CAT Operations on Natural Numbers, Whole Numbers, Integers, Rational Numbers, and Complex Numbers - Practice Questions & MCQ

Operations on Natural Numbers

Addition: To add two or more natural numbers, we simply add them together. For example, 2 + 3 = 5.

Subtraction: To subtract one natural number from another, we subtract the smaller number from the larger. For example, 7 - 4 = 3.

Multiplication: To multiply two or more natural numbers, we simply multiply them together. For example, 4 * 5 = 20.

Division: To divide one natural number by another, we find how many times the divisor can fit into the dividend. For example, 12 ÷ 3 = 4.

Operations on Whole Numbers

• Addition: Similar to natural numbers, we add two or more whole numbers by adding them together.
• Subtraction: We can subtract one whole number from another by subtracting the smaller number from the larger.
• Multiplication: Similar to natural numbers, we multiply two or more whole numbers together.
• Division: We can divide one whole number by another by finding how many times the divisor can fit into the dividend.

Operations on Integers

Addition: When adding two or more integers, we consider their signs. The rules for adding integers are:

• If the signs are the same (positive or negative), we add their absolute values and keep the same sign.
• If the signs are different, we subtract the absolute value of the smaller number from the absolute value of the larger number and use the sign of the larger number.

Subtraction: Subtraction of integers follows similar rules as addition.

Multiplication: The rules for multiplying integers are:

• If the signs are the same, the product is positive.
• If the signs are different, the product is negative.

Division: The rules for dividing integers include:

• If the signs are the same, the quotient is positive.
• If the signs are different, the quotient is negative.

Operations on Rational Numbers

• Addition and Subtraction: To add or subtract rational numbers, we must have the same denominator. Once we have the same denominator, we can add or subtract the numerators and keep the common denominator.
• Multiplication: When multiplying rational numbers, we multiply the numerators together and the denominators together.
• Division: Dividing rational numbers is similar to multiplying, except we multiply the first number by the reciprocal of the second number.

Operations on Complex Numbers

• Addition and Subtraction: To add or subtract complex numbers, we add or subtract their real parts separately and their imaginary parts separately.
• Multiplication: When multiplying complex numbers, we use the distributive property and combine like terms.
• Division: To divide complex numbers, we multiply both the numerator and denominator by the conjugate of the denominator, and simplify the result.

Tips and Tricks: 

- For natural and whole numbers, practise mental calculations to improve speed.
- Understand the rules for adding, subtracting, multiplying, and dividing integers and rational numbers thoroughly.
- Memorise the rules for operations on complex numbers and practice solving examples to become proficient.
- Work on previous year management entrance exam questions related to these operations to get familiar with the type of questions asked.

EXAMPLE: 

Q. What is the value of (3/4) + (-7/8)? 

Solution: To add these rational numbers, we need the same denominators. 

Step 1: Find the least common multiple (LCM) of 4 and 8, which is 8.
Step 2: Rewrite the fractions with the common denominator: 

(3/4) + (-7/8) = (3/4) * (2/2) + (-7/8) * (1/1) = 6/8 + (-7/8) 

Step 3: Add the numerators together and keep the common denominator: 

6/8 + (-7/8) = (6 - 7)/8 = -1/8 So, (3/4) + (-7/8) = -1/8.