Home MATHEMATICS TOPIC 8: NUMBERS II MATHEMATICS FORM 1

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NUMBERS II MATHEMATICS FORM 1

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.

NUMBERS II MATHEMATICS FORM 1

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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