HOLIDAY HOMEWORKOF

MATHEMATCSBY-MUSKAAN MALHOTRA

7-G

DISCOVERING

RATIONAL

NUMBERS….

INDEX

INTRODUCTION History of Rational Numbers . Rules of mathematical operations on Rational

numbers . Uses and Applications . Bibliography and Acknowledgement .

INTRODUCTION

All numbers including whole numbers ,integers ,fractions and decimal numbers can be written in numerator – denominator form.

A rational number is a number that can be written in the form p/q , where p and q are integers and q is not equal to 0 .

Eg- 2/5, -2 /5 . The denominator can never be 0 in rational

numbers.

Positive rational numberRational number is positive if its numerator and denominator are both either positive integers or negative integers. Eg : 2/5 , 3/4 , 1/5 , -8/-5. Negative rational numberIf either the numerator or the denominator of a rational number is a negative integer ,then the rational number is called a negative rational number. Standard formA rational number is said to be in its standard form if its numerator and denominator have no common factor other than 1,and its denominator is a positive integer .

HISTORY

The history of rational numbers goes way back to the beginning of historical times . It is believed that knowledge of rational numbers precedes history but no evidence of this survives today the earliest evidence is in the ancient Egyptian document the kahuna papyrus . Ancient Greeks also worked on rational numbers as a part of their number theory . Euclid elements dates to around 300 BC .

OPERATION ON RATIONAL NUMBERS

Rational numbers provide the first number system in which all the operations of airthematic , addition , subtraction , multiplication and division are possible . Operation with rational numbers , multiplication “ makes number bigger” and division “makes the number smaller ’’. The arithmetical operations are reduced to operations between 2 real numbers with rational numbers

ADDITION – It is the first operation . This operation uses only one sign[+] .

Subtraction – It is the second operation . The operation uses only one sign [-] .

Multiplication – It is often described as a sort of short hand for addition . This operation uses sign [*]

DIVISION- It is last and important operation .The operation uses sign [ /] .

Adding Rational Numbers with CommonDenominators

To add rational numbers that have a common denominator, we add the numerators, but we do not add the denominators

ADDING RATIONAL NUMBERS WITH DIFFERENTDENOMINATORS

To add rational numbers with different denominators, first we equalize the denominators by enlarging each rational number by the lowest common denominator (LCD). Then we add the numerators.

SUBTRACTING RATIONAL NUMBERS WITH COMMON DENOMINATORS

Subtraction is the inverse operation of addition. To subtract rational numbers that have a common denominator, we subtract the numerator, but we do not subtract the denominators.

SUBTRACTING RATIONAL NUMBERS WITH DIFFERENT DENOMINATORS

To subtract rational numbers with different denominators, first equalize the denominators and then subtract the numerators.

MULTIPLYING RATIONAL NUMBERS

Multiplying Two Rational Numbers To multiply two rational numbers, we multiply the

numerators to get the new numerator and multiply the denominators to get the new denominator

For example:

DIVISION IN RATIONAL NUMBERS

APPLICATION AND USESRational Numbers are important! They are used in the real world EVERYDAY!

Even though we are not thinking about if the number is rational or not, we still use them in our everyday lives. At school or in the kitchen. We even see them on T.V!

EXAMPLES:

1)Baking: Ingredients in recipes are often listed as fractions to show the measurements. For example, a 1/2 cup of flour going into a batch of cookie dough. 1/2 is a rational number.

2)Commercials: Many commercials use rational numbers as statistics to get you to buy their products. For example, 4/5 dentists approve this toothpaste, or 9/10 women like this lipstick best.

3)Medical Field: Medical journals use statistics to inform people about the risks of certain things. Such as 1/5 deaths in America are related to smoking or 1/4 Americans are overweight.

BIBLIOGRAPHY

http://en.wikipedia.org/wiki/Rational_number

http://www.themathpage.com/aPrecalc/rational-irrational-numbers.htm

http://www.mathsisfun.com/rational-numbers.html.

http://www.themathpage.com/Arith/multiply-fractions-divide-fractions.htm

ACKNOWLEDGEMENT

› I take this opportunity to express my profound gratitude and deep regards to my guide mr.abrar ahmed for his exemplary guidance, monitoring and constant encouragement throughout the course of this project. The blessing, help and guidance given by him time to time shall carry me a long way in the journey of life on which I am about to embark.