Math for 8th graders

Here we are going to discuss about the topic rational number. We will study about the rational numbers in detail in 8th Grade Math.

We define the set of rational numbers as the numbers which we can write in the form of p / q, where p and q are any integers, such that q <> 0. Further exploring the definition of rational numbers we say that any number which can be either written in the form of terminating decimal number or a repeating decimal number, then we say that the given fraction number is a rational number. All the natural numbers, whole numbers, positive or negative integers and the fraction numbers are the part of the family of rational numbers.

Let us look at the properties of the rational numbers. They are as follows :

1. Closure Property: If we have a pair of rational numbers, then we say that the sum, product, difference and the quotient of the given two rational numbers is also a rational number. Thus we say it mathematically as follows : If p1/ q1, p2 /q2 are any two rational numbers, then we have

P1/ q1 + p2 / q2,

P1/ q1 - p2 / q2 ,

P1/ q1 * p2 / q2 .

P1/ q1 divided by p2 / q2 are also the rational numbers.

2. Associative property of rational numbers also holds true for the addition and multiplication, but not for the operation of division and subtraction. So we have

( P1/ q1 + p2 / q2 ) + p3 / q3 = P1/ q1 + (p2 / q2 + p3 / q3) ,

( P1/ q1 * p2 / q2 ) * p3 / q3 = P1/ q1 * (p2 / q2 * p3 / q3) .

Also we have the commutative property, Additive identity, Multiplicative identity, Additive and multiplicative inverse property which holds true for the rational numbers.

Questions based on Osmosis and Diffusion can be seen in the cbse latest sample papers.