find the rational number between A and b if:. (b)- a=1/8, b= 7/
Answers
Answer:
The rational number between \frac{1}{8}
8
1
and \frac{7}{12}
12
7
are \frac{4}{24},\frac{5}{24},\frac{6}{24},\frac{7}{24},\frac{8}{24},\frac{9}{24},\frac{10}{24},\frac{11}{24},\frac{12}{24},\frac{13}{24}
24
4
,
24
5
,
24
6
,
24
7
,
24
8
,
24
9
,
24
10
,
24
11
,
24
12
,
24
13
Step-by-step explanation:
Given : a=\frac{1}{8}, b=\frac{7}{12}a=
8
1
,b=
12
7
To find : The rational number between a and b ?
Solution :
The rational number between \frac{1}{8}
8
1
and \frac{7}{12}
12
7
Make the denominator same,
\frac{1}{8}=\frac{1\times 3}{8\times 3}=\frac{3}{24}
8
1
=
8×3
1×3
=
24
3
\frac{7}{12}=\frac{7\times 2}{12\times 2}=\frac{14}{24}
12
7
=
12×2
7×2
=
24
14
The rational number between \frac{3}{24}
24
3
and \frac{14}{24}
24
14
are \frac{4}{24},\frac{5}{24},\frac{6}{24},\frac{7}{24},\frac{8}{24},\frac{9}{24},\frac{10}{24},\frac{11}{24},\frac{12}{24},\frac{13}{24}
24
4
,
24
5
,
24
6
,
24
7
,
24
8
,
24
9
,
24
10
,
24
11
,
24
12
,
24
13
Answer:
a=1/5 and b = 1/4 or we may write
a = 8/40 and b = 10/40
So one rational between a and b will be 9/40.
We may introduce more rational be changing the denominator, suitably.
a = 12/60 and b = 15/60. Here we can have 13/60 and 14/60 as the two rational numbers which may be written as 13/60 and 7/30.
a = 16/80 and b = 20/80. Here we can have 17/80, 18/80, and 19/80 as the three rational numbers which may be written as 17/80, 9/40, and 19/80.
We may continue further, but the principle is the same.