ID : ae-6-Fractions-Ascending-Descending-Order-Reduce-to-simplest-form [1]
Grade 6
Fractions - Ascending|Descending Order, Reduce to
simplest form
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Fill in t he blanks
(1)
Reduce the f ollowing f ractions to the lowest terms:
A)
B)
585
C)
928
=
1395
1296
D)
F)
1320
=
684
I)
840
=
1520
L)
343
=
1536
=
470
O)
400
568
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=
770
N)
205
640
=
602
M)
=
1260
K)
944
825
=
1302
J)
=
1152
H)
480
1040
=
1880
G)
=
1079
E)
603
468
=
=
246
=
420
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ID : ae-6-Fractions-Ascending-Descending-Order-Reduce-to-simplest-form [2]
Answers
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ID : ae-6-Fractions-Ascending-Descending-Order-Reduce-to-simplest-form [3]
(1)
A)
13
31
Step 1
If we divide the numerator and the denominator of
585
by their HCF (Highest
1395
Common Factor), the resulting f raction will be in the lowest f orm.
Step 2
Let us now f ind the HCF of 585 and 1395.
Step 3
All prime f actors of 1395:
3
| 1395
3 is a factor of 1395
3
| 465
3 is a factor of 465
5
| 155
5 is a factor of 155
31 | 31
31 is a factor of 31
|1
T hus,
1395 = 3 × 3 × 5 × 31.
Step 4
All prime f actors of 585:
3
| 585
3 is a factor of 585
3
| 195
3 is a factor of 195
5
| 65
5 is a factor of 65
13 | 13
13 is a factor of 13
|1
T hus,
585 = 3 × 3 × 5 × 13.
Step 5
Let's multiply all common f actors of 1395 and 585 to f ind the HCF.
T he HCF = 3 × 3 × 5
= 45.
Step 6
T o f ind the lowest term of
585
, let us divide both the numerator and the
1395
denominator by the HCF:
585
1395
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ID : ae-6-Fractions-Ascending-Descending-Order-Reduce-to-simplest-form [4]
585
=
45
1395
45
=
13
.
31
Step 7
T hus the lowest f orm of the f raction
585
1395
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is
13
.
31
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ID : ae-6-Fractions-Ascending-Descending-Order-Reduce-to-simplest-form [5]
B)
58
81
Step 1
If we divide the numerator and the denominator of
928
by their HCF (Highest
1296
Common Factor), the resulting f raction will be in the lowest f orm.
Step 2
Let us now f ind the HCF of 928 and 1296.
Step 3
All prime f actors of 1296:
2 | 1296
2 is a factor of 1296
2 | 648
2 is a factor of 648
2 | 324
2 is a factor of 324
2 | 162
2 is a factor of 162
3 | 81
3 is a factor of 81
3 | 27
3 is a factor of 27
3 |9
3 is a factor of 9
3 |3
3 is a factor of 3
|1
T hus,
1296 = 2 × 2 × 2 × 2 × 3 × 3 × 3 × 3.
Step 4
All prime f actors of 928:
2
| 928
2 is a factor of 928
2
| 464
2 is a factor of 464
2
| 232
2 is a factor of 232
2
| 116
2 is a factor of 116
2
| 58
2 is a factor of 58
29 | 29
29 is a factor of 29
|1
T hus,
928 = 2 × 2 × 2 × 2 × 2 × 29.
Step 5
Let's multiply all common f actors of 1296 and 928 to f ind the HCF.
T he HCF = 2 × 2 × 2 × 2
= 16.
Step 6
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ID : ae-6-Fractions-Ascending-Descending-Order-Reduce-to-simplest-form [6]
T o f ind the lowest term of
928
, let us divide both the numerator and the
1296
denominator by the HCF:
928
1296
928
=
16
1296
16
=
58
.
81
Step 7
T hus the lowest f orm of the f raction
928
1296
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is
58
.
81
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ID : ae-6-Fractions-Ascending-Descending-Order-Reduce-to-simplest-form [7]
C)
36
83
Step 1
If we divide the numerator and the denominator of
468
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 468 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 468:
2
| 468
2 is a factor of 468
2
| 234
2 is a factor of 234
3
| 117
3 is a factor of 117
3
| 39
3 is a factor of 39
13 | 13
13 is a factor of 13
|1
T hus,
468 = 2 × 2 × 3 × 3 × 13.
