Home MATHEMATICS TOPIC 8: NUMBERS (II) ~ MATHEMATICS FORM 1

TOPIC 8: NUMBERS (II) ~ MATHEMATICS FORM 1

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NUMBERS

NUMBERS

A Rational Number

Define a rational number

ARational Numberis a real number that can be written as a simple fraction (i.e. as aratio).

Most numbers we use in everyday life are Rational Numbers.

Number As a Fraction Rational?
5 5/1 Yes
1.75 7/4 Yes
.001 1/1000 Yes
-0.1 -1/10 Yes
0.111… 1/9 Yes
√2(square root of 2) ? NO !

The square root of 2 cannot be written as a simple fraction! And there are many more such numbers, and because they arenot rationalthey are calledIrrational.

The Basic Operations on Rational Numbers
Perform the basic operations on rational numbers

To
add two or morerational numbers, the denominator of all the rational
numbers should be the same. If the denominators of all rational numbers
are same, then you can simply add all the numerators and the denominator
value will the same. If all the denominator values are not the same,
then you have to make the denominator value as same, by multiplying the
numerator and denominator value by a common factor.

Example 1

1⁄3+4⁄3=5⁄3

1⁄3 +1⁄5=5⁄15 +3⁄15 =8⁄15

Subtraction of Rational Numbers:

To
subtract two or more rational numbers, the denominator of all the
rational numbers should be the same. If the denominators of all rational
numbers are same, then you can simply subtract the numerators and the
denominator value will the same. If all the denominator values are not
the same, then you have to make the denominator value as same by
multiplying the numerator and denominator value by a common factor.
Example 2
4⁄3 -2⁄3 =2⁄3
1⁄3-1⁄5=5⁄15-3⁄15=2⁄15

Multiplication of Rational Numbers:

Multiplication
of rational numbers is very easy. You should simply multiply all the
numerators and it will be the resulting numerator and multiply all the
denominators and it will be the resulting denominator.
Example 3
4⁄3×2⁄3=8⁄9
Division of Rational Numbers:
Division
of rational numbers requires multiplication of rational numbers. If you
are dividing two rational numbers, then take the reciprocal of the
second rational number and multiply it with the first rational number.

Example 4

4⁄3÷2⁄5=4⁄3×5⁄2=20⁄6=10⁄3

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