Lesson 91: PEMDAS with Fractions and Decimals

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• Lesson Description
• Learning Objectives
• Topics Covered
• Key Terms
• Lesson Examples
• Practice Problems
• Tips & Common Mistakes
• Summary
• Challenge Problems
• Unit Navigation

Lesson Description

This lesson demonstrates how to solve order-of-operations problems that include fractions and decimals. Students will practice converting, combining, and calculating values accurately while following PEMDAS.

Learning Objectives

• Apply PEMDAS rules to problems containing fractions and decimals.
• Convert fractions to decimals and vice versa to simplify calculations.
• Combine fractions and decimals correctly in multi-step operations.

Topics Covered

• PEMDAS applied to fractions
• PEMDAS applied to decimals
• Mixed fraction and decimal calculations

Key Terms

• Fraction: A number expressed as a ratio of two integers (numerator/denominator).
• Decimal: A number expressed in base-10 notation, using a decimal point.
• PEMDAS: The order of operations—Parentheses, Exponents, Multiplication/Division, Addition/Subtraction.

Lesson Examples

Example 1: Fraction Addition and Subtraction

1. Problem: 1/2 + 3/4 − 1/3
2. Step 1: Find a common denominator (12): 6/12 + 9/12 − 4/12
3. Step 2: Combine numerators: 6 + 9 − 4 = 11
4. Step 3: Result = 11/12

Example 2: Multiplying Decimals

1. Problem: 0.6 × 0.5
2. Step 1: Multiply as whole numbers ignoring decimals: 6 × 5 = 30
3. Step 2: Count decimal places: 0.6 has 1, 0.5 has 1 → total 2 decimal places
4. Step 3: Place decimal: 30 → 0.30 = 0.3

Example 3: Mixed Fractions and Decimals with PEMDAS

1. Problem: (1/2 + 0.25) × 0.4
2. Step 1: Add inside parentheses: 1/2 + 0.25 = 0.5 + 0.25 = 0.75
3. Step 2: Multiply by 0.4: 0.75 × 0.4 = 0.3

Practice Problems

1. 2/3 + 0.5
2. (3/4 − 1/2) × 0.6
3. 0.8 ÷ 0.2 + 1/5
4. (1.5 + 2/3) × 0.4

Tips & Common Mistakes

• Always follow PEMDAS even when fractions and decimals are mixed.
• Convert fractions to decimals if it makes multiplication/division easier.
• Check decimal places carefully when multiplying or dividing decimals.

Summary

PEMDAS is essential for accurate calculation with fractions and decimals. Converting between forms, careful arithmetic, and correct application of parentheses ensures reliable results in multi-step problems.

Challenge Problems

1. (2/5 + 0.3) × 0.6
2. 0.75 ÷ (3/4) + 0.2
3. (1/2 + 0.25)² − 0.1