ch-1rationalnumbers-201017103609.pdf
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Rational numbers include all integers as well as numbers that can be expressed as fractions p/q where p and q are integers and q is not equal to 0. Rational numbers are closed under addition, subtraction, and multiplication but not division. They have identities and inverses. Rational numbers can be represented on a number line and there are an infinite number of rational numbers between any two given rational numbers, found using methods like the equivalent fractions method or mean method.
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ch-1rationalnumbers-201017103609.pdf
- 2. INTRODUCTION A number expressed in the form of where both are integers and q is not equal to 0. Every integer is a rational numbers. They are also represented with an mimic symbol like fractions. If are multiplied with a non-zero integer like:- = = }The rational number is equivalent to
- 3. PROPERTIES OF RATIONAL NUMBERS PROPERTIES RATIONAL NUMBERS INTEGERS WHOLE NUMBERS OPERATION + - 歎 + - 歎 + - 歎 CLOSURE YES YES YES NO YES YES YES NO YES YES YES NO COMMUTATIVE YES NO YES NO YES NO YES NO YES NO YES NO ASSOCIATIVE YES NO YES NO YES NO YES NO YES NO YES NO DISTRIBUTIVE YES D YES D YES D YES D YES D YES D
- 4. IDENTITY ELEMENT/INVERSE PROPERTY The identity element property says that:- Additive identity:- 1 Multiplicative identity:- 1 Multiplicative property:- 0 Inverse element:- Additive inverse:- The operations of the number changes from positive to negative or from negative to positive. Multiplicative inverse:- Also called Reciprocal of a number. The numerator becomes denominator and the denominator becomes numerator.
- 5. REPRESENTATION OF RATIONAL NUMBER ON A NUMBER LINE When a number is represented according to its position on a line, is called representation on number line. The points on the number line are systemic and should be equally distributed. They should be named with capital letters or numbers. For example. Express on a number line. 0 1
- 6. NUMBERS BETWEEN TWO NUMBERS There can be many numbers between two numbers. These numbers are called projectors. Each number is called projections. For example. Find two numbers between 1 and 2. Hence, and are the numbers between 1 and 2
- 7. RATIONAL NUMBERS BETWEEN TWO RATIONAL NUMBERS There are two ways through which we can find numbers between the two. Equivalent Rational method. Mean Rational method.
- 8. MEAN/FORMULA METHOD OF FINDING RATION NUMBERS Let a and b be any two given rational numbers. We can find many rational numbers q1, q2, q3,...in between a and b as follows : The numbers q2, q3 lie to the left of q1. Similarly, q4, q5 are the rational numbers between a and b lie to the right of q1 as follows:
- 9. EQUIVALENT RATIONAL METHOD Let a and b be two rational numbers. i. Convert the denominator of both the fractions into the same denominator by taking LCM. Now, if there is a number between numerators there is a rational number between them. ii. If there is no number between their numerators, then multiply their numerators and denominators by 10 to get rational numbers between them. To get more rational numbers, multiply by 100, 1000 and so on.
- 11. EXERCISE TIME
- 12. PROVE: LHS = RHS