Application: Order of Operations with Decimals
Application: Order of Operations with Decimals is a Grade 6 math skill from Big Ideas Math, Course 1, Chapter 2. Students apply PEMDAS/BODMAS to evaluate expressions that include decimal multiplication. The key rule: perform multiplication before addition or subtraction unless parentheses override the order. Example: 4.5 + 2 × 1.1 = 4.5 + 2.2 = 6.7 (multiply first, then add). Parentheses change this: (9.3 - 5.3) × 0.5 = 4 × 0.5 = 2.0 (subtract first because of parentheses). The rules are identical to whole number order of operations.
Key Concepts
To evaluate expressions with multiple operations, follow the order of operations (PEMDAS/BODMAS): 1. P arentheses 2. E xponents 3. M ultiplication and D ivision (from left to right) 4. A ddition and S ubtraction (from left to right).
Common Questions
What is the order of operations?
PEMDAS: Parentheses first, then Exponents, then Multiplication and Division (left to right), then Addition and Subtraction (left to right). In the UK this is called BODMAS: Brackets, Orders, Division/Multiplication, Addition/Subtraction.
How do you apply order of operations with decimals?
The rules are identical to whole numbers. In 4.5 + 2 × 1.1, multiply first: 2 × 1.1 = 2.2, then add: 4.5 + 2.2 = 6.7. Parentheses override: (9.3 - 5.3) × 0.5 = 4 × 0.5 = 2.0 (subtract inside parentheses first).
Why do you multiply before you add?
Order of operations is a universal convention that ensures everyone gets the same answer to a multi-step expression. Without this agreement, 4.5 + 2 × 1.1 could equal 6.7 or 7.15 depending on order — PEMDAS establishes the correct answer is 6.7.
What do parentheses do in an expression?
Parentheses indicate that the operation inside must be performed first, overriding the usual order. (9.3 - 5.3) × 0.5: the parentheses force the subtraction first, giving 4 × 0.5 = 2.0 instead of 9.3 - (5.3 × 0.5) = 6.65.
When do Grade 6 students practice order of operations with decimals?
This is covered in Big Ideas Math, Course 1, Chapter 2: Fractions and Decimals, as a Grade 6 skill extending order of operations to decimal contexts.
What is a common mistake with order of operations?
The most common mistake is adding or subtracting before multiplying or dividing. Remember: multiplication and division always happen before addition and subtraction unless parentheses tell you otherwise.