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Lesson 1-3: Fraction & Decimal Operations

Scenario: Baking & Measurements - Learn to scale recipes and solve complex measurement problems!

Duration: 60-75 minutesScenario: Baking & Measurements

Learning Objectives

  • Perform mixed operations with fractions and decimals
  • Scale recipes and measurements using multiplication
  • Convert between fractions and decimals in calculations
  • Apply operations to solve real-world measurement problems

Recipe Scaling Scenario

The Problem

A recipe calls for 3/4 cup of sugar. You want to make 1½ times the original amount. How much sugar do you need?

Calculation: 3/4 × 1½ = 3/4 × 3/2 = 9/8 = 1⅛ cups

You need 1⅛ cups of sugar for the scaled recipe.

Step-by-Step Solution

Step 1: Convert mixed number to improper fraction

1½ = 1 + ½ = 2/2 + 1/2 = 3/2

Step 2: Multiply fractions

3/4 × 3/2 = (3×3)/(4×2) = 9/8

Step 3: Convert to mixed number

9/8 = 8/8 + 1/8 = 1 + 1/8 = 1⅛

Decimal Mixed Operations

Complex Calculation

Calculate: 2.5 + (-3.8) × 2

Solution: 2.5 + (-3.8) × 2 = 2.5 - 7.6 = -5.1

Remember: Multiplication before addition (order of operations)

Step-by-Step Process

Step 1: Perform multiplication first

(-3.8) × 2 = -7.6

Step 2: Add the result to 2.5

2.5 + (-7.6) = 2.5 - 7.6 = -5.1

Real-World Application

Elevation Problem

A diver is at -20.5 meters depth. They rise 15.8 meters, then descend 7.3 meters. What is their final depth?

Calculation: -20.5 + 15.8 - 7.3 = -12.0 meters

The diver ends up 12 meters below sea level.

Calculation Steps

Step 1: Start at -20.5 meters

Step 2: Rise 15.8 meters: -20.5 + 15.8 = -4.7 meters

Step 3: Descend 7.3 meters: -4.7 - 7.3 = -12.0 meters

Practice Problems

Problem 1: Recipe Scaling

A recipe needs 2/3 cup of flour. You want to make 2¼ times the recipe. How much flour do you need?

Your solution:

2/3 × 2¼ = 2/3 × 9/4 =
Simplified:

Problem 2: Mixed Operations

Calculate: 1.5 - 2.3 × 0.5 + 1.2

Your solution:

Step 1: 2.3 × 0.5 =
Step 2: 1.5 - 1.15 + 1.2 =

Problem 3: Real-World Application

A construction worker needs to cut a 12.75-foot board into 3 equal pieces. Each piece will be 0.5 inches shorter than the calculated length due to saw blade width. What is the final length of each piece?

Your calculation: