ID : ca-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)
1020
C)
912
=
1940
1248
D)
F)
516
=
830
I)
576
=
1598
L)
369
=
1980
=
984
O)
205
460
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=
1530
N)
768
867
=
891
M)
=
1246
K)
920
644
=
900
J)
=
1577
H)
799
855
=
1128
G)
=
1264
E)
560
848
=
=
480
=
1125
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ID : ca-6-Fractions-Ascending-Descending-Order-Reduce-to-simplest-form [2]
Answers
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ID : ca-6-Fractions-Ascending-Descending-Order-Reduce-to-simplest-form [3]
(1)
A)
51
97
Step 1
If we divide the numerator and the denominator of
1020
by their HCF (Highest
1940
Common Factor), the resulting f raction will be in the lowest f orm.
Step 2
Let us now f ind the HCF of 1020 and 1940.
Step 3
All prime f actors of 1940:
2
| 1940
2 is a factor of 1940
2
| 970
2 is a factor of 970
5
| 485
5 is a factor of 485
97 | 97
97 is a factor of 97
|1
T hus,
1940 = 2 × 2 × 5 × 97.
Step 4
All prime f actors of 1020:
2
| 1020
2 is a factor of 1020
2
| 510
2 is a factor of 510
3
| 255
3 is a factor of 255
5
| 85
5 is a factor of 85
17 | 17
17 is a factor of 17
|1
T hus,
1020 = 2 × 2 × 3 × 5 × 17.
Step 5
Let's multiply all common f actors of 1940 and 1020 to f ind the HCF.
T he HCF = 2 × 2 × 5
= 20.
Step 6
T o f ind the lowest term of
1020
, let us divide both the numerator and the
1940
denominator by the HCF:
1020
1940
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ID : ca-6-Fractions-Ascending-Descending-Order-Reduce-to-simplest-form [4]
1020
=
20
1940
20
=
51
.
97
Step 7
T hus the lowest f orm of the f raction
1020
1940
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51
.
97
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ID : ca-6-Fractions-Ascending-Descending-Order-Reduce-to-simplest-form [5]
B)
19
26
Step 1
If we divide the numerator and the denominator of
912
by their HCF (Highest
1248
Common Factor), the resulting f raction will be in the lowest f orm.
Step 2
Let us now f ind the HCF of 912 and 1248.
Step 3
All prime f actors of 1248:
2
| 1248
2 is a factor of 1248
2
| 624
2 is a factor of 624
2
| 312
2 is a factor of 312
2
| 156
2 is a factor of 156
2
| 78
2 is a factor of 78
3
| 39
3 is a factor of 39
13 | 13
13 is a factor of 13
|1
T hus,
1248 = 2 × 2 × 2 × 2 × 2 × 3 × 13.
Step 4
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 5
Let's multiply all common f actors of 1248 and 912 to f ind the HCF.
T he HCF = 2 × 2 × 2 × 2 × 3
= 48.
Step 6
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ID : ca-6-Fractions-Ascending-Descending-Order-Reduce-to-simplest-form [6]
T o f ind the lowest term of
912
, let us divide both the numerator and the
1248
denominator by the HCF:
912
1248
912
=
48
1248
48
=
19
.
26
Step 7
T hus the lowest f orm of the f raction
912
1248
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is
19
.
26
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ID : ca-6-Fractions-Ascending-Descending-Order-Reduce-to-simplest-form [7]
C)
53
79
Step 1
If we divide the numerator and the denominator of
848
by their HCF (Highest
1264
Common Factor), the resulting f raction will be in the lowest f orm.
Step 2
Let us now f ind the HCF of 848 and 1264.
Step 3
All prime f actors of 1264:
2
| 1264
2 is a factor of 1264
2
| 632
2 is a factor of 632
2
| 316
2 is a factor of 316
2
| 158
2 is a factor of 158
79 | 79
79 is a factor of 79
|1
T hus,
1264 = 2 × 2 × 2 × 2 × 79.
Step 4
All prime f actors of 848:
2
| 848
2 is a factor of 848
2
| 424
2 is a factor of 424
2
| 212
2 is a factor of 212
2
| 106
2 is a factor of 106
53 | 53
53 is a factor of 53
|1
T hus,
848 = 2 × 2 × 2 × 2 × 53.
Step 5
Let's multiply all common f actors of 1264 and 848 to f ind the HCF.
T he HCF = 2 × 2 × 2 × 2
= 16.
Step 6
T o f ind the lowest term of
848
, let us divide both the numerator and the
1264
denominator by the HCF:
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ID : ca-6-Fractions-Ascending-Descending-Order-Reduce-to-simplest-form [8]
848
1264
848
=
16
1264
16
=
53
.
79
Step 7
T hus the lowest f orm of the f raction
848
1264
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is
53
.
79
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ID : ca-6-Fractions-Ascending-Descending-Order-Reduce-to-simplest-form [9]
D)
56
83
Step 1
If we divide the numerator and the denominator of
560
by their HCF (Highest
830
Common Factor), the resulting f raction will be in the lowest f orm.
Step 2
Let us now f ind the HCF of 560 and 830.
Step 3
All prime f actors of 830:
2
| 830
2 is a factor of 830
5
| 415
5 is a factor of 415
83 | 83
83 is a factor of 83
|1
T hus,
830 = 2 × 5 × 83.
Step 4
All prime f actors of 560:
2 | 560
2 is a factor of 560
2 | 280
2 is a factor of 280
2 | 140
2 is a factor of 140
2 | 70
2 is a factor of 70
5 | 35
5 is a factor of 35
7 |7
7 is a factor of 7
|1
T hus,
560 = 2 × 2 × 2 × 2 × 5 × 7.
Step 5
Let's multiply all common f actors of 830 and 560 to f ind the HCF.
T he HCF = 2 × 5
= 10.
Step 6
T o f ind the lowest term of
560
, let us divide both the numerator and the
830
denominator by the HCF:
560
830
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ID : ca-6-Fractions-Ascending-Descending-Order-Reduce-to-simplest-form [10]
560
=
10
830
10
=
56
.
83
Step 7
T hus the lowest f orm of the f raction
560
830
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is
56
.
83
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ID : ca-6-Fractions-Ascending-Descending-Order-Reduce-to-simplest-form [11]
E)
43
94
Step 1
If we divide the numerator and the denominator of
516
by their HCF (Highest
1128
Common Factor), the resulting f raction will be in the lowest f orm.
Step 2
Let us now f ind the HCF of 516 and 1128.
Step 3
All prime f actors of 1128:
2
| 1128
2 is a factor of 1128
2
| 564
2 is a factor of 564
2
| 282
2 is a factor of 282
3
| 141
3 is a factor of 141
47 | 47
47 is a factor of 47
|1
T hus,
1128 = 2 × 2 × 2 × 3 × 47.
Step 4
All prime f actors of 516:
2
| 516
2 is a factor of 516
2
| 258
2 is a factor of 258
3
| 129
3 is a factor of 129
43 | 43
43 is a factor of 43
|1
T hus,
516 = 2 × 2 × 3 × 43.
Step 5
Let's multiply all common f actors of 1128 and 516 to f ind the HCF.
T he HCF = 2 × 2 × 3
= 12.
Step 6
T o f ind the lowest term of
516
, let us divide both the numerator and the
1128
denominator by the HCF:
516
1128
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ID : ca-6-Fractions-Ascending-Descending-Order-Reduce-to-simplest-form [12]
516
=
12
1128
12
=
43
.
94
Step 7
T hus the lowest f orm of the f raction
516
1128
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is
43
.
94
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ID : ca-6-Fractions-Ascending-Descending-Order-Reduce-to-simplest-form [13]
F)
45
83
Step 1
If we divide the numerator and the denominator of
855
by their HCF (Highest
1577
Common Factor), the resulting f raction will be in the lowest f orm.
Step 2
Let us now f ind the HCF of 855 and 1577.
Step 3
All prime f actors of 1577:
19 | 1577
19 is a factor of 1577
83 | 83
83 is a factor of 83
|1
T hus,
1577 = 19 × 83.
Step 4
All prime f actors of 855:
3
| 855
3 is a factor of 855
3
| 285
3 is a factor of 285
5
| 95
5 is a factor of 95
19 | 19
19 is a factor of 19
|1
T hus,
855 = 3 × 3 × 5 × 19.
Step 5
Let's multiply all common f actors of 1577 and 855 to f ind the HCF.
