Important Concepts and Formulas
2. A rational number p/q is said to be
in standard form if q is positive and the integers p and q are co-primes.
3. By multiplying or dividing the numerator
and denominator of a rational number by the same non-zero integer, we can
obtain another rational number equivalent to the given rational number.
4. If both the numerator and the
denominator of a rational number are positive or negative, then it is called a
positive rational number. For example, 4/5, 8/15, -3/-5 are positive rational
numbers.
5. A rational number is called negative,
if one of its numerator or denominator is negative. For example, -4/9, 5/-7,
-11/16 are negative rational numbers.
7. When the denominator of a rational
number has factors 2 or 5 (or both) only, then the decimal representation of
the rational number will be terminating.
8. On a number line, a rational number
is greater than every rational number on its left.
9. To compare two negative rational
numbers, we compare them ignoring their negative signs and then reverse the
order.
10. While adding rational numbers with
same denominators, we add numerators keeping the denominator same.
11. While subtracting a rational number,
we add the additive inverse of the rational number that is being subtracted
from the other rational number.
12. The product of rational number with
its reciprocal is always 1.
13. To divide one rational number by
another non-zero rational number, we multiply the rational number by the
reciprocal of the divisor.
15. The reciprocal of 1 is 1, the
reciprocal of –1 is –1 and zero has no reciprocal.