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Lesson 2-4

Fractions & Whole Numbers Conversion

Learn to convert between mixed numbers and improper fractions using visual models. Master fraction form conversion with shape assembly activities.

Learning Scenario: Shape Assembly

Scenario: You're building with shape blocks! You have 1 complete circle and 1/2 of another circle. How can you express this as a single fraction? What if you have 3/2 circles - how many complete circles and how many halves is that?

This is where mixed numbers and improper fractions come in! Mixed numbers show whole numbers and fractions together, while improper fractions have numerators larger than denominators.

Mixed Numbers

A mixed number combines a whole number and a proper fraction. It shows "how many wholes plus how many parts."

Examples:

  • • 1 1/2 (one and one-half)
  • • 2 3/4 (two and three-fourths)
  • • 3 1/3 (three and one-third)
Improper Fractions

An improper fraction has a numerator that is equal to or greater than the denominator. It represents one or more wholes plus parts.

Examples:

  • • 3/2 (three halves)
  • • 11/4 (eleven fourths)
  • • 10/3 (ten thirds)
Step-by-Step Learning
1

Mixed Number to Improper Fraction

To convert a mixed number to an improper fraction, multiply the whole number by the denominator, add the numerator, and keep the denominator.

Example: 2 3/4 = (2×4 + 3)/4 = (8 + 3)/4 = 11/4

2

Improper Fraction to Mixed Number

To convert an improper fraction to a mixed number, divide the numerator by the denominator. The quotient is the whole number, and the remainder is the numerator of the fraction.

Example: 11/4 = 11 ÷ 4 = 2 remainder 3, so 11/4 = 2 3/4

3

Visual Representation

Use shape models to visualize the conversion. Draw complete shapes for whole numbers and partial shapes for fractions.

Example: 1 1/2 = 1 complete circle + 1/2 circle = 3/2 circles total

Interactive Activities

Activity 1: Shape Assembly

Use shape blocks to practice conversion:

  • • Build 1 1/2 circles with blocks
  • • Count total parts: 3/2
  • • Build 2 1/3 rectangles with blocks
  • • Count total parts: 7/3
  • • Practice with different shapes!

Activity 2: Conversion Practice

Practice converting between forms:

  • • 3 1/4 = ?/4
  • • 5/2 = ? 1/2
  • • 2 2/3 = ?/3
  • • 9/4 = ? 1/4
  • • Check with visual models!
Practice Problems

Problem Set 1: Mixed to Improper

1. 2 1/3 = ?/3

2. 3 2/5 = ?/5

3. 1 3/4 = ?/4

4. 4 1/2 = ?/2

Problem Set 2: Improper to Mixed

5. 7/3 = ? 1/3

6. 11/4 = ? 3/4

7. 9/2 = ? 1/2

8. 13/5 = ? 3/5

Problem Set 3: Mixed Operations

9. Convert 2 1/4 to improper, then add 1/4

10. Convert 5/2 to mixed, then add 1/2

11. Convert 3 2/3 to improper, then subtract 1/3

12. Convert 7/3 to mixed, then subtract 1/3

Common Mistakes to Avoid

❌ Forgetting to multiply the whole number

Wrong: 2 1/3 = 1/3 (Forgot to multiply 2 by 3)

Correct: 2 1/3 = (2×3 + 1)/3 = 7/3

❌ Confusing numerator and remainder

Wrong: 7/3 = 2 1/3 (Used quotient as numerator)

Correct: 7/3 = 2 1/3 (Remainder 1 becomes numerator)

Key Takeaways

Mixed numbers combine whole numbers and proper fractions

Improper fractions have numerators equal to or greater than denominators

Use the formula: Mixed to Improper = (whole × denominator + numerator)/denominator

Use division to convert improper fractions to mixed numbers