what are three rational numbers between -6/7 and5/7
Answers
Answer:
140
85
and
140
86
are required two rational numbers.
Step-by-step explanation:
\begin{gathered}Given\\\: two \: rational \: < /p > < p > numbers \: \frac{3}{5}\: and \: \frac{5}{7}\end{gathered}
Given
tworational</p><p>numbers
5
3
and
7
5
\begin{gathered}i)\frac{3}{5}\\=\frac{3\times 7}{5\times 7 }\\ = \frac{21}{35}\\=\frac{21\times 4}{35\times 4}\\=\frac{84}{140}--(1)\end{gathered}
i)
5
3
=
5×7
3×7
=
35
21
=
35×4
21×4
=
140
84
−−(1)
\begin{gathered}ii)\frac{5}{7}\\=\frac{5\times 5}{7\times 5 }\\ = \frac{25}{35}\\=\frac{25\times 4}{35\times 4}\\=\frac{100}{140}--(2)\end{gathered}
ii)
7
5
=
7×5
5×5
=
35
25
=
35×4
25×4
=
140
100
−−(2)
Now,
Then the rational numbers between \frac{3}{5} \: and \frac{5}{7}
5
3
and
7
5
\frac{3}{5}=\frac{84}{140} < (\frac{85}{140},\frac{86}{140}) < \frac{100}{140}=\frac{5}{7}
5
3
=
140
84
<(
140
85
,
140
86
)<
140
100
=
7
5
Note :
There exist infinite number of rational numbers between any two given rational number