Basic Arithmetic Operations

Basic Understandings

• The result of addition is a sum or total.
• The result of subtraction in a difference.
• The result of multiplication is a product.
• The result of division is a quotient.
• In the expression 52, the 2 is called an exponent.

Exponents

Many numbers are the product of the same factor multiplied over and over again. For example, 32 = 2 × 2 × 2 × 2 × 2. Another way to write this would be 32 = 25, or “thirty-two equals two to the fifth power.” The little number, or exponent, denotes the number of times that 2 is to be used as a factor. In the same way, 103 = 10 × 10 × 10, or 1,000, or “ten to the third power,” or “ten cubed.” In this example, the 10 is called the base and the 3 is called the exponent. (You won’t need to know these terms on the GAT, but you will need to know them to follow my explanations).

Multiplication

When you multiply two numbers with the same base, you simply add the exponents.

Example:

2³ × 2⁵ = 2³⁺⁵ = 2⁸

Division

When you divide two numbers with the same base, you simply subtract the exponents. For example, $\genfrac{}{}{1px}{}{\mathrm{2⁵}}{\mathrm{2³}}$ = 2^{5 - 3} = 2² = 4

Multiplication First

6(53) + 6(47) = 318 +282 = 600 You get the same answer each way, so why get involved with ugly arithmetic? If you use the distributive law, you don’t even need to use you calculator.

Raising a Power to a Power

When you raise a power to a power, you multiply the exponents. For example, (2³)⁴ = 2^{3 × 4} = 2¹²

Finding Square Root

Finding Square root is the reverse process of finding square of a quantity.

You should not be worried about finding the square roots without calculator, as you are not required to go up to fractions, rather the calculation remains in square root partially.