T he HCF = 19
= 19.
Step 6
T o f ind the lowest term of
855
, let us divide both the numerator and the
1577
denominator by the HCF:
855
1577
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ID : ca-6-Fractions-Ascending-Descending-Order-Reduce-to-simplest-form [14]
855
19
=
1577
19
=
45
.
83
Step 7
T hus the lowest f orm of the f raction
855
1577
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is
45
.
83
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ID : ca-6-Fractions-Ascending-Descending-Order-Reduce-to-simplest-form [15]
G)
1
2
Step 1
If we divide the numerator and the denominator of
799
by their HCF (Highest
1598
Common Factor), the resulting f raction will be in the lowest f orm.
Step 2
Let us now f ind the HCF of 799 and 1598.
Step 3
All prime f actors of 1598:
2
| 1598
2 is a factor of 1598
17 | 799
17 is a factor of 799
47 | 47
47 is a factor of 47
|1
T hus,
1598 = 2 × 17 × 47.
Step 4
All prime f actors of 799:
17 | 799
17 is a factor of 799
47 | 47
47 is a factor of 47
|1
T hus,
799 = 17 × 47.
Step 5
Let's multiply all common f actors of 1598 and 799 to f ind the HCF.
T he HCF = 17 × 47
= 799.
Step 6
T o f ind the lowest term of
799
, let us divide both the numerator and the
1598
denominator by the HCF:
799
1598
799
=
799
1598
799
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ID : ca-6-Fractions-Ascending-Descending-Order-Reduce-to-simplest-form [16]
=
1
.
2
Step 7
T hus the lowest f orm of the f raction
799
1598
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is
1
.
2
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ID : ca-6-Fractions-Ascending-Descending-Order-Reduce-to-simplest-form [17]
H)
16
25
Step 1
If we divide the numerator and the denominator of
576
by their HCF (Highest
900
Common Factor), the resulting f raction will be in the lowest f orm.
Step 2
Let us now f ind the HCF of 576 and 900.
Step 3
All prime f actors of 900:
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,
900 = 2 × 2 × 3 × 3 × 5 × 5.
Step 4
All prime f actors of 576:
2 | 576
2 is a factor of 576
2 | 288
2 is a factor of 288
2 | 144
2 is a factor of 144
2 | 72
2 is a factor of 72
2 | 36
2 is a factor of 36
2 | 18
2 is a factor of 18
3 |9
3 is a factor of 9
3 |3
3 is a factor of 3
|1
T hus,
576 = 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3.
Step 5
Let's multiply all common f actors of 900 and 576 to f ind the HCF.
T he HCF = 2 × 2 × 3 × 3
= 36.
Step 6
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ID : ca-6-Fractions-Ascending-Descending-Order-Reduce-to-simplest-form [18]
T o f ind the lowest term of
576
, let us divide both the numerator and the
900
denominator by the HCF:
576
900
576
=
36
900
36
=
16
.
25
Step 7
T hus the lowest f orm of the f raction
576
900
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16
.
25
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ID : ca-6-Fractions-Ascending-Descending-Order-Reduce-to-simplest-form [19]
I)
46
89
Step 1
If we divide the numerator and the denominator of
644
by their HCF (Highest
1246
Common Factor), the resulting f raction will be in the lowest f orm.
Step 2
Let us now f ind the HCF of 644 and 1246.
Step 3
All prime f actors of 1246:
2
| 1246
2 is a factor of 1246
7
| 623
7 is a factor of 623
89 | 89
89 is a factor of 89
|1
T hus,
1246 = 2 × 7 × 89.
Step 4
All prime f actors of 644:
2
| 644
2 is a factor of 644
2
| 322
2 is a factor of 322
7
| 161
7 is a factor of 161
23 | 23
23 is a factor of 23
|1
T hus,
644 = 2 × 2 × 7 × 23.
Step 5
Let's multiply all common f actors of 1246 and 644 to f ind the HCF.
T he HCF = 2 × 7
= 14.
Step 6
T o f ind the lowest term of
644
, let us divide both the numerator and the
1246
denominator by the HCF:
644
1246
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ID : ca-6-Fractions-Ascending-Descending-Order-Reduce-to-simplest-form [20]
644
=
14
1246
14
=
46
.
