ID : cn-6-Fractions-Ascending-Descending-Order-Reduce-to-simplest-form [1]
Grade 6
Fractions - Ascending|Descending Order, Reduce to
simplest form
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(1)
Reduce the f ollowing f ractions to the lowest terms:
A)
B)
714
C)
952
=
1377
1496
D)
F)
676
=
979
I)
222
=
1649
L)
384
=
1079
=
1001
O)
368
584
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=
1190
N)
671
969
=
912
M)
=
1148
K)
754
700
=
588
J)
=
774
H)
697
306
=
1040
G)
=
1168
E)
682
992
=
=
1180
=
1800
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ID : cn-6-Fractions-Ascending-Descending-Order-Reduce-to-simplest-form [2]
Answers
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ID : cn-6-Fractions-Ascending-Descending-Order-Reduce-to-simplest-form [3]
(1)
A)
14
27
Step 1
If we divide the numerator and the denominator of
714
by their HCF (Highest
1377
Common Factor), the resulting f raction will be in the lowest f orm.
Step 2
Let us now f ind the HCF of 714 and 1377.
Step 3
All prime f actors of 1377:
3
| 1377
3 is a factor of 1377
3
| 459
3 is a factor of 459
3
| 153
3 is a factor of 153
3
| 51
3 is a factor of 51
17 | 17
17 is a factor of 17
|1
T hus,
1377 = 3 × 3 × 3 × 3 × 17.
Step 4
All prime f actors of 714:
2
| 714
2 is a factor of 714
3
| 357
3 is a factor of 357
7
| 119
7 is a factor of 119
17 | 17
17 is a factor of 17
|1
T hus,
714 = 2 × 3 × 7 × 17.
Step 5
Let's multiply all common f actors of 1377 and 714 to f ind the HCF.
T he HCF = 3 × 17
= 51.
Step 6
T o f ind the lowest term of
714
, let us divide both the numerator and the
1377
denominator by the HCF:
714
1377
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ID : cn-6-Fractions-Ascending-Descending-Order-Reduce-to-simplest-form [4]
714
51
=
1377
51
=
14
.
27
Step 7
T hus the lowest f orm of the f raction
714
1377
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is
14
.
27
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ID : cn-6-Fractions-Ascending-Descending-Order-Reduce-to-simplest-form [5]
B)
7
11
Step 1
If we divide the numerator and the denominator of
952
by their HCF (Highest
1496
Common Factor), the resulting f raction will be in the lowest f orm.
Step 2
Let us now f ind the HCF of 952 and 1496.
Step 3
All prime f actors of 1496:
2
| 1496
2 is a factor of 1496
2
| 748
2 is a factor of 748
2
| 374
2 is a factor of 374
11 | 187
11 is a factor of 187
17 | 17
17 is a factor of 17
|1
T hus,
1496 = 2 × 2 × 2 × 11 × 17.
Step 4
All prime f actors of 952:
2
| 952
2 is a factor of 952
2
| 476
2 is a factor of 476
2
| 238
2 is a factor of 238
7
| 119
7 is a factor of 119
17 | 17
17 is a factor of 17
|1
T hus,
952 = 2 × 2 × 2 × 7 × 17.
Step 5
Let's multiply all common f actors of 1496 and 952 to f ind the HCF.
T he HCF = 2 × 2 × 2 × 17
= 136.
Step 6
T o f ind the lowest term of
952
, let us divide both the numerator and the
1496
denominator by the HCF:
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ID : cn-6-Fractions-Ascending-Descending-Order-Reduce-to-simplest-form [6]
952
1496
952
136
=
1496
136
=
7
.
11
Step 7
T hus the lowest f orm of the f raction
952
1496
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is
7
.
11
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ID : cn-6-Fractions-Ascending-Descending-Order-Reduce-to-simplest-form [7]
C)
62
73
Step 1
If we divide the numerator and the denominator of
992
by their HCF (Highest
1168
Common Factor), the resulting f raction will be in the lowest f orm.
Step 2
Let us now f ind the HCF of 992 and 1168.
