Real numbers: The numbers that can represent physical quantities in a complete manner. All real numbers can be measured and can be represented on a number line. They are of two types: Rational numbers: A number that can be represented in the form p/q where p and q are integers and q is not zero. Example: 2/3, 1/10, 8/3 etc. They can be finite decimal numbers, whole numbers, integers, fractions. Irrational numbers: A number that cannot be represented in the form p/q where p and q are integers and q is not zero. An infinite non recurring decimal is an irrational number. Example: √2, √5 , √7 and Π(pie)=3.1416. The rational numbers are classified into Integers and fractions Integers: The set of numbers on the number line, with the natural numbers, zero and the negative numbers are called integers, I = {…..-3, -2, -1, 0, 1, 2, 3…….}

Fractions:

A fraction denotes part or parts of an integer. For example 1/6, which can represent 1/6th part of the whole, the type of fractions are: 1. Common fractions: The fractions where the denominator is not 10 or a multiple of it. Example: 2/3, 4/5 etc. 2. Decimal fractions: The fractions where the denominator is 10 or a multiple of 10. Example 7/10, 9/100 etc. 3. Proper fractions: The fractions where the numerator is less than the denominator. Example ¾, 2/5 etc. its value is always less than 1. 4. Improper fractions: The fractions where the numerator is greater than or equal to the denominator. Example 4/3, 5/3 etc. Its value is always greater than or equal to 1. 5. Compound fraction: A fraction of a fraction is called a compound fraction

Example 3/5 of 7/9 = 3/5 x 7/9 = 21/45

6. Complex fractions: The combination of fractions is called a complex fraction.

Example (3/5)/ (2/9)

7. Mixed fractions: A fraction which consists of two parts, an integer and a fraction. Example 3 ½, 6 ¾ Example: Express 27/8 as a mixed fraction

Ans. Divide the numerator by denominator; note the multiplier, whatever remainder is left divide it with the original denominator. For 27/8, 24/8 = 3, and remainder left is 3, therefore 3 3/8 is the mixed fraction Example: Express 35 7/17as an improper fraction.

Ans. Here we need to multiply the denominator with the non-fraction part and add it to numerator and using same denominator. For 35 7/17= = 602/17

The integers are classified into negative numbers and whole numbers Negative numbers: All the negative numbers on the number line, {…..-3, -2, -1} Whole numbers: The set of all positive numbers and 0 are called whole numbers, W = {0, 1, 2, 3, 4…….}. Natural numbers: The counting numbers 1, 2, 3, 4, 5……. are known as natural numbers, N = {1, 2, 3, 4, 5…..}. The natural numbers along with zero make the set of the whole numbers.

Even numbers: The numbers divisible by 2 are even numbers. e.g., 2, 4, 6,8,10 etc. Even numbers can be expressed in the form 2n where n is an integer other than 0. Odd numbers: The numbers not divisible by 2 are odd numbers. e.g. 1, 3, 5, 7, 9 etc. Odd numbers are expressible in the form (2n + 1) where n is an integer other than 0. Composite numbers: A composite number has other...