Download Rational Numbers

WELCOME
CHAPTER - 2
RATIONAL NUMBERS
REAL NUMBERS
• Numbers that can be found on the
number line.
Two Kinds of Real Numbers
• Rational Numbers
• Irrational Numbers
RATIONAL NUMBERS
• A rational number is a real number that can
be written as a ratio of two integers.
• Each rational number can be written in the
form x/y ,where x and y are integers.
• A rational number written in decimal form
is terminating or repeating.
EXAMPLES OF RATIONAL
NUMBERS
•
•
•
•
•
½
-3.5
-7/6
0.345…
3.14
• If we multiplying the numerator and
denominator of a rational number by
the same integer, we can get
another form of the same rational
number.
In the language of algebra ,
a/b = ax/bx
ADDITION AND
MULTIPLICATION
• 2+2=4
&
2*2= 4
• 3 + 3/2 = 9/2 & 3 * 3/2 = 9/2
Can you find other pairs of numbers
such that the sum and product are
equal?
ADDITION AND
SUBTRACTION
•
•
•
•
Let us find the sum of 2/3 and 1/5
2/3 = 2*5/3*5 = 10/15
1/5 = 1*3/5*3 = 3/15
2/3 + 1/5 = 10/15 + 3/15
=10 + 3 /15
=(2*5 + 1* 3)/3*5
There fore, a/b + p/q = aq + bp / bq
When the sum is one
• There are many pairs of fractions
whose sum is 1 such as
• ½ +½ =1
• ¼+¾ =1
• NOTE : If we take the reciprocals
of the pairs of numbers having sum
and product equal, there sum is one.
• Example : 3 + 3/2 = 9/2 and 3 * 3/2 =
9/2
Reciprocal of 3 = 1/3
Reciprocal of 3/2 = 2/3
Sum of the Reciprocals = 1/3 + 2/3
=1
Note :If we take a pair of numbers
whose sum is one, then the product and
sum of their reciprocals are equal.
Multiplication and Division
• In algebraic method multiplication
and division of functions can be said
as
a/b * p/q = ap / bq
In the case of division
a/b / p/q = aq / bp
Equal Fractions
• To check equality of two fractions ,
it is enough to check whether their
simplified forms are equal.
• Example : consider the fractions
36/48 and 42/56
36/48 = 3/4
42/56 = 3/4
Then 36/48 = 42/56
• If a/b = p/q ,then aq = bp
• If a/b = p/q ,then a/p =b/q
COMPARISON
• If the fractions a/b and p/q are
equal, then
aq = pb
• If two fractions have same
denominator, greater fraction has
greater numerator.
• If aq > pb , then a/b > p/q
• If aq < bp , then a/b < p/q
Decimal Forms
• In the decimal form of any fraction,
the digits after the decimal point
will be terminating or non
terminating.
REFERENCES
• Gilbert, Jimmie; Linda, Gilbert
(2005). Elements of Modern Algebra
(6th ed.). Belmont, CA: Thomson
Brooks/Cole. pp. 243–244. ISBN 0534-40264-X.
• SCERT Text book, Class 5,(2015).