Step 3
All prime f actors of 1168:
2
| 1168
2 is a factor of 1168
2
| 584
2 is a factor of 584
2
| 292
2 is a factor of 292
2
| 146
2 is a factor of 146
73 | 73
73 is a factor of 73
|1
T hus,
1168 = 2 × 2 × 2 × 2 × 73.
Step 4
All prime f actors of 992:
2
| 992
2 is a factor of 992
2
| 496
2 is a factor of 496
2
| 248
2 is a factor of 248
2
| 124
2 is a factor of 124
2
| 62
2 is a factor of 62
31 | 31
31 is a factor of 31
|1
T hus,
992 = 2 × 2 × 2 × 2 × 2 × 31.
Step 5
Let's multiply all common f actors of 1168 and 992 to f ind the HCF.
T he HCF = 2 × 2 × 2 × 2
= 16.
Step 6
T o f ind the lowest term of
992
, let us divide both the numerator and the
1168
denominator by the HCF:
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ID : cn-6-Fractions-Ascending-Descending-Order-Reduce-to-simplest-form [8]
992
1168
992
=
16
1168
16
=
62
.
73
Step 7
T hus the lowest f orm of the f raction
992
1168
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is
62
.
73
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ID : cn-6-Fractions-Ascending-Descending-Order-Reduce-to-simplest-form [9]
D)
62
89
Step 1
If we divide the numerator and the denominator of
682
by their HCF (Highest
979
Common Factor), the resulting f raction will be in the lowest f orm.
Step 2
Let us now f ind the HCF of 682 and 979.
Step 3
All prime f actors of 979:
11 | 979
11 is a factor of 979
89 | 89
89 is a factor of 89
|1
T hus,
979 = 11 × 89.
Step 4
All prime f actors of 682:
2
| 682
2 is a factor of 682
11 | 341
11 is a factor of 341
31 | 31
31 is a factor of 31
|1
T hus,
682 = 2 × 11 × 31.
Step 5
Let's multiply all common f actors of 979 and 682 to f ind the HCF.
T he HCF = 11
= 11.
Step 6
T o f ind the lowest term of
682
, let us divide both the numerator and the
979
denominator by the HCF:
682
979
682
=
11
979
11
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ID : cn-6-Fractions-Ascending-Descending-Order-Reduce-to-simplest-form [10]
=
62
.
89
Step 7
T hus the lowest f orm of the f raction
682
979
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62
.
89
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E)
13
20
Step 1
If we divide the numerator and the denominator of
676
by their HCF (Highest
1040
Common Factor), the resulting f raction will be in the lowest f orm.
Step 2
Let us now f ind the HCF of 676 and 1040.
Step 3
All prime f actors of 1040:
2
| 1040
2 is a factor of 1040
2
| 520
2 is a factor of 520
2
| 260
2 is a factor of 260
2
| 130
2 is a factor of 130
5
| 65
5 is a factor of 65
13 | 13
13 is a factor of 13
|1
T hus,
1040 = 2 × 2 × 2 × 2 × 5 × 13.
Step 4
All prime f actors of 676:
2
| 676
2 is a factor of 676
2
| 338
2 is a factor of 338
13 | 169
13 is a factor of 169
13 | 13
13 is a factor of 13
|1
T hus,
676 = 2 × 2 × 13 × 13.
Step 5
Let's multiply all common f actors of 1040 and 676 to f ind the HCF.
T he HCF = 2 × 2 × 13
= 52.
Step 6
T o f ind the lowest term of
676
, let us divide both the numerator and the
1040
denominator by the HCF:
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ID : cn-6-Fractions-Ascending-Descending-Order-Reduce-to-simplest-form [12]
676
1040
676
=
52
1040
52
=
13
.
20
Step 7
T hus the lowest f orm of the f raction
676
1040
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is
13
.
20
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ID : cn-6-Fractions-Ascending-Descending-Order-Reduce-to-simplest-form [13]
F)
17
43
Step 1
If we divide the numerator and the denominator of
306
by their HCF (Highest
774
Common Factor), the resulting f raction will be in the lowest f orm.
Step 2
Let us now f ind the HCF of 306 and 774.