Step 5
Let's multiply all common f actors of 1079 and 468 to f ind the HCF.
T he HCF = 13
= 13.
Step 6
T o f ind the lowest term of
468
, let us divide both the numerator and the
1079
denominator by the HCF:
468
1079
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ID : ae-6-Fractions-Ascending-Descending-Order-Reduce-to-simplest-form [8]
468
=
13
1079
13
=
36
.
83
Step 7
T hus the lowest f orm of the f raction
468
1079
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is
36
.
83
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ID : ae-6-Fractions-Ascending-Descending-Order-Reduce-to-simplest-form [9]
D)
67
76
Step 1
If we divide the numerator and the denominator of
603
by their HCF (Highest
684
Common Factor), the resulting f raction will be in the lowest f orm.
Step 2
Let us now f ind the HCF of 603 and 684.
Step 3
All prime f actors of 684:
2
| 684
2 is a factor of 684
2
| 342
2 is a factor of 342
3
| 171
3 is a factor of 171
3
| 57
3 is a factor of 57
19 | 19
19 is a factor of 19
|1
T hus,
684 = 2 × 2 × 3 × 3 × 19.
Step 4
All prime f actors of 603:
3
| 603
3 is a factor of 603
3
| 201
3 is a factor of 201
67 | 67
67 is a factor of 67
|1
T hus,
603 = 3 × 3 × 67.
Step 5
Let's multiply all common f actors of 684 and 603 to f ind the HCF.
T he HCF = 3 × 3
= 9.
Step 6
T o f ind the lowest term of
603
, let us divide both the numerator and the
684
denominator by the HCF:
603
684
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ID : ae-6-Fractions-Ascending-Descending-Order-Reduce-to-simplest-form [10]
603
=
9
684
9
=
67
.
76
Step 7
T hus the lowest f orm of the f raction
603
684
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is
67
.
76
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ID : ae-6-Fractions-Ascending-Descending-Order-Reduce-to-simplest-form [11]
E)
33
47
Step 1
If we divide the numerator and the denominator of
1320
by their HCF (Highest
1880
Common Factor), the resulting f raction will be in the lowest f orm.
Step 2
Let us now f ind the HCF of 1320 and 1880.
Step 3
All prime f actors of 1880:
2
| 1880
2 is a factor of 1880
2
| 940
2 is a factor of 940
2
| 470
2 is a factor of 470
5
| 235
5 is a factor of 235
47 | 47
47 is a factor of 47
|1
T hus,
1880 = 2 × 2 × 2 × 5 × 47.
Step 4
All prime f actors of 1320:
2
| 1320
2 is a factor of 1320
2
| 660
2 is a factor of 660
2
| 330
2 is a factor of 330
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,
1320 = 2 × 2 × 2 × 3 × 5 × 11.
Step 5
Let's multiply all common f actors of 1880 and 1320 to f ind the HCF.
T he HCF = 2 × 2 × 2 × 5
= 40.
Step 6
T o f ind the lowest term of
1320
, let us divide both the numerator and the
1880
denominator by the HCF:
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ID : ae-6-Fractions-Ascending-Descending-Order-Reduce-to-simplest-form [12]
1320
1880
1320
=
40
1880
40
=
33
.
47
Step 7
T hus the lowest f orm of the f raction
1320
1880
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is
33
.
47
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ID : ae-6-Fractions-Ascending-Descending-Order-Reduce-to-simplest-form [13]
F)
65
72
Step 1
If we divide the numerator and the denominator of
1040
by their HCF (Highest
1152
Common Factor), the resulting f raction will be in the lowest f orm.
Step 2
Let us now f ind the HCF of 1040 and 1152.
Step 3
All prime f actors of 1152:
2 | 1152
2 is a factor of 1152
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,
1152 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3.
Step 4
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 5
Let's multiply all common f actors of 1152 and 1040 to f ind the HCF.
