Page 56 - ICSE Math 7

• Zero is a rational number.
0 0 0 0 0 0 0 0
,
,
,
,
,
We can write 0 in any one of the forms +1 –1 +2 –2 +3 –3 +4 –4 and so on. Thus, 0 can
,
,
p
be expressed as where p = 0 and q is any non-zero integer (q ≠ 0). Hence 0 is a rational
q
number.
• Every fraction is a rational number but a rational number need not be a fraction.
p
In a fraction , p is a whole number and q is a natural number since every whole number and
q
p
natural number is an integer, therefore, p and q are integers. Thus, the fraction is the quotient
q
p 4
of two integers such that q ≠ 0. Hence, is a rational number. But, a rational number like is
q –9
not a fraction since its denominator –9 is not a natural number.
Positive rational numbers
A rational number is said to be positive if its numerator and denominator Maths Info
7 8 –2
are either both positive or both negative. For example, , , and Zero is neither a positive nor a
–11 are positive rational numbers. 12 19 –5 negative rational number.
–23
Negative rational numbers
A rational number is said to be negative if its numerator and denominator have opposite signs.

,
For example, –63 4 and –7 are negative rational numbers.
71 –9 29
Absolute value of a rational number Try This
We know that the absolute value of an integer is always positive. Write the absolute value of the
Similarly, the absolute value of a rational number is positive. It is following rational numbers.
6
obtained by dividing the absolute value of numerator with the absolute (a) (b) 0 (c) –3
7
5
5 5 –3 3 –4 –2
value of the denominator. For example, = , = (d) (e) 3 (f)
6 6 4 4 9 7
Equivalent rational numbers
p p × n
Let (q ≠ 0) be a rational number and n be a non-zero integer, then is a rational number
q q × n
p
equivalent to . In other words, a rational number remains same if we multiply the numerator and
q
6
2
denominator by the same non-zero integer n. For example, = 2 × 3 =
2 6 3 3 × 3 9
Here and are equivalent rational numbers.
3 9 Try This
Just as multiplication, the division of the numerator and denominator
Fill in the boxes.
by the same non-zero integer, also gives equivalent rational numbers. 7 12 

For example, 14 = 14 ÷ 7 = 2 (a) 12 =   = 32 3
35 ÷ 7
35
5
–4
14 2 (b) 7 = =
14

Here, and are equivalent rational numbers.
35 5
Test of equality of two rational numbers
p r
Two rational numbers and are equal iff p × s = r × q.
q s
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