Step 3
All prime f actors of 774:
2
| 774
2 is a factor of 774
3
| 387
3 is a factor of 387
3
| 129
3 is a factor of 129
43 | 43
43 is a factor of 43
|1
T hus,
774 = 2 × 3 × 3 × 43.
Step 4
All prime f actors of 306:
2
| 306
2 is a factor of 306
3
| 153
3 is a factor of 153
3
| 51
3 is a factor of 51
17 | 17
17 is a factor of 17
|1
T hus,
306 = 2 × 3 × 3 × 17.
Step 5
Let's multiply all common f actors of 774 and 306 to f ind the HCF.
T he HCF = 2 × 3 × 3
= 18.
Step 6
T o f ind the lowest term of
306
, let us divide both the numerator and the
774
denominator by the HCF:
306
774
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ID : cn-6-Fractions-Ascending-Descending-Order-Reduce-to-simplest-form [14]
306
=
18
774
18
=
17
.
43
Step 7
T hus the lowest f orm of the f raction
306
774
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is
17
.
43
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ID : cn-6-Fractions-Ascending-Descending-Order-Reduce-to-simplest-form [15]
G)
41
97
Step 1
If we divide the numerator and the denominator of
697
by their HCF (Highest
1649
Common Factor), the resulting f raction will be in the lowest f orm.
Step 2
Let us now f ind the HCF of 697 and 1649.
Step 3
All prime f actors of 1649:
17 | 1649
17 is a factor of 1649
97 | 97
97 is a factor of 97
|1
T hus,
1649 = 17 × 97.
Step 4
All prime f actors of 697:
17 | 697
17 is a factor of 697
41 | 41
41 is a factor of 41
|1
T hus,
697 = 17 × 41.
Step 5
Let's multiply all common f actors of 1649 and 697 to f ind the HCF.
T he HCF = 17
= 17.
Step 6
T o f ind the lowest term of
697
, let us divide both the numerator and the
1649
denominator by the HCF:
697
1649
697
=
17
1649
17
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ID : cn-6-Fractions-Ascending-Descending-Order-Reduce-to-simplest-form [16]
=
41
.
97
Step 7
T hus the lowest f orm of the f raction
697
1649
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is
41
.
97
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H)
37
98
Step 1
If we divide the numerator and the denominator of
222
by their HCF (Highest
588
Common Factor), the resulting f raction will be in the lowest f orm.
Step 2
Let us now f ind the HCF of 222 and 588.
Step 3
All prime f actors of 588:
2 | 588
2 is a factor of 588
2 | 294
2 is a factor of 294
3 | 147
3 is a factor of 147
7 | 49
7 is a factor of 49
7 |7
7 is a factor of 7
|1
T hus,
588 = 2 × 2 × 3 × 7 × 7.
Step 4
All prime f actors of 222:
2
| 222
2 is a factor of 222
3
| 111
3 is a factor of 111
37 | 37
37 is a factor of 37
|1
T hus,
222 = 2 × 3 × 37.
Step 5
Let's multiply all common f actors of 588 and 222 to f ind the HCF.
T he HCF = 2 × 3
= 6.
Step 6
T o f ind the lowest term of
222
, let us divide both the numerator and the
588
denominator by the HCF:
222
588
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ID : cn-6-Fractions-Ascending-Descending-Order-Reduce-to-simplest-form [18]
222
=
6
588
6
=
37
.
98
Step 7
T hus the lowest f orm of the f raction
222
588
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is
37
.
98
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I)
25
41
Step 1
If we divide the numerator and the denominator of
700
by their HCF (Highest
1148
Common Factor), the resulting f raction will be in the lowest f orm.
Step 2
Let us now f ind the HCF of 700 and 1148.
Step 3
All prime f actors of 1148:
2
| 1148
2 is a factor of 1148
2
| 574
2 is a factor of 574
7
| 287
7 is a factor of 287
41 | 41
41 is a factor of 41
|1
T hus,
1148 = 2 × 2 × 7 × 41.
