Page 65 - ICSE Math 7

AT A GLANCE

p
¾ A number that can be expressed in the form , where p and q are integers and q ≠ 0 is called a
q
rational number.
¾ All fractions and integers are rational numbers but the converse is not true.
p
¾ A rational number is positive if both a and b are positive or both are negative. If a and b have
q
p
different signs then is negative. 0 is a rational number which is neither positive nor negative.
q
p p pn
¾ For any rational number and a non-zero number n we have, = .
q q qn
p
r
¾ Equality of rational numbers: = iff p × s = r × q.
q
s
p
¾ A rational number is in standard form if p, q are co-prime and q is a positive integer.
q
p r
¾ Addition of rational numbers: If and are to be added we add their numerators keeping the
q q
p r p + r
denominator same, i.e., + = . In case the denominators are different, we find equivalent
q q q
rational numbers with denominator equal to their LCM and add as above.
¾ Subtraction of rational numbers: To subtract two rational numbers, we add the additive inverse
of a rational number that is to be subtracted.
¾ Multiplication of rational numbers: To multiply two rational numbers, we multiply the numerators
and denominators separately.
¾ Reciprocal of a rational number is same as its multiplicative inverse, i.e., reciprocal of
p q
p
q is provided p ≠ 0, q ≠ 0.
¾ Division of a rational number: To divide one rational number by another non-zero rational number,
we multiply the rational number with the reciprocal of the other.
¾ Decimals are of two types—terminating and non-terminating decimals. Non-terminating decimals
are further of two types—non-terminating recurring (or repeating) and non-terminating non-
recurring decimals.
¾ Every rational number is either terminating or non-terminating repeating decimal number. Every
irrational number is non-terminating, non-repeating decimal number.

MENTAL MATHS

1. Choose the correct answer.
0
(a) The expression which best describes the rational number is ___________.
3
(i) 0 (ii) 1 (ii) 3 (iv) undefined

24
(b) The rational number , when reduced to standard form is ___________.
–18
12 4 –4 –24
(i) (ii) (iii) (iv)
–9 3 3 18

51