Order of Operations With Whole Numbers and Grouping Symbols

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Math expressions use grouping symbols like brackets [], braces {} and parentheses (). We now evaluate expressions involving order of operations with whole numbers using such grouping symbols.

Evaluate the following expression

[3 +(15 + 6) ÷ 7] × 4

Solution

Step 1:

We must follow the rule of order of operations PEMDAS.

We start with the innermost grouping, the parentheses (15 + 6)

[3 +(15 + 6) ÷ 7] × 4 =

[3 + 21 ÷ 7] × 4

Step 2:

We next evaluate the remaining grouping, brackets [3 + 21 ÷ 7]

Step 3:

We perform all multiplication and division before any addition or subtraction

[3 + 21 ÷ 7]

[3 + 3]=

6

Step 4:

We then evaluate the last expression

6 × 4 = 24

Step 5:

So [3 +(15 + 6) ÷ 7] × 4 = 24

Evaluate the following expression

[37󠄀 − (12 − 9) × 3] ÷ 7󠄀

Solution

Step 1:

We follow the rule of order of operations PEMDAS.

We start with the innermost grouping, the parentheses (12 − 9)

[37 −(12 − 9) × 3] ÷ 7 =

[37 − 3 × 3] ÷ 7

Step 2:

We next evaluate the remaining grouping, brackets [37 −3 × 3]

Step 3:

We perform all multiplication and division before any addition or subtraction

[37󠄀 − 3 × 3]=

[37󠄀 − 9] =

28

Step 4:

We then evaluate the last expression

28 ÷ 7 = 4

Step 5:

[37󠄀 − (12 − 9) × 3] ÷ 7󠄀 = 4