Step 4
All prime f actors of 700:
2 | 700
2 is a factor of 700
2 | 350
2 is a factor of 350
5 | 175
5 is a factor of 175
5 | 35
5 is a factor of 35
7 |7
7 is a factor of 7
|1
T hus,
700 = 2 × 2 × 5 × 5 × 7.
Step 5
Let's multiply all common f actors of 1148 and 700 to f ind the HCF.
T he HCF = 2 × 2 × 7
= 28.
Step 6
T o f ind the lowest term of
700
, let us divide both the numerator and the
1148
denominator by the HCF:
700
1148
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ID : cn-6-Fractions-Ascending-Descending-Order-Reduce-to-simplest-form [20]
700
=
28
1148
28
=
25
.
41
Step 7
T hus the lowest f orm of the f raction
700
1148
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25
.
41
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J)
58
83
Step 1
If we divide the numerator and the denominator of
754
by their HCF (Highest
1079
Common Factor), the resulting f raction will be in the lowest f orm.
Step 2
Let us now f ind the HCF of 754 and 1079.
Step 3
All prime f actors of 1079:
13 | 1079
13 is a factor of 1079
83 | 83
83 is a factor of 83
|1
T hus,
1079 = 13 × 83.
Step 4
All prime f actors of 754:
2
| 754
2 is a factor of 754
13 | 377
13 is a factor of 377
29 | 29
29 is a factor of 29
|1
T hus,
754 = 2 × 13 × 29.
Step 5
Let's multiply all common f actors of 1079 and 754 to f ind the HCF.
T he HCF = 13
= 13.
Step 6
T o f ind the lowest term of
754
, let us divide both the numerator and the
1079
denominator by the HCF:
754
1079
754
=
13
1079
13
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=
58
.
83
Step 7
T hus the lowest f orm of the f raction
754
1079
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58
.
83
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K)
8
19
Step 1
If we divide the numerator and the denominator of
384
by their HCF (Highest
912
Common Factor), the resulting f raction will be in the lowest f orm.
Step 2
Let us now f ind the HCF of 384 and 912.
Step 3
All prime f actors of 912:
2
| 912
2 is a factor of 912
2
| 456
2 is a factor of 456
2
| 228
2 is a factor of 228
2
| 114
2 is a factor of 114
3
| 57
3 is a factor of 57
19 | 19
19 is a factor of 19
|1
T hus,
912 = 2 × 2 × 2 × 2 × 3 × 19.
Step 4
All prime f actors of 384:
2 | 384
2 is a factor of 384
2 | 192
2 is a factor of 192
2 | 96
2 is a factor of 96
2 | 48
2 is a factor of 48
2 | 24
2 is a factor of 24
2 | 12
2 is a factor of 12
2 |6
2 is a factor of 6
3 |3
3 is a factor of 3
|1
T hus,
384 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3.
Step 5
Let's multiply all common f actors of 912 and 384 to f ind the HCF.
T he HCF = 2 × 2 × 2 × 2 × 3
= 48.
Step 6
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T o f ind the lowest term of
384
, let us divide both the numerator and the
912
denominator by the HCF:
384
912
384
=
48
912
48
=
8
.
19
Step 7
T hus the lowest f orm of the f raction
384
912
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8
.
19
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L)
57
70
Step 1
If we divide the numerator and the denominator of
969
by their HCF (Highest
1190
Common Factor), the resulting f raction will be in the lowest f orm.
Step 2
Let us now f ind the HCF of 969 and 1190.
Step 3
All prime f actors of 1190:
2
| 1190
2 is a factor of 1190
5
| 595
5 is a factor of 595
7
| 119
7 is a factor of 119
17 | 17
17 is a factor of 17
|1
T hus,
1190 = 2 × 5 × 7 × 17.
Step 4
All prime f actors of 969:
3
| 969
3 is a factor of 969
17 | 323
17 is a factor of 323
19 | 19
19 is a factor of 19
|1
T hus,
969 = 3 × 17 × 19.
Step 5
Let's multiply all common f actors of 1190 and 969 to f ind the HCF.
T he HCF = 17
= 17.
Step 6
T o f ind the lowest term of
969
, let us divide both the numerator and the
1190
denominator by the HCF:
969
1190
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969
=
17
1190
17
=
57
.
