MathIsimple

Lesson 1-5: Mixed Fraction Operations

Apply all fraction operations in complex real-world scenarios with multi-step problems!

Learning Scenario: Community Service

Scenario: Your school is organizing a community service project. Volunteers are packing care packages for families in need. Each package needs 3/2 kilograms of rice. If you have 15 kilograms of rice total, how many complete packages can you make? If each package goes to 2 families, how many families will receive help?

What We Need to Find:

  • • Number of complete packages
  • • Number of families helped
  • • Total rice: 15 kg
  • • Rice per package: 3/2 kg
  • • Families per package: 2

Operations We'll Use:

  • • Division: 15 ÷ 3/2
  • • Multiplication: packages × 2
  • • Multi-step problem solving
  • • Real-world verification

Step 1: Calculate Number of Packages

Division Problem

We need to find how many complete packages of 3/2 kg we can make from 15 kg of rice:

15 ÷ 3/2 = ?

Using Reciprocal Method:

  • • 15 ÷ 3/2 = 15 × 2/3
  • • 15 × 2/3 = (15×2)/3
  • • = 30/3 = 10

Verification:

  • • 10 packages × 3/2 kg = 30/2 kg
  • • = 15 kg ✓

Answer to Step 1

15 ÷ 3/2 = 10 complete packages

We can make exactly 10 complete packages

Great! We can make 10 complete packages with no rice left over.

Step 2: Calculate Number of Families

Multiplication Problem

Now we need to find how many families will receive help. Since each package goes to 2 families:

10 packages × 2 families/package = ?

Calculation:

  • • 10 × 2 = 20 families
  • • This is a simple whole number multiplication

Verification:

  • • 20 families ÷ 2 families/package = 10 packages ✓

Answer to Step 2

10 packages × 2 = 20 families

20 families will receive help

Excellent! 20 families will receive care packages.

Combined Solution

Multi-Step Approach

We can also solve this as one combined expression:

15 ÷ 3/2 × 2 = ?

(Number of packages) × (Families per package)

= 15 × 2/3 × 2

(Convert division to multiplication)

= (15 × 2 × 2)/3

(Multiply numerators and denominators)

= 60/3 = 20

(Simplify)

Extension Problem

Additional Challenge

Extension: If each family needs 1/4 kg of rice per week, how many weeks will the rice in one package last for a family?

(3/2 kg per package ÷ 2 families) ÷ 1/4 kg per week = ?

Rice per family ÷ Weekly consumption

= (3/2 ÷ 2) ÷ 1/4

(Rice per family)

= 3/4 ÷ 1/4

(3/2 ÷ 2 = 3/4)

= 3/4 × 4/1 = 12/4 = 3 weeks

(Reciprocal method)

Answer: The rice in one package will last each family for 3 weeks.

Problem-Solving Strategy

Systematic Approach

Step-by-Step Process:

  1. 1. Read carefully - Identify what's given and what's needed
  2. 2. Plan your approach - Break into smaller steps
  3. 3. Solve step by step - Work through each part
  4. 4. Check your work - Verify each step
  5. 5. Answer the question - Make sure you answered what was asked

Key Skills:

  • • Identify the operations needed
  • • Choose the right order of operations
  • • Convert between different representations
  • • Check if answers make sense
  • • Use real-world context to verify

Key Takeaways

Multi-Step Problem Solving

  • •Break complex problems into smaller steps
  • •Identify which operations to use
  • •Work through each step carefully
  • •Verify your answer makes sense

Real-World Applications

  • •Fraction operations solve practical problems
  • •Always check if your answer is reasonable
  • •Use context to understand what you're calculating
  • •Practice with different types of problems
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