Integres ratinoal numbers
3/2 -23/2
Answers
Answer:
Step-by-step explanation:
In Maths, arithmetic operations are the basic operations we perform on integers. Let us discuss here how we can perform these operations on rational numbers, say p/q and s/t.
Addition: When we add p/q and s/t, we need to make the denominator the same. Hence, we get (pt+qs)/qt.
Example: 1/2 + 3/4 = (2+3)/4 = 5/4
Subtraction: Similarly, if we subtract p/q and s/t, then also, we need to make the denominator same, first, and then do the subtraction.
Example: 1/2 – 3/4 = (2-3)/4 = -1/4
Multiplication: In case of multiplication, while multiplying two rational numbers, the numerator and denominators of the rational numbers are multiplied, respectively. If p/q is multiplied by s/t, then we get (p×s)/(q×t).
Example: 1/2 × 3/4 = (1×3)/(2×4) = 3/8
Division: If p/q is divided by s/t, then it is represented as:
(p/q)÷(s/t) = pt/qs
Example: 1/2 ÷ 3/4 = (1×4)/(2×3) = 4/6 = 2/3
How to Find the Rational Numbers between Two Rational Numbers?
There are “n” numbers of rational numbers between two rational numbers. The rational numbers between two rational numbers can be found easily using two different methods. Now, let us have a look at the two different methods.
Method 1:
Find out the equivalent fraction for the given rational numbers and find out the rational numbers in between them. Those numbers should be the required rational numbers.
Method 2:
Find out the mean value for the two given rational numbers. The mean value should be the required rational number. In order to find more rational numbers, repeat the same process with the old and the newly obtained rational numbers.
Solved Examples
Example 1:
Identify each of the following as irrational or rational: ¾ , 90/12007, 12 and √5.
Solution:
Since a rational number is the one that can be expressed as a ratio. This indicates that it can be expressed as a fraction wherein both denominator and numerator are whole numbers.
¾ is a rational number as it can be expressed as a fraction. 3/4 = 0.75
Fraction 90/12007 is rational.
12, also be written as 12/1. Again a rational number.
Value of √5 = 2.2360679775…….. It is a non-terminating value and hence cannot be written as a fraction. It is an irrational number.
Example 2:
Identify whether mixed fraction, 11/2 is a rational number.
Solution:
The Simplest form of 11/2 is 3/2
Numerator = 3, which is an integer
Denominator = 2, is an integer and not equal to zero.
So, yes, 3/2 is a rational number.
Example 3:
Determine whether the given numbers are rational or irrational.
(a) 1.75 (b) 0.01 (c) 0.5 (d) 0.09 (d) √3
Solution:
The given numbers are in decimal format. To find whether the given number is decimal or not, we have to convert it into the fraction form (i.e., p/q)
If the denominator of the fraction is not equal to zero, then the number is rational, or else, it is irrational.