89
Step 7
T hus the lowest f orm of the f raction
644
1246
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is
46
.
89
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ID : ca-6-Fractions-Ascending-Descending-Order-Reduce-to-simplest-form [21]
J)
46
99
Step 1
If we divide the numerator and the denominator of
920
by their HCF (Highest
1980
Common Factor), the resulting f raction will be in the lowest f orm.
Step 2
Let us now f ind the HCF of 920 and 1980.
Step 3
All prime f actors of 1980:
2
| 1980
2 is a factor of 1980
2
| 990
2 is a factor of 990
3
| 495
3 is a factor of 495
3
| 165
3 is a factor of 165
5
| 55
5 is a factor of 55
11 | 11
11 is a factor of 11
|1
T hus,
1980 = 2 × 2 × 3 × 3 × 5 × 11.
Step 4
All prime f actors of 920:
2
| 920
2 is a factor of 920
2
| 460
2 is a factor of 460
2
| 230
2 is a factor of 230
5
| 115
5 is a factor of 115
23 | 23
23 is a factor of 23
|1
T hus,
920 = 2 × 2 × 2 × 5 × 23.
Step 5
Let's multiply all common f actors of 1980 and 920 to f ind the HCF.
T he HCF = 2 × 2 × 5
= 20.
Step 6
T o f ind the lowest term of
920
, let us divide both the numerator and the
1980
denominator by the HCF:
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ID : ca-6-Fractions-Ascending-Descending-Order-Reduce-to-simplest-form [22]
920
1980
920
=
20
1980
20
=
46
.
99
Step 7
T hus the lowest f orm of the f raction
920
1980
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is
46
.
99
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K)
41
99
Step 1
If we divide the numerator and the denominator of
369
by their HCF (Highest
891
Common Factor), the resulting f raction will be in the lowest f orm.
Step 2
Let us now f ind the HCF of 369 and 891.
Step 3
All prime f actors of 891:
3
| 891
3 is a factor of 891
3
| 297
3 is a factor of 297
3
| 99
3 is a factor of 99
3
| 33
3 is a factor of 33
11 | 11
11 is a factor of 11
|1
T hus,
891 = 3 × 3 × 3 × 3 × 11.
Step 4
All prime f actors of 369:
3
| 369
3 is a factor of 369
3
| 123
3 is a factor of 123
41 | 41
41 is a factor of 41
|1
T hus,
369 = 3 × 3 × 41.
Step 5
Let's multiply all common f actors of 891 and 369 to f ind the HCF.
T he HCF = 3 × 3
= 9.
Step 6
T o f ind the lowest term of
369
, let us divide both the numerator and the
891
denominator by the HCF:
369
891
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ID : ca-6-Fractions-Ascending-Descending-Order-Reduce-to-simplest-form [24]
369
=
9
891
9
=
41
.
99
Step 7
T hus the lowest f orm of the f raction
369
891
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41
.
99
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ID : ca-6-Fractions-Ascending-Descending-Order-Reduce-to-simplest-form [25]
L)
17
30
Step 1
If we divide the numerator and the denominator of
867
by their HCF (Highest
1530
Common Factor), the resulting f raction will be in the lowest f orm.
Step 2
Let us now f ind the HCF of 867 and 1530.
Step 3
All prime f actors of 1530:
2
| 1530
2 is a factor of 1530
3
| 765
3 is a factor of 765
3
| 255
3 is a factor of 255
5
| 85
5 is a factor of 85
17 | 17
17 is a factor of 17
|1
T hus,
1530 = 2 × 3 × 3 × 5 × 17.
Step 4
All prime f actors of 867:
3
| 867
3 is a factor of 867
17 | 289
17 is a factor of 289
17 | 17
17 is a factor of 17
|1
T hus,
867 = 3 × 17 × 17.
Step 5
Let's multiply all common f actors of 1530 and 867 to f ind the HCF.
T he HCF = 3 × 17
= 51.
Step 6
T o f ind the lowest term of
867
, let us divide both the numerator and the
1530
denominator by the HCF:
867
1530
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ID : ca-6-Fractions-Ascending-Descending-Order-Reduce-to-simplest-form [26]
867
=
51
1530
51
=
17
.
30
Step 7
T hus the lowest f orm of the f raction
867
1530
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17
.
