Practice Set 6.1
1) Compare the following fractions.
(i)
8
3
,
5
2
Solution
The LCM of 3 and 2 is 6.
Making the denominators of the given fractions 6.
8
3
=
8 × 2
3 × 2
=
16
6
and
5
2
=
5 × 3
2 × 3
=
15
6
But
16
6
>
15
6
∴
8
3
>
5
2
(ii)
4
9
,
3
7
Solution
The LCM of 9 and 7 is 63.
Making the denominators of the given fractions 63.
4
9
=
4 × 7
9 × 7
=
28
63
and
3
7
=
3 × 9
7 × 9
=
27
63
But
28
63
>
27
63
∴
4
9
>
3
7
(iii)
7
10
,
9
14
Solution
The LCM of 10 and 14 is 70.
Making the denominators of the given fractions 70.
7
10
=
7 × 7
10 × 7
=
49
70
and
9
14
=
9 × 5
14 × 5
=
45
70
But
49
70
>
45
70
∴
7
10
>
9
14
2) Write the following fractions in ascending and descending order.
(i)
11
8
,
2
4
,
7
2
Solution
Finding the LCM of 8, 4, 2.
The LCM of these denominators is 8.
11
8
=
11 × 1
8 × 1
=
11
8
2
4
=
2 × 2
4 × 2
=
4
8
7
2
=
7 × 4
2 × 4
=
28
8
Ascending order :
4
8
,
11
8
,
28
8
Descending order :
28
8
,
11
8
,
4
8
∴ Ascending order :
2
4
,
11
8
,
7
2
∴ Descending order : 7 2 , 11 8 , 2 4
∴ Descending order : 7 2 , 11 8 , 2 4
(ii)
16
9
,
5
3
,
7
4
Solution
Finding the LCM of 9, 3, 4.
The LCM of these denominators is 36.
16
9
=
16 × 4
9 × 4
=
64
36
5
3
=
5 × 12
3 × 12
=
60
36
7
4
=
7 × 9
4 × 9
=
63
36
Ascending order :
60
36
,
63
36
,
64
36
Descending order :
64
36
,
63
36
,
60
36
∴ Ascending order :
5
3
,
7
4
,
16
9
∴ Descending order : 16 9 , 7 4 , 5 3
∴ Descending order : 16 9 , 7 4 , 5 3
3) Solve.
(i)
7
10
+
3
10
Solution
7
10
+
3
10
=
7 + 3
10
=
10
10
= 1
∴ The answer is 1.
(ii)
3
4
+
2
6
Solution
The LCM of 4 and 6 is 12.
Making the denominators of both fractions 12.
3 × 3
4 × 3
+
2 × 2
6 × 2
=
9
12
+
4
12
=
9 + 4
12
=
13
12
∴ The answer is
13
12
.
(iii)
1
3
+
7
5
Solution
The LCM of 3 and 5 is 15.
Making the denominators of both fractions 15.
1 × 5
3 × 5
+
7 × 3
5 × 3
=
5
15
+
21
15
=
5 + 21
15
=
26
15
∴ The answer is
26
15
.
(iv)
3
10
+
4
5
Solution
The LCM of 10 and 5 is 10.
Making the denominators of both fractions 10.
3
10
+
4 × 2
5 × 2
=
3
10
+
8
10
=
3 + 8
10
=
11
10
∴ The answer is
11
10
.
(v)
5
3
−
2
3
Solution
5
3
−
2
3
=
5 − 2
3
=
3
3
= 1
∴ The answer is 1.
(vi)
3
5
−
3
7
Solution
The LCM of 5 and 7 is 35.
Making the denominators of both fractions 35.
3 × 7
5 × 7
−
3 × 5
7 × 5
=
21
35
−
15
35
=
21 − 15
35
=
6
35
∴ The answer is
6
35
.
4) A house is built on
2
5
part of a plot and a garden is made on the remaining part.
What part of the plot is made for the garden?
Solution
House is built in
2
5
part of the plot and garden in the remaining part of the plot.
Part of the garden =
1
−
2
5
i.e., Part of the garden =
1
1
−
2
5
LCM of 1 and 5 is 5.
i.e., Part of the garden =
1 × 5
1 × 5
−
2
5
=
5
5
−
2
5
=
5 − 2
5
=
3
5
Ans.
3
5
part of the plot is made for the garden.