3. INTRODUCTION
History of Rational Numbers .
Rules of mathematical operations on Rational
numbers .
Uses and Applications .
Bibliography and Acknowledgement .
4. 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.
5. Positive rational number
Rational 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 number
If 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 form
A 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 .
6. 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 .
7. 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
[ /] .
8. To add rational numbers that have a common
denominator, we add the numerators, but we do
not add the denominators
9. 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.
10. 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.
11. To subtract rational numbers with different
denominators, first equalize the denominators and
then subtract the numerators.
12. 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:
13.
14. Rational 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.
16. › 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.
