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Back to Unit 2

Lesson 2-1: Mixed Number Operations

Scenario: Carpentry Work - Calculate precise measurements with mixed numbers!

Duration: 50-65 minutesScenario: Carpentry Work

Learning Objectives

  • Convert mixed numbers to improper fractions
  • Perform operations with mixed numbers step by step
  • Apply order of operations with parentheses
  • Solve real-world measurement problems

Carpentry Measurement Problem

Wood Cutting Scenario

A carpenter has a piece of wood that is 5½ meters long. They cut off 1¾ meters, then cut off another 2 meters. How much wood is left?

Problem: 5½ - 1¾ - 2 = ?

Step-by-Step Solution

Step 1: Convert mixed numbers to improper fractions

5½: 5 + ½ = 10/2 + 1/2 = 11/2

1¾: 1 + ¾ = 4/4 + 3/4 = 7/4

2: 2/1 = 8/4 (to match denominators)

Step 2: Find common denominator

LCD of 2 and 4 is 4
11/2 = 22/4
So: 22/4 - 7/4 - 8/4

Step 3: Perform subtraction

22/4 - 7/4 - 8/4 = (22 - 7 - 8)/4 = 7/4

Step 4: Convert back to mixed number

7/4 = 1¾ meters

Answer: 1¾ meters of wood is left.

Operations with Parentheses

Order of Operations

Remember: Parentheses first, then multiplication/division, then addition/subtraction.

Example: (¾ + ½) × ⅔ = ?

Step 1: Parentheses first: ¾ + ½

¾ + ½ = ¾ + 2/4 = 5/4

Step 2: Multiply: 5/4 × ⅔

5/4 × ⅔ = (5×2)/(4×3) = 10/12 = 5/6

Practice Problems

Problem 1

A carpenter needs 3⅔ meters of wood. They already have 1¼ meters. How much more do they need?

Your solution:

Problem 2

Calculate: (2⅓ + 1½) × ⅔

Your solution: