irst convert them to like f ractions.
Step 3
Let us f ind the LCM of the denominators 12 and 39.The LCM of 12 and 39 is 156.
Step 4
What should we multiply with the denominator 12 to get the LCM 156?
It is 156
12 = 13.
So, the f irst f raction can be written as:
251 × 13
156 =
3263
156
Step 5
Similarly, the second f raction can be written as:
178 × 4
156 =
712
156
Step 6
Let us now add the two like f ractions:
3263
156 +
712
156
ID : ae-6-Mixed-Fractions-Addition-and-Subtraction [6]
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= 3263 + 712
156
= 3975
156
= 2525
52
Step 7
Thus, the sum of the f ractions 2011
12 and 4
22
39 is 25
25
52 .
ID : ae-6-Mixed-Fractions-Addition-and-Subtraction [7]
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C) 21
29
30 + 1
3
17 = 23
73
510
Step 1
Let us f irst convert the given mixed f ractions into improper f ractions. In order to
convert the mixed f raction 2129
30 into an improper f raction, we will need to
multiply the denominator 30 by 21 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:
2129
30 =
21 × 30 + 29
30 =
659
30
Similarly, the mixed f raction 13
17 can be converted to an improper f raction as:
13
17 =
1 × 17 + 3
17 =
20
17
Step 2
We now need to add the f ollowing unlike f ractions: 659
30 and
20
17 .
Let us f irst convert them to like f ractions.
Step 3
Let us f ind the LCM of the denominators 30 and 17.The LCM of 30 and 17 is 510.
Step 4
What should we multiply with the denominator 30 to get the LCM 510?
It is 510
30 = 17.
So, the f irst f raction can be written as:
659 × 17
510 =
11203
510
Step 5
Similarly, the second f raction can be written as:
20 × 30
510 =
600
510
Step 6
Let us now add the two like f ractions:
11203
510 +
600
510
ID : ae-6-Mixed-Fractions-Addition-and-Subtraction [8]
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= 11203 + 600
510
= 11803
510
= 2373
510
Step 7
Thus, the sum of the f ractions 2129
30 and 1
3
17 is 23
73
510 .
ID : ae-6-Mixed-Fractions-Addition-and-Subtraction [9]
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D) 13
27
28 + 1
7
16 = 15
45
112
Step 1
Let us f irst convert the given mixed f ractions into improper f ractions. In order to
convert the mixed f raction 1327
28 into an improper f raction, we will need to
multiply the denominator 28 by 13 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:
1327
28 =
13 × 28 + 27
28 =
391
28
Similarly, the mixed f raction 17
16 can be converted to an improper f raction as:
17
16 =
1 × 16 + 7
16 =
23
16
Step 2
We now need to add the f ollowing unlike f ractions: 391
28 and
23
16 .
Let us f irst convert them to like f ractions.
Step 3
Let us f ind the LCM of the denominators 28 and 16.The LCM of 28 and 16 is 112.
Step 4
What should we multiply with the denominator 28 to get the LCM 112?
It is 112
28 = 4.
So, the f irst f raction can be written as:
391 × 4
112 =
1564
112
Step 5
Similarly, the second f raction can be written as:
23 × 7
112 =
161
112
Step 6
Let us now add the two like f ractions:
1564
112 +
161
112
ID : ae-6-Mixed-Fractions-Addition-and-Subtraction [10]
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= 1564 + 161
112
= 1725
112
= 1545
112
Step 7
Thus, the sum of the f ractions 1327
28 and 1
7
16 is 15
45
112 .
ID : ae-6-Mixed-Fractions-Addition-and-Subtraction [11]
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E) 17
7
8 + 6
22
35 = 24
141
280
Step 1
Let us f irst convert the given mixed f ractions into improper f ractions. In order to
convert the mixed f raction 177
8 into an improper f raction, we will need to
multiply the denominator 8 by 17 and add the numerator 7 to the result. Theresulting number will be the numerator of the improper f raction and thedenominator will remain the same:
177
8 =
17 × 8 + 7
8 =
143
8
Similarly, the mixed f raction 622
35 can be converted to an improper f raction as:
622
35 =
6 × 35 + 22
35 =
232
35
Step 2
We now need to add the f ollowing unlike f ractions: 143
8 and
232
35 .
Let us f irst convert them to like f ractions.
Step 3
Let us f ind the LCM of the denominators 8 and 35.The LCM of 8 and 35 is 280.
Step 4
What should we multiply with the denominator 8 to get the LCM 280?
It is 280
8 = 35.
So, the f irst f raction can be written as:
143 × 35
280 =
5005
280
Step 5
Similarly, the second f raction can be written as:
232 × 8
280 =
1856
280
Step 6
Let us now add the two like f ractions:
5005
280 +
1856
280
ID : ae-6-Mixed-Fractions-Addition-and-Subtraction [12]
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= 5005 + 1856
280
= 6861
280
= 24141
280
Step 7
Thus, the sum of the f ractions 177
8 and 6
22
35 is 24
141
280 .
ID : ae-6-Mixed-Fractions-Addition-and-Subtraction [13]
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F) 14
21
23 + 4
11
25 = 19
203
575
Step 1
Let us f irst convert the given mixed f ractions into improper f ractions. In order to
convert the mixed f raction 1421
23 into an improper f raction, we will need to
multiply the denominator 23 by 14 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:
1421
23 =
14 × 23 + 21
23 =
343
23
Similarly, the mixed f raction 411
25 can be converted to an improper f raction as:
411
25 =
4 × 25 + 11
25 =
111
25
Step 2
We now need to add the f ollowing unlike f ractions: 343
23 and
111
25 .
Let us f irst convert them to like f ractions.
Step 3
Let us f ind the LCM of the denominators 23 and 25.The LCM of 23 and 25 is 575.
Step 4
What should we multiply with the denominator 23 to get the LCM 575?
It is 575
23 = 25.
So, the f irst f raction can be written as:
343 × 25
575 =
8575
575
Step 5
Similarly, the second f raction can be written as:
111 × 23
575 =
2553
575
Step 6
Let us now add the two like f ractions:
8575
575 +
2553
575
ID : ae-6-Mixed-Fractions-Addition-and-Subtraction [14]
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= 8575 + 2553
575
= 11128
575
= 19203
575
Step 7
Thus, the sum of the f ractions 1421
23 and 4
11
25 is 19
203
575 .
ID : ae-6-Mixed-Fractions-Addition-and-Subtraction [15]
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G) 20
7
8 + 7
12
37 = 28
59
296
Step 1
Let us f irst convert the given mixed f ractions into improper f ractions. In order to
convert the mixed f raction 207
8 into an improper f raction, we will need to
multiply the denominator 8 by 20 and add the numerator 7 to the result. Theresulting number will be the numerator of the improper f raction and thedenominator will remain the same:
207
8 =
20 × 8 + 7
8 =
167
8
Similarly, the mixed f raction 712
37 can be converted to an improper f raction as:
712
37 =
7 × 37 + 12
37 =
271
37
Step 2
We now need to add the f ollowing unlike f ractions: 167
8 and
271
37 .
Let us f irst convert them to like f ractions.
Step 3
Let us f ind the LCM of the denominators 8 and 37.The LCM of 8 and 37 is 296.
Step 4
What should we multiply with the denominator 8 to get the LCM 296?
It is 296
8 = 37.
So, the f irst f raction can be written as:
167 × 37
296 =
6179
296
Step 5
Similarly, the second f raction can be written as:
271 × 8
296 =
2168
296
Step 6
Let us now add the two like f ractions:
6179
296 +
2168
296
ID : ae-6-Mixed-Fractions-Addition-and-Subtraction [16]
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= 6179 + 2168
296
= 8347
296
= 2859
296
Step 7
Thus, the sum of the f ractions 207
8 and 7
12
37 is 28
59
296 .
ID : ae-6-Mixed-Fractions-Addition-and-Subtraction [17]
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H) 20
28
33 + 2
4
9 = 23
29
99
Step 1
Let us f irst convert the given mixed f ractions into improper f ractions. In order to
convert the mixed f raction 2028
33 into an improper f raction, we will need to
multiply the denominator 33 by 20 and add the numerator 28 to the result. Theresulting number will be the numerator of the improper f raction and thedenominator will remain the same:
2028
33 =
20 × 33 + 28
33 =
688
33
Similarly, the mixed f raction 24
9 can be converted to an improper f raction as:
24
9 =
2 × 9 + 4
9 =
22
9
Step 2
We now need to add the f ollowing unlike f ractions: 688
33 and
22
9 .
Let us f irst convert them to like f ractions.
Step 3
Let us f ind the LCM of the denominators 33 and 9.The LCM of 33 and 9 is 99.
Step 4
What should we multiply with the denominator 33 to get the LCM 99?
It is 99
33 = 3.
So, the f irst f raction can be written as:
688 × 3
99 =
2064
99
Step 5
Similarly, the second f raction can be written as:
22 × 11
99 =
242
99
Step 6
Let us now add the two like f ractions:
2064
99 +
242
99
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= 2064 + 242
99
= 2306
99
= 2329
99
Step 7
Thus, the sum of the f ractions 2028
33 and 2
4
9 is 23
29
99 .
ID : ae-6-Mixed-Fractions-Addition-and-Subtraction [19]
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I) 20
16
17 + 4
4
11 = 25
57
187
Step 1
Let us f irst convert the given mixed f ractions into improper f ractions. In order to
convert the mixed f raction 2016
17 into an improper f raction, we will need to
multiply the denominator 17 by 20 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:
2016
17 =
20 × 17 + 16
17 =
356
17
Similarly, the mixed f raction 44
11 can be converted to an improper f raction as:
44
11 =
4 × 11 + 4
11 =
48
11
Step 2
We now need to add the f ollowing unlike f ractions: 356
17 and
48
11 .
Let us f irst convert them to like f ractions.
Step 3
Let us f ind the LCM of the denominators 17 and 11.The LCM of 17 and 11 is 187.
Step 4
What should we multiply with the denominator 17 to get the LCM 187?
It is 187
17 = 11.
So, the f irst f raction can be written as:
356 × 11
187 =
3916
187
Step 5
Similarly, the second f raction can be written as:
48 × 17
187 =
816
187
Step 6
Let us now add the two like f ractions:
3916
187 +
816
187
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= 3916 + 816
187
= 4732
187
= 2557
187
Step 7
Thus, the sum of the f ractions 2016
17 and 4
4
11 is 25
57
187 .
ID : ae-6-Mixed-Fractions-Addition-and-Subtraction [21]
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J) 15
24
29 + 7
6
29 = 23
1
29
Step 1
Let us f irst convert the given mixed f ractions into improper f ractions. In order to
convert the mixed f raction 1524
29 into an improper f raction, we will need to
multiply the denominator 29 by 15 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:
1524
29 =
15 × 29 + 24
29 =
459
29
Similarly, the mixed f raction 76
29 can be converted to an improper f raction as:
76
29 =
7 × 29 + 6
29 =
209
29
Step 2
We now need to add the f ollowing like f ractions: 459
29 and
209
29 .
Step 3
Let us add the two like f ractions:
459
29 +
209
29
= 459 + 209
29
= 668
29
= 231
29
Step 4
Thus, the sum of the f ractions 1524
29 and 7
6
29 is 23
1
29 .
ID : ae-6-Mixed-Fractions-Addition-and-Subtraction [22]
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K) 10
21
25 + 5
8
13 = 16
148
325
Step 1
Let us f irst convert the given mixed f ractions into improper f ractions. In order to
convert the mixed f raction 1021
25 into an improper f raction, we will need to
multiply the denominator 25 by 10 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:
1021
25 =
10 × 25 + 21
25 =
271
25
Similarly, the mixed f raction 58
13 can be converted to an improper f raction as:
58
13 =
5 × 13 + 8
13 =
73
13
Step 2
We now need to add the f ollowing unlike f ractions: 271
25 and
73
13 .
Let us f irst convert them to like f ractions.
Step 3
Let us f ind the LCM of the denominators 25 and 13.The LCM of 25 and 13 is 325.
Step 4
What should we multiply with the denominator 25 to get the LCM 325?
It is 325
25 = 13.
So, the f irst f raction can be written as:
271 × 13
325 =
3523
325
Step 5
Similarly, the second f raction can be written as:
73 × 25
325 =
1825
325
Step 6
Let us now add the two like f ractions:
3523
325 +
1825
325
ID : ae-6-Mixed-Fractions-Addition-and-Subtraction [23]
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= 3523 + 1825
325
= 5348
325
= 16148
325
Step 7
Thus, the sum of the f ractions 1021
25 and 5
8
13 is 16
148
325 .
ID : ae-6-Mixed-Fractions-Addition-and-Subtraction [24]
(C) 2016 Edugain (www.Edugain.com) Personal use only, commercial use is strictly prohibited
L) 15
15
16 + 4
18
23 = 20
265
368
Step 1
Let us f irst convert the given mixed f ractions into improper f ractions. In order to
convert the mixed f raction 1515
16 into an improper f raction, we will need to
multiply the denominator 16 by 15 and add the numerator 15 to the result. Theresulting number will be the numerator of the improper f raction and thedenominator will remain the same:
1515
16 =
15 × 16 + 15
16 =
255
16
Similarly, the mixed f raction 418
23 can be converted to an improper f raction as:
418
23 =
4 × 23 + 18
23 =
110
23
Step 2
We now need to add the f ollowing unlike f ractions: 255
16 and
110
23 .
Let us f irst convert them to like f ractions.
Step 3
Let us f ind the LCM of the denominators 16 and 23.The LCM of 16 and 23 is 368.
Step 4
What should we multiply with the denominator 16 to get the LCM 368?
It is 368
16 = 23.
So, the f irst f raction can be written as:
255 × 23
368 =
5865
368
Step 5
Similarly, the second f raction can be written as:
110 × 16
368 =
1760
368
Step 6
Let us now add the two like f ractions:
5865
368 +
1760
368
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= 5865 + 1760
368
= 7625
368
= 20265
368
Step 7
Thus, the sum of the f ractions 1515
16 and 4
18
23 is 20
265
368 .
ID : ae-6-Mixed-Fractions-Addition-and-Subtraction [26]
(C) 2016 Edugain (www.Edugain.com) Personal use only, commercial use is strictly prohibited
M) 19
15
16 + 4
18
29 = 24
259
464
Step 1
Let us f irst convert the given mixed f ractions into improper f ractions. In order to
convert the mixed f raction 1915
16 into an improper f raction, we will need to
multiply the denominator 16 by 19 and add the numerator 15 to the result. Theresulting number will be the numerator of the improper f raction and thedenominator will remain the same:
1915
16 =
19 × 16 + 15
16 =
319
16
Similarly, the mixed f raction 418
29 can be converted to an improper f raction as:
418
29 =
4 × 29 + 18
29 =
134
29
Step 2
We now need to add the f ollowing unlike f ractions: 319
16 and
134
29 .
Let us f irst convert them to like f ractions.
Step 3
Let us f ind the LCM of the denominators 16 and 29.The LCM of 16 and 29 is 464.
Step 4
What should we multiply with the denominator 16 to get the LCM 464?
It is 464
16 = 29.
So, the f irst f raction can be written as:
319 × 29
464 =
9251
464
Step 5
Similarly, the second f raction can be written as:
134 × 16
464 =
2144
464
Step 6
Let us now add the two like f ractions:
9251
464 +
2144
464
ID : ae-6-Mixed-Fractions-Addition-and-Subtraction [27]
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= 9251 + 2144
464
= 11395
464
= 24259
464
Step 7
Thus, the sum of the f ractions 1915
16 and 4
18
29 is 24
259
464 .
ID : ae-6-Mixed-Fractions-Addition-and-Subtraction [28]
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N) 23
19
23 + 6
23
32 = 30
401
736
Step 1
Let us f irst convert the given mixed f ractions into improper f ractions. In order to
convert the mixed f raction 2319
23 into an improper f raction, we will need to
multiply the denominator 23 by 23 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:
2319
23 =
23 × 23 + 19
23 =
548
23
Similarly, the mixed f raction 623
32 can be converted to an improper f raction as:
623
32 =
6 × 32 + 23
32 =
215
32
Step 2
We now need to add the f ollowing unlike f ractions: 548
23 and
215
32 .
Let us f irst convert them to like f ractions.
Step 3
Let us f ind the LCM of the denominators 23 and 32.The LCM of 23 and 32 is 736.
Step 4
What should we multiply with the denominator 23 to get the LCM 736?
It is 736
23 = 32.
So, the f irst f raction can be written as:
548 × 32
736 =
17536
736
Step 5
Similarly, the second f raction can be written as:
215 × 23
736 =
4945
736
Step 6
Let us now add the two like f ractions:
17536
736 +
4945
736
ID : ae-6-Mixed-Fractions-Addition-and-Subtraction [29]
(C) 2016 Edugain (www.Edugain.com) Personal use only, commercial use is strictly prohibited
= 17536 + 4945
736
= 22481
736
= 30401
736
Step 7
Thus, the sum of the f ractions 2319
23 and 6
23
32 is 30
401
736 .
ID : ae-6-Mixed-Fractions-Addition-and-Subtraction [30]
(C) 2016 Edugain (www.Edugain.com) Personal use only, commercial use is strictly prohibited
O) 20
29
33 + 1
16
39 = 22
124
429
Step 1
Let us f irst convert the given mixed f ractions into improper f ractions. In order to
convert the mixed f raction 2029
33 into an improper f raction, we will need to
multiply the denominator 33 by 20 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:
2029
33 =
20 × 33 + 29
33 =
689
33
Similarly, the mixed f raction 116
39 can be converted to an improper f raction as:
116
39 =
1 × 39 + 16
39 =
55
39
Step 2
We now need to add the f ollowing unlike f ractions: 689
33 and
55
39 .
Let us f irst convert them to like f ractions.
Step 3
Let us f ind the LCM of the denominators 33 and 39.The LCM of 33 and 39 is 429.
Step 4
What should we multiply with the denominator 33 to get the LCM 429?
It is 429
33 = 13.
So, the f irst f raction can be written as:
689 × 13
429 =
8957
429
Step 5
Similarly, the second f raction can be written as:
55 × 11
429 =
605
429
Step 6
Let us now add the two like f ractions:
8957
429 +
605
429
ID : ae-6-Mixed-Fractions-Addition-and-Subtraction [31]
(C) 2016 Edugain (www.Edugain.com) Personal use only, commercial use is strictly prohibited
= 8957 + 605
429
= 9562
429
= 22124
429
Step 7
Thus, the sum of the f ractions 2029
33 and 1
16
39 is 22
124
429 .
ID : ae-6-Mixed-Fractions-Addition-and-Subtraction [32]
(C) 2016 Edugain (www.Edugain.com) Personal use only, commercial use is strictly prohibited
(2) A) 29
35
99 - 5
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 2935
99 into an improper f raction, we will need to
multiply the denominator 99 by 29 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:
2935
99 =
29 × 99 + 35
99 =
2906
99
Similarly, the mixed f raction 59
22 can be converted into an improper f raction
as:
59
22 =
5 × 22 + 9
22 =
119
22
Step 2
We now need to subtract the f ollowing unlike f ractions: 2906
99 and
119
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:
2906 × 2
99 × 2 =
5812
198
Step 5
Similarly, the second f raction can be written as:
119 × 9
22 × 9 =
1071
198
Step 6
Let us now subtract the two like f ractions:
5812
198 -
1071
198
ID : ae-6-Mixed-Fractions-Addition-and-Subtraction [33]
(C) 2016 Edugain (www.Edugain.com) Personal use only, commercial use is strictly prohibited
= 5812 - 1071
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 .
ID : ae-6-Mixed-Fractions-Addition-and-Subtraction [34]
(C) 2016 Edugain (www.Edugain.com) Personal use only, commercial use is strictly prohibited
B) 27
47
119 - 4
4
7 = 22
14
17
Step 1
Let us f irst convert the given mixed f ractions into improper f ractions. In order to
convert the mixed f raction 2747
119 into an improper f raction, we will need to
multiply the denominator 119 by 27 and add the numerator 47 to the result. Theresulting number will be the numerator of the improper f raction and thedenominator will remain the same:
2747
119 =
27 × 119 + 47
119 =
3260
119
Similarly, the mixed f raction 44
7 can be converted into an improper f raction as:
44
7 =
4 × 7 + 4
7 =
32
7
Step 2
We now need to subtract the f ollowing unlike f ractions: 3260
119 and
32
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 119 and 7.The LCM of 119 and 7 is 119.
Step 4
What should we multiply with the denominator 119 to get the LCM 119?
It is 119
119 = 1.
So, the f irst f raction can be written as:
3260 × 1
119 × 1 =
3260
119
Step 5
Similarly, the second f raction can be written as:
32 × 17
7 × 17 =
544
119
Step 6
Let us now subtract the two like f ractions:
3260
119 -
544
119
ID : ae-6-Mixed-Fractions-Addition-and-Subtraction [35]
(C) 2016 Edugain (www.Edugain.com) Personal use only, commercial use is strictly prohibited
= 3260 - 544
119
= 2716
119
= 2716 ÷ 7
119 ÷ 7 ...[ Dividing both numerator and denominator by their HCF to bring ]
= 388
17
= 2214
17
Step 7
Thus, the simplif ied value of the given f ractions is 2214
17 .
ID : ae-6-Mixed-Fractions-Addition-and-Subtraction [36]
(C) 2016 Edugain (www.Edugain.com) Personal use only, commercial use is strictly prohibited
C) 21
83
114 - 7
5
6 = 13
17
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 2183
114 into an improper f raction, we will need to
multiply the denominator 114 by 21 and add the numerator 83 to the result. Theresulting number will be the numerator of the improper f raction and thedenominator will remain the same:
2183
114 =
21 × 114 + 83
114 =
2477
114
Similarly, the mixed f raction 75
6 can be converted into an improper f raction as:
75
6 =
7 × 6 + 5
6 =
47
6
Step 2
We now need to subtract the f ollowing unlike f ractions: 2477
114 and
47
6 .
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 114 and 6.The LCM of 114 and 6 is 114.
Step 4
What should we multiply with the denominator 114 to get the LCM 114?
It is 114
114 = 1.
So, the f irst f raction can be written as:
2477 × 1
114 × 1 =
2477
114
Step 5
Similarly, the second f raction can be written as:
47 × 19
6 × 19 =
893
114
Step 6
Let us now subtract the two like f ractions:
2477
114 -
893
114
ID : ae-6-Mixed-Fractions-Addition-and-Subtraction [37]
(C) 2016 Edugain (www.Edugain.com) Personal use only, commercial use is strictly prohibited
= 2477 - 893
114
= 1584
114
= 1584 ÷ 6
114 ÷ 6 ...[ Dividing both numerator and denominator by their HCF to bring ]
= 264
19
= 1317
19
Step 7
Thus, the simplif ied value of the given f ractions is 1317
19 .
ID : ae-6-Mixed-Fractions-Addition-and-Subtraction [38]
(C) 2016 Edugain (www.Edugain.com) Personal use only, commercial use is strictly prohibited
D) 28
167
234 - 4
10
13 = 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 28167
234 into an improper f raction, we will need to
multiply the denominator 234 by 28 and add the numerator 167 to the result. Theresulting number will be the numerator of the improper f raction and thedenominator will remain the same:
28167
234 =
28 × 234 + 167
234 =
6719
234
Similarly, the mixed f raction 410
13 can be converted into an improper f raction
as:
410
13 =
4 × 13 + 10
13 =
62
13
Step 2
We now need to subtract the f ollowing unlike f ractions: 6719
234 and
62
13 .
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 13.The LCM of 234 and 13 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:
6719 × 1
234 × 1 =
6719
234
Step 5
Similarly, the second f raction can be written as:
62 × 18
13 × 18 =
1116
234
Step 6
Let us now subtract the two like f ractions:
6719
234 -
1116
234
ID : ae-6-Mixed-Fractions-Addition-and-Subtraction [39]
(C) 2016 Edugain (www.Edugain.com) Personal use only, commercial use is strictly prohibited
= 6719 - 1116
234
= 5603
234
= 5603 ÷ 13
234 ÷ 13 ...[ 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 .
ID : ae-6-Mixed-Fractions-Addition-and-Subtraction [40]
(C) 2016 Edugain (www.Edugain.com) Personal use only, commercial use is strictly prohibited
E) 21
113
182 - 4
9
13 = 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 21113
182 into an improper f raction, we will need to
multiply the denominator 182 by 21 and add the numerator 113 to the result. Theresulting number will be the numerator of the improper f raction and thedenominator will remain the same:
21113
182 =
21 × 182 + 113
182 =
3935
182
Similarly, the mixed f raction 49
13 can be converted into an improper f raction
as:
49
13 =
4 × 13 + 9
13 =
61
13
Step 2
We now need to subtract the f ollowing unlike f ractions: 3935
182 and
61
13 .
