Order of Operations with Mixed Numbers
Order of Operations with Mixed Numbers is a Grade 6 math skill from Big Ideas Math, Course 1, Chapter 2: Fractions and Decimals. Students apply PEMDAS to evaluate multi-step expressions involving mixed numbers by first converting all mixed numbers to improper fractions, then following the standard order: parentheses, exponents, multiplication/division (left to right), addition/subtraction (left to right). Example: 4 1/2 + 3 1/5 ÷ 1 3/5 = 9/2 + 16/5 ÷ 8/5 = 9/2 + 2 = 9/2 + 4/2 = 13/2 = 6 1/2. Converting first prevents errors from working with mixed numbers in multi-step expressions.
Key Concepts
When evaluating expressions with multiple operations, follow the order of operations (PEMDAS). Before calculating, convert all mixed numbers to improper fractions.
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
How do you apply order of operations with mixed numbers?
First convert all mixed numbers to improper fractions. Then apply PEMDAS: parentheses first, then exponents, then multiplication and division left to right, then addition and subtraction left to right. Never try to operate on mixed numbers without converting first.
Why do you convert mixed numbers to improper fractions first?
Mixed numbers are harder to multiply and divide directly. Converting to improper fractions first makes all operations straightforward and avoids confusion about which part of the mixed number to operate on.
What is a worked example of order of operations with mixed numbers?
Evaluate 4 1/2 + 3 1/5 ÷ 1 3/5: Convert: 9/2 + 16/5 ÷ 8/5. Division first: 16/5 ÷ 8/5 = 16/5 × 5/8 = 2. Then add: 9/2 + 2 = 9/2 + 4/2 = 13/2 = 6 1/2.
What happens if you add before dividing in an expression?
Adding before dividing (ignoring PEMDAS) gives wrong answers. In 9/2 + 16/5 ÷ 8/5: doing addition first gives (9/2 + 16/5) ÷ 8/5 = (45/10 + 32/10) ÷ 8/5 = 77/10 × 5/8 = 385/80, which is wrong. Division must come first.
When do Grade 6 students learn this skill?
This is covered in Big Ideas Math, Course 1, Chapter 2: Fractions and Decimals, extending PEMDAS to expressions involving mixed number fractions as part of Grade 6 rational number operations.
What is the hardest part of order of operations with mixed numbers?
Two things trip students up: forgetting to convert mixed numbers to improper fractions first, and not applying the correct order (dividing before adding). Always write the conversion step explicitly before proceeding.