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5. Compare and put >, < or = in the given .

1 3 2 − 3 −4 9 −2 −9
(a) (b) (c) (d)
3 9 7 4 9 4 3 27
6. Arrange the following rational numbers in ascending order.

1 1 3 − 7 2 1 − 4 − 7
(a) ,, , (b) ,, ,
3 4 5 11 5 7 5 11
7. Arrange the following rational numbers in descending order.
1 3 − 3 − 9 2 1 − 4 7
(a) 1 ,, , (b) 1 , 1 , ,
3 4 5 11 5 7 5 11

1 1
8. Find five rational numbers between and .
8 3
9. Find three rational numbers between 1.2 and 1.3.
1 1
10. Write ten rational numbers between − and − .
7 7
Addition of Rational Numbers

We can perform all four fundamental operations on rational numbers as with integers and
fractions. The addition of rational numbers follows the same process as for fractions.

Example 6: Evaluate the following:

(a) −5 + 3 (b) 7 + 4 (c) 6 + 4 (d) 5 + 3
8 8 9 18 11 5 21 14

−5 3
Solution: (a) + ; since the denominator is the same, we simply add the numerators and keep
8 8
the denominator as it is.

−5 3 −+53 −2 −1 Note: Always express the result in its
So, + = = = .
8 8 8 8 4 standard form.

(b) 7 + 4 ; here, the denominator of second rational number is multiple of the first, so
9 18
we use the larger denominator as the common denominator and write the rational
number equivalent to the smaller one having the common denominator, then add
the numerators.

7 4 72 4 14 4 18
×
So, + = + = + = = 1
9 18 92 18 18 18 18
×
(c) 6 + 4 ; here, the denominators are co-prime, so product of the denominators will
11 5
be the common denominator. Write the rational numbers equivalent to the given
rational numbers with the same denominator and add them.
+
×
6 4 65 411 30 44 30 44 74 1 19 .
×
×
11 + 5 = 11 5 + 511 = 55 + 55 = 55 = 55 = 55
×
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