List five rational numbers between
(0)
1
1
and
2 3
(ii)
1
and
2
Answers
(i) –1 and 0 (ii) –2 and –1 (iii)-\frac{4}{5}\ and\ -\frac{2}{3}−
5
4
and −
3
2
(iv) -\frac{1}{2}\ and\ \frac{2}{3}−
2
1
and
3
2
Solution 1:
(i) Let's, write, rational no with denominator 6
-\frac{6}{6}<\ -\frac{5}{6}<-\frac{4}{6}<-\frac{3}{6}<-\frac{2}{6}<-\frac{1}{6}<0\ −
6
6
< −
6
5
<−
6
4
<−
6
3
<−
6
2
<−
6
1
<0
-\frac{5}{6},-\frac{4}{6},-\frac{3}{6},-\frac{2}{6},-\frac{1}{6}−
6
5
,−
6
4
,−
6
3
,−
6
2
,−
6
1
(ii) Lets write, rational no with denominator 6
-2=-\frac{12}{6}−
6
12
, -1=-\frac{6}{6\ }−
6
6
-\frac{12}{6}<-\frac{11}{6}<-\frac{10}{6}<-\frac{9}{6}<-\frac{8}{6}<-\frac{7}{6}<-\frac{6}{6}−
6
12
<−
6
11
<−
6
10
<−
6
9
<−
6
8
<−
6
7
<−
6
6
=-\frac{11}{6},-\frac{5}{6},-\frac{3}{2},-\frac{4}{2},-\frac{7}{6}=−
6
11
,−
6
5
,−
2
3
,−
2
4
,−
6
7
(iii)Let us write rational number with same denominator
-\frac{4}{5},\ -\frac{2}{3}−
5
4
, −
3
2
LCM of the two rational no 3 and 5 = 45
-\frac{36}{45},\ -\frac{30}{45}−
45
36
, −
45
30
-\frac{36}{45}<\ -\frac{35}{45}<-\frac{34}{45}<-\frac{33}{45}<-\frac{32}{45}<-\frac{31}{45}<-\frac{30}{45}−
45
36
< −
45
35
<−
45
34
<−
45
33
<−
45
32
<−
45
31
<−
45
30
therefore, five rational no
-\frac{7}{9},\ -\frac{34}{45},\ -\frac{11}{15},-\frac{32}{45},\ -\frac{31}{45},\ -\frac{2}{3}−
9
7
, −
45
34
, −
15
11
,−
45
32
, −
45
31
, −
3
2
(iv) Let the denominator of rational no be same
-\frac{1}{2}\times3\ =\ -\frac{3}{2}\ \ ,\ \ \ \frac{2}{3}\times2\ =\ \frac{4}{6}−
2
1
×3 = −
2
3
,
3
2
×2 =
6
-\frac{1}{2}\times3\ =\ -\frac{3}{2}\ \ ,\ \ \ \frac{2}{3}\times2\ =\ \frac{4}{6}− 4
therefore, -\frac{3}{6}<-\frac{2}{6}<-\frac{1}{6}<0<\frac{1}{6}<\frac{2}{6}<\frac{3}{6}<\frac{2}{3}<\frac{4}{6}−
6
3
<−
6
2
<−
6
1
<0<
6
1
<
6
2
<
6
3
<
3
2
<
6
4
therefore, five rational no between -\frac{1}{2}\ and\ \frac{2}{3}−
2
1
and
3
2
will be
-\frac{1}{3},\ -\frac{1}{6},\ 0,\ \frac{1}{6},\ \frac{1}{3}−
3
1
, −
6
1
, 0,
6
1
,
1