ORDER OF OPERATIONS

Order of Operations is a set of rules that dictate the sequence in which mathematical operations should be performed to avoid ambiguity and ensure that the correct result is obtained. The order of operations is usually abbreviated as PEMDAS, which stands for:

Parentheses: Perform operations inside parentheses first.

Exponents: Perform any operations involving exponents or roots.

Multiplication and Division: Perform multiplication and division, working from left to right.

Addition and Subtraction: Perform addition and subtraction, working from left to right.

Here's an example of how the order of operations works using PEMDAS:

Example 1:

6 + 3 * 2² - 8 ÷ 4

= 6 + 3 * 4 - 2

= 6 + 12 - 2

= 16

First, we perform the exponent operation (2² = 4). Then, we perform the multiplication operation (3 * 4 = 12) and the division operation (8 ÷ 4 = 2). Next, we perform the subtraction operation (3 * 4 - 2 = 10). Finally, we perform the addition operation (6 + 10 = 16).

Example 2:

4 + 5 * 3² ÷ 6 - 2

• Step 1: Parentheses ( )

        There are no parentheses in this expression, so we skip this step.

• Step 2: Exponents ^

        The expression contains an exponent, so we perform this operation next:

            4 + 5 * 9 ÷ 6 - 2

           3² means 3 raised to the power of 2, which equals 9.

• Step 3: Multiplication and Division * ÷

        The next step is to perform any multiplication or division operations, working from left to

        right. In this case, we have a multiplication and a division operation, so we perform them

        in the order that they appear from left to right:

            4 + 45 ÷ 6 - 2

            5 times 9 equals 45. 3² was already evaluated in the previous step.

        Dividing 45 by 6 gives 7.5.

• Step 4: Addition and Subtraction + -

        The final step is to perform any addition or subtraction operations, working from left to

        right:

        4 + 7.5 - 2

        Adding 4 and 7.5 gives 11.5.

        Subtracting 2 from 11.5 gives the final answer: 9.5

        Therefore, the expression 4 + 5 * 3² ÷ 6 - 2 evaluates to 9.5, following the order of

        operations (PEMDAS).

Example 3:

(12 + 3) * 2 - 8 ÷ 4

• Step 1: Parentheses ( )

        We start by performing the operations inside parentheses first. In this case,

        we have (12 + 3), which equals 15.

                15 * 2 - 8 ÷ 4

• Step 2: Exponents ^

        There are no exponents in this expression, so we move on to the next step.

• Step 3: Multiplication and Division * ÷

        Next, we perform multiplication and division from left to right. In this case, we have

        division, which we perform first:

                15 * 2 - 2

        We divide 8 by 4, which gives 2.

• Step 4: Addition and Subtraction + -

        Finally, we perform addition and subtraction from left to right: 30 - 2

        Multiplying 15 by 2 gives 30.

        The final result is 28.

        Therefore, the expression (12 + 3) * 2 - 8 ÷ 4 evaluates to 28, following the order of

        operations (PEMDAS).