# PROPERTIES OF OPERATION ON RATIONAL NUMBERS

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### PROPERTIES OF OPERATION ON RATIONAL NUMBERS:

PROPERTIES OF OPERATION ON RATIONAL NUMBERS

### Slide 2:

Natural numbers = The counting numbers are called natural numbers. E.g. 1,2,3,4,5……………… Whole numbers = All natural numbers together with 0. E.g. 0,1,2,3,4,5,6,…………… Integers = All natural numbers, 0 and negative of counting numbers are called integers. E.g. -1,-2,-3,-4,-5,0,1,2,3,4,5………………… Fractions = The numbers in the form of where a and b are not whole numbers and b is not equal to 0. E.g. 2/3, 3/8,11/5………………… a b Let us recall something-

### Define Rational Numbers:

Define Rational Numbers The number of the form , , where p and q are integers and q is not equal to 0, are called rational numbers. P q

### Examples of Rational Numbers:

Examples of Rational Numbers 16 1/2 3.56 -8 1.3333… - 3/4

### Rational Numbers :

Rational Numbers A rational number is a real number that can be written as a ratio of two integers. A rational number written in decimal form is terminating or repeating.

Addition of rational numbers With same denominators In order to add the rational numbers with same denominators we follow the following steps Step 1 Obtain the numerators of two given rational numbers and their common denominator. Step 2 Add the numerators obtained in step 1 Step 3 Write the rational no. whose numerator is the sum obtained in step 2 and whose denominator is the common denominator of given rational numbers. p r p+r q q q

### Slide 7:

Add and We have See an Example 5 9 -13 9 5 9 + -13 9 = 5 + (-13) 9 -8 9 = [5+(-13)=(8)]

### Slide 8:

With different denominators Step 1 See whether the denominators are positive or not. If the denominator of one or two are negative rewrite it so that it becomes positive. Step 2 Obtain the denominators of rational of the rational numbers in then Step 1 Step 3 Find the LCM of denominators obtained in Step 2. Step 4 Express each one of rational number in step 1 so that LCM obtained in the step 3 become their common denominator. Step 5 Write a rational number whose numerator s equal to the sum of numerators of rational numbers obtained n step 4 and denominators as the LCM obtained in the step 3. Step 6 The rational number obtained in the step 5 is the required sum. Addition of rational numbers

### See an Example:

See an Example Add and 5 12 3 8 5 2 10 3 3 3 9 12 12 2 24 8 8 3 24 = = = = and, 5 3 10 9 10+9 19 12 8 24 24 24 24 + + = = =

### Subtraction of rational numbers:

Subtraction of rational numbers If and are two rational numbers, then subtracting from means adding additive inverse (negative) of to . The subtraction of from is written as - .thus, we have a b c d a b c d c d a b a b c d c d a b a b c d - = [ ] - +

### See an Example:

See an Example Subtract from The additive inverse of is 3 4 5 6 3 4 3 4 5 3 5 (-3) 6 4 6 4 - = - 5 3 5 2 (-3) 3 10 (-9) 10+(-9) 1 6 4 6 2 4 3 12 12 12 12 - = = = = + +

### Multiplication of Rational Numbers:

Multiplication of Rational Numbers The product of two rational numbers is defined below Product of two rational numbers = Thus we have, Product of their numerators Product of their denominators a c (a c) b d (b d) =

### See an example :

See an example 5 7 (2 5) 10 (3 7) 21 =

### Reciprocal of a number :

Reciprocal of a number If the product of two rational numbers is 1 then each one is called the reciprocal of the other. Thus, the reciprocal of is and we write = . a b a b b a b a [ ] - 1

### See some example :

See some example Find the reciprocal of 13 7 7 13 = 1. 2. -8 9 9 -8 = 3. -6 1 -6 = 4. 5 12 12 5 =

### Division of rational numbers:

Division of rational numbers If and are two rational numbers such that is not equal to 0, then we define: a b c d c d a c a d b d b c =

### See an example:

See an example 2 15 3 3 15 2 = = = 3 15 2 5 1 7 10

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