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Back to Unit 2

Lesson 2-2: Fraction-Decimal Operations

Scenario: Running Competition - Compare performance times using fractions and decimals!

Duration: 55-70 minutesScenario: Running Competition

Learning Objectives

  • Convert between fractions and decimals fluently
  • Perform mixed operations with fractions and decimals
  • Compare and order mixed numbers and decimals
  • Solve real-world problems involving mixed operations

Running Competition Scenario

Race Time Comparison

In a 1-kilometer race, Xiao Ming finished in 5.2 minutes, and Xiao Hong finished in 5¼ minutes. Who ran faster, and by how much?

Problem: Compare 5.2 minutes vs 5¼ minutes

Step-by-Step Solution

Step 1: Convert mixed number to decimal

5¼ = 5 + ¼ = 5 + 0.25 = 5.25 minutes

Step 2: Compare the times

Xiao Ming: 5.2 minutes
Xiao Hong: 5.25 minutes
Since 5.2 < 5.25, Xiao Ming ran faster

Step 3: Calculate the difference

5.25 - 5.2 = 0.05 minutes = 3 seconds

Answer: Xiao Ming ran faster by 0.05 minutes (3 seconds).

Fraction-Decimal Conversion Methods

Common Conversions

Fraction to Decimal

¼ = 0.25

½ = 0.5

¾ = 0.75

⅓ = 0.333...

⅔ = 0.666...

Decimal to Fraction

0.25 = ¼

0.5 = ½

0.75 = ¾

0.2 = ⅕

0.4 = ⅖

Mixed Operations Examples

Example 1: Addition

3.5 + ½ = ?

Solution: 3.5 + 0.5 = 4.0

Example 2: Subtraction

2¾ - 1.2 = ?

Solution: 2.75 - 1.2 = 1.55

Example 3: Multiplication

0.75 × ⅔ = ?

Solution: 0.75 × ⅔ = ¾ × ⅔ = 6/12 = ½ = 0.5

Shopping Application

Apple Purchase

You buy 1.5 kilograms of apples at $3½ per kilogram. How much do you pay in total?

Solution: 1.5 kg × $3.5/kg = $5.25

Convert 3½ to 3.5, then multiply: 1.5 × 3.5 = 5.25

Practice Problems

Problem 1

Compare: 4.8 vs 4⅗. Which is larger?

Your solution:

Problem 2

Calculate: 2.4 + 1⅓ - 0.8

Your solution: