
- Ordering Rounding and Order of Operations
- Home
- Introduction to Inequalities
- Comparing a Numerical Expression With a Number
- Ordering Large Numbers
- Rounding to Tens or Hundreds
- Rounding to Hundreds or Thousands
- Rounding to Thousands, Ten Thousand, or Hundred Thousand
- Estimating a Sum of Whole Numbers
- Estimating a Difference of Whole Numbers
- Estimating a Product of Whole Numbers
- Estimating a Quotient of Whole Numbers
- Writing Expressions Using Exponents
- Introduction to Exponents
- Power of 10: Positive Exponent
- Power of 10: Negative Exponent
- Introduction to Parentheses
- Comparing Numerical Expressions With Parentheses
- Introduction to Order of Operations
- Order of Operations With Whole Numbers
- Order of Operations With Whole Numbers and Grouping Symbols
- Order of Operations With Whole Numbers and Exponents: Basic
- Selected Reading
- UPSC IAS Exams Notes
- Developer's Best Practices
- Questions and Answers
- Effective Resume Writing
- HR Interview Questions
- Computer Glossary
- Who is Who
Order of Operations With Whole Numbers and Grouping Symbols
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