Which is the greater of the following pairs of ratio?
(a)2/3,3/2
(b)3:5,1:2
(c)7:10,11:15
(d)4:2,4^2:7^2
(e)1/2:1/3,1/4:1/9
(f )5/18,13/48
Explain with step by step.please
Answers
(iii) 4 : 7 or 5 : 8
(iv) 9 : 20 or 8 : 13
(v) 1 : 2 or 13 : 27
ANSWER:
(i) Writing the ratios as fractions, we have
3 : 4 =
3
4
and 9 : 16 =
9
16
Now, LCM of 4 and 16 = 16.
Making the denominator of each fraction = 16, we have
3
4
=
3 × 4
4 × 4
=
12
16
and the other fraction =
9
16
Of
12
16
and
9
16
, clearly
12
16
>
9
16
.
Therefore,
3
4
>
9
16
.
(ii) Writing the ratios as fractions, we have
15 : 16 =
15
16
and 24 : 25 =
24
25
Now, LCM of 16 and 25 = 400.
Making the denominator of each fraction = 400, we have
15
16
=
15 × 25
16 × 25
=
375
400
and the other fraction =
24 × 16
25 × 16
=
384
400
Clearly, 384 > 375. So,
384
400
>
375
400
.
Therefore,
24
25
>
15
16
.
(iii) Writing the ratios as fractions, we have
4 : 7 =
4
7
and 5 : 8 =
5
8
Now, LCM of 7 and 8 = 56.
Making the denominator of each fraction = 56, we have
4× 8
7 × 8
=
32
56
and the other fraction =
5 × 7
8 × 7
=
35
56
Clearly, 36 > 32. So,
35
56
>
32
56
.
Therefore,
5
8
>
4
7
.
(iv) Writing the ratios as fractions, we have
9 : 20 =
9
20
and 8 : 13 =
8
13
Now, LCM of 20 and 13 = 260.
Making the denominator of each fraction = 260, we have
9× 13
20 × 13
=
117
260
and the other fraction =
8 × 20
13 × 20
=
160
260
Clearly, 160 > 117. So,
160
260
>
117
260
.
Therefore,
8
13
>
9
20
.
(v) Writing the ratios as fractions, we have
1 : 2 =
1
2
and 13 : 27 =
13
27
Now, LCM of 2 and 27 = 54.
Making the denominator of each fraction = 54, we have
1× 27
2 × 27
=
27
54
and the other fraction =
13 × 2
27 × 2
=
26
54
Clearly, 27 > 26. So,
27
54
>
26
54
.
Therefore,
1
2
>
13
27
.