30
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ID : ca-6-Fractions-Ascending-Descending-Order-Reduce-to-simplest-form [27]
M)
32
41
Step 1
If we divide the numerator and the denominator of
768
by their HCF (Highest
984
Common Factor), the resulting f raction will be in the lowest f orm.
Step 2
Let us now f ind the HCF of 768 and 984.
Step 3
All prime f actors of 984:
2
| 984
2 is a factor of 984
2
| 492
2 is a factor of 492
2
| 246
2 is a factor of 246
3
| 123
3 is a factor of 123
41 | 41
41 is a factor of 41
|1
T hus,
984 = 2 × 2 × 2 × 3 × 41.
Step 4
All prime f actors of 768:
2 | 768
2 is a factor of 768
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,
768 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3.
Step 5
Let's multiply all common f actors of 984 and 768 to f ind the HCF.
T he HCF = 2 × 2 × 2 × 3
= 24.
Step 6
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ID : ca-6-Fractions-Ascending-Descending-Order-Reduce-to-simplest-form [28]
T o f ind the lowest term of
768
, let us divide both the numerator and the
984
denominator by the HCF:
768
984
768
=
24
984
24
=
32
.
41
Step 7
T hus the lowest f orm of the f raction
768
984
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.
41
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N)
41
92
Step 1
If we divide the numerator and the denominator of
205
by their HCF (Highest
460
Common Factor), the resulting f raction will be in the lowest f orm.
Step 2
Let us now f ind the HCF of 205 and 460.
Step 3
All prime f actors of 460:
2
| 460
2 is a factor of 460
2
| 230
2 is a factor of 230
5
| 115
5 is a factor of 115
23 | 23
23 is a factor of 23
|1
T hus,
460 = 2 × 2 × 5 × 23.
Step 4
All prime f actors of 205:
5
| 205
41 | 41
5 is a factor of 205
41 is a factor of 41
|1
T hus,
205 = 5 × 41.
Step 5
Let's multiply all common f actors of 460 and 205 to f ind the HCF.
T he HCF = 5
= 5.
Step 6
T o f ind the lowest term of
205
, let us divide both the numerator and the
460
denominator by the HCF:
205
460
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ID : ca-6-Fractions-Ascending-Descending-Order-Reduce-to-simplest-form [30]
205
=
5
460
5
=
41
.
92
Step 7
T hus the lowest f orm of the f raction
205
460
(C) 2016 Edugain (www.Edugain.com)
is
41
.
92
Personal use only, commercial use is strictly prohibited
ID : ca-6-Fractions-Ascending-Descending-Order-Reduce-to-simplest-form [31]
O)
32
75
Step 1
If we divide the numerator and the denominator of
480
by their HCF (Highest
1125
Common Factor), the resulting f raction will be in the lowest f orm.
Step 2
Let us now f ind the HCF of 480 and 1125.
Step 3
All prime f actors of 1125:
3 | 1125
3 is a factor of 1125
3 | 375
3 is a factor of 375
5 | 125
5 is a factor of 125
5 | 25
5 is a factor of 25
5 |5
5 is a factor of 5
|1
T hus,
1125 = 3 × 3 × 5 × 5 × 5.
Step 4
All prime f actors of 480:
2 | 480
2 is a factor of 480
2 | 240
2 is a factor of 240
2 | 120
2 is a factor of 120
2 | 60
2 is a factor of 60
2 | 30
2 is a factor of 30
3 | 15
3 is a factor of 15
5 |5
5 is a factor of 5
|1
T hus,
480 = 2 × 2 × 2 × 2 × 2 × 3 × 5.
Step 5
Let's multiply all common f actors of 1125 and 480 to f ind the HCF.
T he HCF = 3 × 5
= 15.
Step 6
T o f ind the lowest term of
480
, let us divide both the numerator and the
1125
(C) 2016 Edugain (www.Edugain.com)
Personal use only, commercial use is strictly prohibited
ID : ca-6-Fractions-Ascending-Descending-Order-Reduce-to-simplest-form [32]
denominator by the HCF:
480
1125
480
=
15
1125
15
=
32
.
75
Step 7
T hus the lowest f orm of the f raction
480
1125
(C) 2016 Edugain (www.Edugain.com)
is
32
.
75
Personal use only, commercial use is strictly prohibited