T he HCF = 2 × 2 × 2 × 2
= 16.
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ID : ae-6-Fractions-Ascending-Descending-Order-Reduce-to-simplest-form [14]
Step 6
T o f ind the lowest term of
1040
, let us divide both the numerator and the
1152
denominator by the HCF:
1040
1152
1040
=
16
1152
16
=
65
.
72
Step 7
T hus the lowest f orm of the f raction
1040
1152
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is
65
.
72
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ID : ae-6-Fractions-Ascending-Descending-Order-Reduce-to-simplest-form [15]
G)
6
19
Step 1
If we divide the numerator and the denominator of
480
by their HCF (Highest
1520
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 1520.
Step 3
All prime f actors of 1520:
2
| 1520
2 is a factor of 1520
2
| 760
2 is a factor of 760
2
| 380
2 is a factor of 380
2
| 190
2 is a factor of 190
5
| 95
5 is a factor of 95
19 | 19
19 is a factor of 19
|1
T hus,
1520 = 2 × 2 × 2 × 2 × 5 × 19.
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 1520 and 480 to f ind the HCF.
T he HCF = 2 × 2 × 2 × 2 × 5
= 80.
Step 6
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ID : ae-6-Fractions-Ascending-Descending-Order-Reduce-to-simplest-form [16]
T o f ind the lowest term of
480
, let us divide both the numerator and the
1520
denominator by the HCF:
480
1520
480
80
=
1520
80
=
6
.
19
Step 7
T hus the lowest f orm of the f raction
480
1520
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is
6
.
19
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ID : ae-6-Fractions-Ascending-Descending-Order-Reduce-to-simplest-form [17]
H)
20
31
Step 1
If we divide the numerator and the denominator of
840
by their HCF (Highest
1302
Common Factor), the resulting f raction will be in the lowest f orm.
Step 2
Let us now f ind the HCF of 840 and 1302.
Step 3
All prime f actors of 1302:
2
| 1302
2 is a factor of 1302
3
| 651
3 is a factor of 651
7
| 217
7 is a factor of 217
31 | 31
31 is a factor of 31
|1
T hus,
1302 = 2 × 3 × 7 × 31.
Step 4
All prime f actors of 840:
2 | 840
2 is a factor of 840
2 | 420
2 is a factor of 420
2 | 210
2 is a factor of 210
3 | 105
3 is a factor of 105
5 | 35
5 is a factor of 35
7 |7
7 is a factor of 7
|1
T hus,
840 = 2 × 2 × 2 × 3 × 5 × 7.
Step 5
Let's multiply all common f actors of 1302 and 840 to f ind the HCF.
T he HCF = 2 × 3 × 7
= 42.
Step 6
T o f ind the lowest term of
840
, let us divide both the numerator and the
1302
denominator by the HCF:
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ID : ae-6-Fractions-Ascending-Descending-Order-Reduce-to-simplest-form [18]
840
1302
840
=
42
1302
42
=
20
.
31
Step 7
T hus the lowest f orm of the f raction
840
1302
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is
20
.
31
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ID : ae-6-Fractions-Ascending-Descending-Order-Reduce-to-simplest-form [19]
I)
55
84
Step 1
If we divide the numerator and the denominator of
825
by their HCF (Highest
1260
Common Factor), the resulting f raction will be in the lowest f orm.
Step 2
Let us now f ind the HCF of 825 and 1260.
Step 3
All prime f actors of 1260:
2 | 1260
2 is a factor of 1260
2 | 630
2 is a factor of 630
3 | 315
3 is a factor of 315
3 | 105
3 is a factor of 105
5 | 35
5 is a factor of 35
7 |7
7 is a factor of 7
|1
T hus,
1260 = 2 × 2 × 3 × 3 × 5 × 7.
Step 4
All prime f actors of 825:
3
| 825
3 is a factor of 825
5
| 275
5 is a factor of 275
5
| 55
5 is a factor of 55
11 | 11
11 is a factor of 11
|1
T hus,
825 = 3 × 5 × 5 × 11.
Step 5
Let's multiply all common f actors of 1260 and 825 to f ind the HCF.
T he HCF = 3 × 5
= 15.
Step 6
T o f ind the lowest term of
825
, let us divide both the numerator and the
1260
denominator by the HCF:
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ID : ae-6-Fractions-Ascending-Descending-Order-Reduce-to-simplest-form [20]
825
1260
825
=
15
1260
15
=
55
.
84
Step 7
T hus the lowest f orm of the f raction
825
1260
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is
55
.
84
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ID : ae-6-Fractions-Ascending-Descending-Order-Reduce-to-simplest-form [21]
J)
59
96
Step 1
If we divide the numerator and the denominator of
944
by their HCF (Highest
1536
Common Factor), the resulting f raction will be in the lowest f orm.
Step 2
Let us now f ind the HCF of 944 and 1536.
Step 3
All prime f actors of 1536:
2 | 1536
2 is a factor of 1536
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,
1536 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3.
Step 4
All prime f actors of 944:
2
| 944
2 is a factor of 944
2
| 472
2 is a factor of 472
2
| 236
2 is a factor of 236
2
| 118
2 is a factor of 118
59 | 59
59 is a factor of 59
|1
T hus,
944 = 2 × 2 × 2 × 2 × 59.
Step 5
Let's multiply all common f actors of 1536 and 944 to f ind the HCF.
T he HCF = 2 × 2 × 2 × 2
= 16.
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ID : ae-6-Fractions-Ascending-Descending-Order-Reduce-to-simplest-form [22]
Step 6
T o f ind the lowest term of
944
, let us divide both the numerator and the
1536
denominator by the HCF:
944
1536
944
=
16
1536
16
=
59
.
96
Step 7
T hus the lowest f orm of the f raction
944
1536
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is
59
.
96
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ID : ae-6-Fractions-Ascending-Descending-Order-Reduce-to-simplest-form [23]
K)
49
86
Step 1
If we divide the numerator and the denominator of
343
by their HCF (Highest
602
Common Factor), the resulting f raction will be in the lowest f orm.
Step 2
Let us now f ind the HCF of 343 and 602.
Step 3
All prime f actors of 602:
2
| 602
2 is a factor of 602
7
| 301
7 is a factor of 301
43 | 43
43 is a factor of 43
|1
T hus,
602 = 2 × 7 × 43.
Step 4
All prime f actors of 343:
7 | 343
7 is a factor of 343
7 | 49
7 is a factor of 49
7 |7
7 is a factor of 7
|1
T hus,
343 = 7 × 7 × 7.
Step 5
Let's multiply all common f actors of 602 and 343 to f ind the HCF.
T he HCF = 7
= 7.
Step 6
T o f ind the lowest term of
343
, let us divide both the numerator and the
602
denominator by the HCF:
343
602
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ID : ae-6-Fractions-Ascending-Descending-Order-Reduce-to-simplest-form [24]
343
=
7
602
7
=
49
.
86
Step 7
T hus the lowest f orm of the f raction
343
602
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is
49
.
86
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ID : ae-6-Fractions-Ascending-Descending-Order-Reduce-to-simplest-form [25]
L)
64
77
Step 1
If we divide the numerator and the denominator of
640
by their HCF (Highest
770
Common Factor), the resulting f raction will be in the lowest f orm.
Step 2
Let us now f ind the HCF of 640 and 770.
Step 3
All prime f actors of 770:
2
| 770
2 is a factor of 770
5
| 385
5 is a factor of 385
7
| 77
7 is a factor of 77
11 | 11
11 is a factor of 11
|1
T hus,
770 = 2 × 5 × 7 × 11.
Step 4
All prime f actors of 640:
2 | 640
2 is a factor of 640
2 | 320
2 is a factor of 320
2 | 160
2 is a factor of 160
2 | 80
2 is a factor of 80
2 | 40
2 is a factor of 40
2 | 20
2 is a factor of 20
2 | 10
2 is a factor of 10
5 |5
5 is a factor of 5
|1
T hus,
640 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 5.
Step 5
Let's multiply all common f actors of 770 and 640 to f ind the HCF.
T he HCF = 2 × 5
= 10.
