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\ 06-Jan-2025 Bharat Arora Proof-7 Reader’s Sign _______________________ Date __________

1. Express the following numbers in the form of p , where p and q are integers and q ≠ 0.
q

(a) 7 (b) 0 (c) –3 (d) 14

2. Fill in the boxes.
3 6 9 30 36 9
(a) = (b) = (c) = (d) =
4 3 27 105 35 31

3. Represent the following rational numbers on the number line.

(a) 3 (b) −7 (c) 2 (d) 11
5 10 7 5
4. Solve the following.
3 1 −3 3 5 2 3 −4 3
(a) + (b) + − (c) × (d) ÷
4 4 24 8 48 15 10 7 14

Rational Numbers

In class VII, we learnt about rational numbers and Rational numbers
5
2
basic mathematical operations involving them. In this 1.2, 3.59, ..., 2 ,− 15 , ...
chapter, we will review what we have learnt about the Integers
rational numbers earlier and explore the properties of ..., –3, –2, –1
operations on rational numbers. Whole numbers
0
p
A number which can be expressed in the form of , Natural numbers
q 1, 2, 3, 4, 5, ..., 100, ...
where p and q are integers and q ≠ 0 is called a rational

number.
3 − 4
For example, , , 9, 0, and 1.2 are all rational numbers. These numbers can be expressed in the
5 7

p 3 − 4 9 0 12
form of as , , , and .
q 5 7 1 1 10

Facts about Rational Numbers:

• All natural numbers are rational numbers but all rational numbers need not be natural numbers.
• All integers are rational numbers but all rational numbers need not be integers.

0 0
• 0 is a rational number as it can be written as , , etc.
1 2
• All fractions are rational numbers but all rational numbers need not be fractions.

• A rational number is positive if its numerator and denominator are either both positive or
both negative. It is negative if its numerator and denominator have different signs, i.e., one is
positive and the other negative.

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