Lesson 101: Word Problems with Fractions, Decimals & Percents

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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 focuses on solving word problems that involve fractions, decimals, and percents. Students will learn when to convert between forms and how to apply proportional reasoning in real-world contexts such as discounts, taxes, interest, and measurement.

Learning Objectives

• Convert between fractions, decimals, and percents fluently.
• Apply percent calculations to real-world financial situations.
• Solve multi-step problems involving rational numbers.

Topics Covered

• Percent increase and decrease
• Discounts, tax, and tips
• Fraction and decimal operations in context
• Choosing the most efficient numerical form

Key Terms

• Percent: A ratio out of 100.
• Discount: A reduction in the original price.
• Proportion: An equation stating that two ratios are equal.

Lesson Examples

Example 1: Store Discount

A jacket costs $80 and is on sale for 25% off. What is the sale price?

1. Convert percent to decimal: 25% = 0.25
2. Find discount: 80 × 0.25 = 20
3. Subtract discount: 80 − 20 = 60
4. Final Answer: The sale price is $60.

Example 2: Recipe Adjustment

A recipe calls for 3/4 cup of sugar. You want to make half the recipe. How much sugar is needed?

1. Multiply by 1/2: 3/4 × 1/2
2. Multiply numerators and denominators: 3/8
3. Final Answer: 3/8 cup of sugar is needed.

Practice Problems

1. A $120 item is discounted by 15%. What is the new price?
2. You score 18 out of 24 on a test. What percent did you earn?
3. A bill of $45 has 8% sales tax. What is the total amount paid?
4. A tank is 3/5 full. If it holds 50 gallons, how many gallons are in the tank?

Tips & Common Mistakes

• Always convert percents to decimals before multiplying.
• Watch for whether the problem asks for the discount amount or final price.
• Keep fractions simplified when possible.

Summary

Word problems involving fractions, decimals, and percents require flexibility in converting between forms. Choosing the correct representation simplifies calculations and improves accuracy in real-world applications.

Challenge Problems

1. A $250 phone is discounted 20%, then taxed 8%. What is the final price?
2. A savings account earns 3% annual interest on $1,200. How much interest is earned in one year?
3. A 5-mile run is completed in 0.75 hours. What is the average speed in miles per hour?