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 182 and 13.The LCM of 182 and 13 is 182.
Step 4
What should we multiply with the denominator 182 to get the LCM 182?
It is 182
182 = 1.
So, the f irst f raction can be written as:
3935 × 1
182 × 1 =
3935
182
Step 5
Similarly, the second f raction can be written as:
61 × 14
13 × 14 =
854
182
Step 6
Let us now subtract the two like f ractions:
3935
182 -
854
182
ID : ae-6-Mixed-Fractions-Addition-and-Subtraction [41]
(C) 2016 Edugain (www.Edugain.com) Personal use only, commercial use is strictly prohibited
= 3935 - 854
182
= 3081
182
= 3081 ÷ 13
182 ÷ 13 ...[ 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 .
ID : ae-6-Mixed-Fractions-Addition-and-Subtraction [42]
(C) 2016 Edugain (www.Edugain.com) Personal use only, commercial use is strictly prohibited
F) 6
246
247 - 2
2
13 = 4
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 6246
247 into an improper f raction, we will need to
multiply the denominator 247 by 6 and add the numerator 246 to the result. Theresulting number will be the numerator of the improper f raction and thedenominator will remain the same:
6246
247 =
6 × 247 + 246
247 =
1728
247
Similarly, the mixed f raction 22
13 can be converted into an improper f raction
as:
22
13 =
2 × 13 + 2
13 =
28
13
Step 2
We now need to subtract the f ollowing unlike f ractions: 1728
247 and
28
13 .
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 247 and 13.The LCM of 247 and 13 is 247.
Step 4
What should we multiply with the denominator 247 to get the LCM 247?
It is 247
247 = 1.
So, the f irst f raction can be written as:
1728 × 1
247 × 1 =
1728
247
Step 5
Similarly, the second f raction can be written as:
28 × 19
13 × 19 =
532
247
Step 6
Let us now subtract the two like f ractions:
1728
247 -
532
247
ID : ae-6-Mixed-Fractions-Addition-and-Subtraction [43]
(C) 2016 Edugain (www.Edugain.com) Personal use only, commercial use is strictly prohibited
= 1728 - 532
247
= 1196
247
= 1196 ÷ 13
247 ÷ 13 ...[ Dividing both numerator and denominator by their HCF to bring
]
= 92
19
= 416
19
Step 7
Thus, the simplif ied value of the given f ractions is 416
19 .
ID : ae-6-Mixed-Fractions-Addition-and-Subtraction [44]
(C) 2016 Edugain (www.Edugain.com) Personal use only, commercial use is strictly prohibited
G) 28
23
198 - 5
7
18 = 22
8
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 2823
198 into an improper f raction, we will need to
multiply the denominator 198 by 28 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:
2823
198 =
28 × 198 + 23
198 =
5567
198
Similarly, the mixed f raction 57
18 can be converted into an improper f raction
as:
57
18 =
5 × 18 + 7
18 =
97
18
Step 2
We now need to subtract the f ollowing unlike f ractions: 5567
198 and
97
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 198 and 18.The LCM of 198 and 18 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:
5567 × 1
198 × 1 =
5567
198
Step 5
Similarly, the second f raction can be written as:
97 × 11
18 × 11 =
1067
198
Step 6
Let us now subtract the two like f ractions:
5567
198 -
1067
198
ID : ae-6-Mixed-Fractions-Addition-and-Subtraction [45]
(C) 2016 Edugain (www.Edugain.com) Personal use only, commercial use is strictly prohibited
= 5567 - 1067
198
= 4500
198
= 4500 ÷ 18
198 ÷ 18 ...[ Dividing both numerator and denominator by their HCF to bring
]
= 250
11
= 228
11
Step 7
Thus, the simplif ied value of the given f ractions is 228
11 .
ID : ae-6-Mixed-Fractions-Addition-and-Subtraction [46]
(C) 2016 Edugain (www.Edugain.com) Personal use only, commercial use is strictly prohibited
H) 11
0
1 - 2
3
14 = 8
11
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 110
1 into an improper f raction, we will need to
multiply the denominator 1 by 11 and add the numerator 0 to the result. Theresulting number will be the numerator of the improper f raction and thedenominator will remain the same:
110
1 =
11 × 1 + 0
1 =
11
1
Similarly, the mixed f raction 23
14 can be converted into an improper f raction
as:
23
14 =
2 × 14 + 3
14 =
31
14
Step 2
We now need to subtract the f ollowing unlike f ractions: 11
1 and
31
14 .
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 1 and 14.The LCM of 1 and 14 is 14.
Step 4
What should we multiply with the denominator 1 to get the LCM 14?
It is 14
1 = 14.
So, the f irst f raction can be written as:
11 × 14
1 × 14 =
154
14
Step 5
Similarly, the second f raction can be written as:
31 × 1
14 × 1 =
31
14
Step 6
Let us now subtract the two like f ractions:
154
14 -
31
14
ID : ae-6-Mixed-Fractions-Addition-and-Subtraction [47]
(C) 2016 Edugain (www.Edugain.com) Personal use only, commercial use is strictly prohibited
= 154 - 31
14
= 123
14
= 811
14
Step 7
Thus, the simplif ied value of the given f ractions is 811
14 .
ID : ae-6-Mixed-Fractions-Addition-and-Subtraction [48]
(C) 2016 Edugain (www.Edugain.com) Personal use only, commercial use is strictly prohibited
I) 30
161
285 - 5
12
19 = 24
14
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 30161
285 into an improper f raction, we will need to
multiply the denominator 285 by 30 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:
30161
285 =
30 × 285 + 161
285 =
8711
285
Similarly, the mixed f raction 512
19 can be converted into an improper f raction
as:
512
19 =
5 × 19 + 12
19 =
107
19
Step 2
We now need to subtract the f ollowing unlike f ractions: 8711
285 and
107
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 285 and 19.The LCM of 285 and 19 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:
8711 × 1
285 × 1 =
8711
285
Step 5
Similarly, the second f raction can be written as:
107 × 15
19 × 15 =
1605
285
Step 6
Let us now subtract the two like f ractions:
8711
285 -
1605
285
ID : ae-6-Mixed-Fractions-Addition-and-Subtraction [49]
(C) 2016 Edugain (www.Edugain.com) Personal use only, commercial use is strictly prohibited
= 8711 - 1605
285
= 7106
285
= 7106 ÷ 19
285 ÷ 19 ...[ Dividing both numerator and denominator by their HCF to bring
]
= 374
15
= 2414
15
Step 7
Thus, the simplif ied value of the given f ractions is 2414
15 .
ID : ae-6-Mixed-Fractions-Addition-and-Subtraction [50]
(C) 2016 Edugain (www.Edugain.com) Personal use only, commercial use is strictly prohibited
J) 27
49
240 - 4
4
15 = 22
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 2749
240 into an improper f raction, we will need to
multiply the denominator 240 by 27 and add the numerator 49 to the result. Theresulting number will be the numerator of the improper f raction and thedenominator will remain the same:
2749
240 =
27 × 240 + 49
240 =
6529
240
Similarly, the mixed f raction 44
15 can be converted into an improper f raction
as:
44
15 =
4 × 15 + 4
15 =
64
15
Step 2
We now need to subtract the f ollowing unlike f ractions: 6529
240 and
64
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:
6529 × 1
240 × 1 =
6529
240
Step 5
Similarly, the second f raction can be written as:
64 × 16
15 × 16 =
1024
240
Step 6
Let us now subtract the two like f ractions:
6529
240 -
1024
240
ID : ae-6-Mixed-Fractions-Addition-and-Subtraction [51]
(C) 2016 Edugain (www.Edugain.com) Personal use only, commercial use is strictly prohibited
= 6529 - 1024
240
= 5505
240
= 5505 ÷ 15
240 ÷ 15 ...[ Dividing both numerator and denominator by their HCF to bring
]
= 367
16
= 2215
16
Step 7
Thus, the simplif ied value of the given f ractions is 2215
16 .
ID : ae-6-Mixed-Fractions-Addition-and-Subtraction [52]
(C) 2016 Edugain (www.Edugain.com) Personal use only, commercial use is strictly prohibited