70
Step 7
T hus the lowest f orm of the f raction
969
1190
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57
.
70
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M)
61
91
Step 1
If we divide the numerator and the denominator of
671
by their HCF (Highest
1001
Common Factor), the resulting f raction will be in the lowest f orm.
Step 2
Let us now f ind the HCF of 671 and 1001.
Step 3
All prime f actors of 1001:
7
| 1001
7 is a factor of 1001
11 | 143
11 is a factor of 143
13 | 13
13 is a factor of 13
|1
T hus,
1001 = 7 × 11 × 13.
Step 4
All prime f actors of 671:
11 | 671
11 is a factor of 671
61 | 61
61 is a factor of 61
|1
T hus,
671 = 11 × 61.
Step 5
Let's multiply all common f actors of 1001 and 671 to f ind the HCF.
T he HCF = 11
= 11.
Step 6
T o f ind the lowest term of
671
, let us divide both the numerator and the
1001
denominator by the HCF:
671
1001
671
=
11
1001
11
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=
61
.
91
Step 7
T hus the lowest f orm of the f raction
671
1001
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61
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91
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N)
46
73
Step 1
If we divide the numerator and the denominator of
368
by their HCF (Highest
584
Common Factor), the resulting f raction will be in the lowest f orm.
Step 2
Let us now f ind the HCF of 368 and 584.
Step 3
All prime f actors of 584:
2
| 584
2 is a factor of 584
2
| 292
2 is a factor of 292
2
| 146
2 is a factor of 146
73 | 73
73 is a factor of 73
|1
T hus,
584 = 2 × 2 × 2 × 73.
Step 4
All prime f actors of 368:
2
| 368
2 is a factor of 368
2
| 184
2 is a factor of 184
2
| 92
2 is a factor of 92
2
| 46
2 is a factor of 46
23 | 23
23 is a factor of 23
|1
T hus,
368 = 2 × 2 × 2 × 2 × 23.
Step 5
Let's multiply all common f actors of 584 and 368 to f ind the HCF.
T he HCF = 2 × 2 × 2
= 8.
Step 6
T o f ind the lowest term of
368
, let us divide both the numerator and the
584
denominator by the HCF:
368
584
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ID : cn-6-Fractions-Ascending-Descending-Order-Reduce-to-simplest-form [30]
368
=
8
584
8
=
46
.
73
Step 7
T hus the lowest f orm of the f raction
368
584
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is
46
.
73
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ID : cn-6-Fractions-Ascending-Descending-Order-Reduce-to-simplest-form [31]
O)
59
90
Step 1
If we divide the numerator and the denominator of
1180
by their HCF (Highest
1800
Common Factor), the resulting f raction will be in the lowest f orm.
Step 2
Let us now f ind the HCF of 1180 and 1800.
Step 3
All prime f actors of 1800:
2 | 1800
2 is a factor of 1800
2 | 900
2 is a factor of 900
2 | 450
2 is a factor of 450
3 | 225
3 is a factor of 225
3 | 75
3 is a factor of 75
5 | 25
5 is a factor of 25
5 |5
5 is a factor of 5
|1
T hus,
1800 = 2 × 2 × 2 × 3 × 3 × 5 × 5.
Step 4
All prime f actors of 1180:
2
| 1180
2 is a factor of 1180
2
| 590
2 is a factor of 590
5
| 295
5 is a factor of 295
59 | 59
59 is a factor of 59
|1
T hus,
1180 = 2 × 2 × 5 × 59.
Step 5
Let's multiply all common f actors of 1800 and 1180 to f ind the HCF.
T he HCF = 2 × 2 × 5
= 20.
Step 6
T o f ind the lowest term of
1180
, let us divide both the numerator and the
1800
denominator by the HCF:
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Personal use only, commercial use is strictly prohibited
ID : cn-6-Fractions-Ascending-Descending-Order-Reduce-to-simplest-form [32]
1180
1800
1180
=
20
1800
20
=
59
.
90
Step 7
T hus the lowest f orm of the f raction
1180
1800
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is
59
.
90
Personal use only, commercial use is strictly prohibited