Order of Operations with Fractions
Order of Operations with Fractions is a Grade 6 math skill from Big Ideas Math, Course 1, Chapter 2: Fractions and Decimals. Students evaluate multi-step fraction expressions using PEMDAS, converting mixed numbers to improper fractions and applying operations in the correct sequence: parentheses first, then multiplication and division (left to right), then addition and subtraction (left to right). Mastering this skill requires combining two earlier skills — fraction arithmetic and order of operations — and directly prepares students for algebraic expressions in Grade 7.
Key Concepts
When an expression involves multiple operations with fractions, we use the same order of operations (PEMDAS) as we do with whole numbers: 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 evaluate a fraction expression using order of operations?
Apply PEMDAS: Parentheses, Exponents, Multiplication/Division (left to right), Addition/Subtraction (left to right). Convert any mixed numbers to improper fractions first, then work through each operation in the correct order.
What is PEMDAS for fractions?
PEMDAS applies identically to fractions. Handle parentheses first, then perform multiplication and division before addition and subtraction. Example: 3/4 + 1/2 × 2/3 → multiply first: 1/2 × 2/3 = 1/3 → then add: 3/4 + 1/3 = 9/12 + 4/12 = 13/12.
What is a common mistake with order of operations and fractions?
Adding or subtracting before multiplying is the most common error. Also, not finding a common denominator for addition/subtraction, and not simplifying before multiplying (which makes numbers larger than necessary).
How do you add fractions and multiply fractions in the same expression?
If the expression has both operations without parentheses, multiply first. Example: 1/4 + 3/4 × 2/3: multiply 3/4 × 2/3 = 6/12 = 1/2 first, then add 1/4 + 1/2 = 1/4 + 2/4 = 3/4.
When do Grade 6 students practice order of operations with fractions?
This skill is in Big Ideas Math, Course 1, Chapter 2: Fractions and Decimals, extending fraction operations and order of operations to combined multi-step problems in Grade 6.
Why is converting mixed numbers before applying operations important?
Mixed numbers are hard to multiply and divide correctly without converting. For example, 1 1/2 × 2/3: multiply as 3/2 × 2/3 = 6/6 = 1. Trying to multiply 1 1/2 directly leads to errors. Always convert first.