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Rational numbers Lo: To represent rational numbers on the number line.. 

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Rational numbers Lo:   To represent rational numbers on the number line.

is said to be in standard form if q is a positive integer and p and q have no
A rational number
q
common factor other than 1.

RATIONAL NUMBERS L, where p and q are Rational numbers are those numbers which can be expressed in the form integers and q 0. 1 2 -912 16-5 Examples: — a. b. c. Positive rational numbers are the numbers in which both the numerator and the denominator are 1 —3 4 either positive or negative, for example, —, — and 4 —11 Negative rational numbers are the numbers in which either the numerator is positive and the denominator is negative or the numerator is negative and the denominator is positive, for example, 4 —, — and — A rational number is said to be in standard form if q is a positive integer and p and q have no common factor other than 1.. 

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RATIONAL NUMBERS
L, where p and q are
Rational numbers are those numbers which can be expressed in the form
integers and q 0.
1 2 -912 16-5
Examples: —
a.
b.
c.
Positive rational numbers are the numbers in which both the numerator and the denominator are
1
—3
4
either positive or negative, for example, —, — and
4 —11
Negative rational numbers are the numbers in which either the numerator is positive and the
denominator is negative or the numerator is negative and the denominator is positive, for example,
4
—, — and —
A rational number is said to be in standard form if q is a positive integer and p and q have no
common factor other than 1.

Rational numbers between two rational numbers. Lo: To find rational numbers between any two rational numbers.. 

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Rational numbers between two rational numbers

Lo: To find rational numbers between any two rational numbers.

Finding Rational Numbers Between any Two Rational Numbers Converting rational numbers into fractions with same denominator If the numerators are consecutive numbers, then multiply the numerator and the denominator of both the rational numbers by (n + 1) to get n rational numbers between them. To get more rational numbers, multiply by 10, 100, 1000 and so on.  
 Converting rational numbers into decimals Conversion to decimal numbers is the simplest way of finding rational numbers between rational numbers.

using *he concep+ of midpoint
Recall that the midpoint between any two numbers a and b is
2

Operations on Rational Numbers. LO: To add and subtract rational numbers To multiply and divide rational number. 

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LO: To add and subtract rational numbers  To multiply and divide rational number

OPERATIONS ON RATIONAL NUMBERS Addition of rational numbers a. To add rational numbers with same denominators, add their numerators by keeping the denominator same and writing the answer in the simplest form b.  To add rational numbers with different denominators, find the LCM of the denominators and write each rational number with the LCM as the common denominator. Add the rational numbers and simplify. Subtraction of rational numbers To subtract two rational numbers, add the additive inverse of the rational number that is to be subtracted to the other rational number. Multiplication of rational numbers Product of two rational numbers = Product of their numerators /Product of their denominators Division of rational numbers To divide a rational number by another rational number, multiply the first rational number by the reciprocal of the other.

Properties of Rational Numbers Lo: To analyse and apply closure property, commutative property and associative property on rational numbers .. 

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Properties of Rational Numbers Lo: To analyse and apply closure property, commutative property and associative property on rational numbers .

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In general, if — is any rational number, then —— is its additive inverse and is a rational number, that is,. 

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In general, if — is any rational number, then —— is its additive inverse and is a rational number, that is,

In general, the reciprocal or the multiplicative inverse ofa number
— is given by — and is denoted by
that is,

Distributive property Lo: To apply distributive properties over addition and subtraction for rational numbers. 

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Distributive property  Lo: To apply distributive properties over addition and subtraction for rational numbers

Distributive Property of Multiplication over Addition Multiplication of rational numbers is distributive over addition, that is, if a, b and c are any three non-zero rational numbers, then a × (b + c) = (a × b) + (a × c). 
 Distributive Property of Multiplication Over Subtraction Multiplication of rational numbers is distributive over subtraction, that is, if a, b and c are any three non-zero rational numbers, then a × (b – c) = (a × b) – (a × c).

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