Step 6
T o f ind the lowest term of
640
, let us divide both the numerator and the
770
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ID : ae-6-Fractions-Ascending-Descending-Order-Reduce-to-simplest-form [26]
denominator by the HCF:
640
770
640
=
10
770
10
=
64
.
77
Step 7
T hus the lowest f orm of the f raction
640
770
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is
64
.
77
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ID : ae-6-Fractions-Ascending-Descending-Order-Reduce-to-simplest-form [27]
M)
41
94
Step 1
If we divide the numerator and the denominator of
205
by their HCF (Highest
470
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 470.
Step 3
All prime f actors of 470:
2
| 470
2 is a factor of 470
5
| 235
5 is a factor of 235
47 | 47
47 is a factor of 47
|1
T hus,
470 = 2 × 5 × 47.
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 470 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
470
denominator by the HCF:
205
470
205
=
5
470
5
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ID : ae-6-Fractions-Ascending-Descending-Order-Reduce-to-simplest-form [28]
=
41
.
94
Step 7
T hus the lowest f orm of the f raction
205
470
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is
41
.
94
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ID : ae-6-Fractions-Ascending-Descending-Order-Reduce-to-simplest-form [29]
N)
50
71
Step 1
If we divide the numerator and the denominator of
400
by their HCF (Highest
568
Common Factor), the resulting f raction will be in the lowest f orm.
Step 2
Let us now f ind the HCF of 400 and 568.
Step 3
All prime f actors of 568:
2
| 568
2 is a factor of 568
2
| 284
2 is a factor of 284
2
| 142
2 is a factor of 142
71 | 71
71 is a factor of 71
|1
T hus,
568 = 2 × 2 × 2 × 71.
Step 4
All prime f actors of 400:
2 | 400
2 is a factor of 400
2 | 200
2 is a factor of 200
2 | 100
2 is a factor of 100
2 | 50
2 is a factor of 50
5 | 25
5 is a factor of 25
5 |5
5 is a factor of 5
|1
T hus,
400 = 2 × 2 × 2 × 2 × 5 × 5.
Step 5
Let's multiply all common f actors of 568 and 400 to f ind the HCF.
T he HCF = 2 × 2 × 2
= 8.
Step 6
T o f ind the lowest term of
400
, let us divide both the numerator and the
568
denominator by the HCF:
(C) 2016 Edugain (www.Edugain.com)
Personal use only, commercial use is strictly prohibited
ID : ae-6-Fractions-Ascending-Descending-Order-Reduce-to-simplest-form [30]
400
568
400
=
8
568
8
=
50
.
71
Step 7
T hus the lowest f orm of the f raction
400
568
(C) 2016 Edugain (www.Edugain.com)
is
50
.
71
Personal use only, commercial use is strictly prohibited
ID : ae-6-Fractions-Ascending-Descending-Order-Reduce-to-simplest-form [31]
O)
41
70
Step 1
If we divide the numerator and the denominator of
246
by their HCF (Highest
420
Common Factor), the resulting f raction will be in the lowest f orm.
Step 2
Let us now f ind the HCF of 246 and 420.
Step 3
All prime f actors of 420:
2 | 420
2 is a factor of 420
2 | 210
2 is a factor of 210
3 | 105
3 is a factor of 105
5 | 35
5 is a factor of 35
7 |7
7 is a factor of 7
|1
T hus,
420 = 2 × 2 × 3 × 5 × 7.
Step 4
All prime f actors of 246:
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,
246 = 2 × 3 × 41.
Step 5
Let's multiply all common f actors of 420 and 246 to f ind the HCF.
T he HCF = 2 × 3
= 6.
Step 6
T o f ind the lowest term of
246
, let us divide both the numerator and the
420
denominator by the HCF:
246
420
(C) 2016 Edugain (www.Edugain.com)
Personal use only, commercial use is strictly prohibited
ID : ae-6-Fractions-Ascending-Descending-Order-Reduce-to-simplest-form [32]
246
=
6
420
6
=
41
.
70
Step 7
T hus the lowest f orm of the f raction
246
420
(C) 2016 Edugain (www.Edugain.com)
is
41
.
70
Personal use only, commercial use is strictly prohibited