Rational Numbers
Question 1.
Represent these numbers on the number line.
(i)
(ii)
Solution:
(i) For , we make 7 markings of distance each on the right of zero and starting from 0. The seven marking is
.
The point P represents the rational number —.
(ii) For , we make 5 markings of distance
each on the left of zero and starting from 0. The fifth marking
The point P represents the 6 rational number
.
Question 2.
Represent on the number line.
Solution:
To represent on a number line, draw a number line and mark a point O on it to represent zero. Now, mark a point P representing integers -1 on the left side of O on the number line.
Divide the segment OP into eleven equal parts. Let A, B, C, D, E, F, G, H, I, J be the points of division so that OA=AB =BC = … = JP. By construction, OB is two-eleventh of OP so B represents OE is five-eleventh of OP so E represents
and OI is nine-eleventh of OP so I represents
.
Question 3.
Write five rational numbers, which are smaller than 2.
Solution:
Five rational numbers less than 2 may be taken
(There can be many more such rational numbers.)
Question 4.
Find ten rational numbers between and
.
Solution:
Converting the given rational numbers with the same denominators
Question 5.
Find five rational numbers between
Solution:
(i) Converting the given rational numbers with the same denominators
(ii) Converting the given rational numbers with the same denominators
(iii) Converting the given rational numbers with the same denominators
Question 6.
Write five rational numbers greater than – 2.
Solution:
Five rational numbers greater than -2 may be taken as
There can be many more such rational numbers.
Question 7.
Find ten rational numbers between and
.
Solution:
Converting the given rational numbers with the same denominators