Class 7 Chapter 4: Rational Numbers

# Class 7 Chapter 4: Rational Numbers

Important Concepts and Formulas

1.      A number of the form p/q , where p, q Z and q 0, is called a rational number.

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.

6.      Every rational number can be represented in decimal form.

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.

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15. The reciprocal of 1 is 1, the reciprocal of –1 is –1 and zero has no reciprocal.