3. Four basic operations on Rational numbers

   The numbers of the form p/q, where p and q are integers and q ≠0 are called rational numbers.

Note :
    •    All natural numbers, whole numbers, integers and fractions are rational numbers.
    •    A fraction is a rational number, but a rational number may or may not be a fraction.
    •    Zero is also a rational number.
    •    Every natural number is a rational number but a rational number need not be a natural number.

EQUIVALENT RATIONAL NUMBERS
    Two rational numbers are said to be equivalent if their standard forms are same.

Four basic operations on Rational numbers

Addition of rational numbers

add all the numerators and write the common denominator. For example, add 1/8 and 3/8. Let us understand this with the help of a number line.

• On the number line, we start from 1/8.
• We will take 3 jumps toward the right as we are adding 3/8 to it. As a result, we reach point 4/8. 1/8 + 3/8 = (1 + 3)/8 = 4/8 =1/2
• Thus, 1/8 + 3/8 = 1/2.

Division of rational numbers

whole number division that the dividend is divided by the divisor. Dividend÷Divisor=Dividend/Divisor. While dividing any two numbers, we have to see how many parts of the divisor are there in the dividend.

• Step 1: Take the reciprocal of the divisor (the second rational number). 2x/9 = 9/2x
• Step 2: Multiply it to the dividend. −4x/3 × 9/2x
• Step 3: The product of these two numbers will be the solution. (−4x × 9) / (3 × 2x) = −6

Multiplication of Rational Numbers

To multiply any two rational numbers, we have to follow three simple steps. Let's multiply the following rational numbers: −2/3×(−4/5). The steps to find the solution are:

• Step 1: Multiply the numerators. (−2)×(−4)=8
• Step 2: Multiply the denominators. (3)×(5)=15
• Step 3: Reduce the resulting number to its lowest term. Since it's already in its lowest term, we can leave it as is. (−23)×(−45) = (−2)×(−4)/ (3)×(5) = 8/15

Subtraction of rational numbers

While subtracting two rational numbers on a number line, we move toward the left. Let us understand this method using an example. Subtract 1/2x−1/3x

• Step 1: Find the LCM of the denominators. LCM (2, 3) = 6.
• Step 2: Convert the numbers into their equivalents with 6 as the common denominator. 1/2x × 3/3 = 3/6x = 1/3x × 2/2 = 2/6x
• Step 3: Subtract the numbers you obtained in step 2.