MathIsimple

Lesson 1-3: Fraction ÷ Integer

Learn to divide fractions by whole numbers using fair sharing and reciprocal concepts!

Learning Scenario: Fruit Salad Sharing

Scenario: You have 3/4 kilograms of fruit salad that you want to share equally among 4 friends. How much fruit salad will each friend receive?

What We Need to Find:

  • • Amount each friend gets
  • • Total fruit salad: 3/4 kg
  • • Number of friends: 4
  • • We need: 3/4 ÷ 4 = ?

Tools We'll Use:

  • • Fraction circles
  • • Fair sharing model
  • • Reciprocal multiplication
  • • Error correction

Method 1: Fair Sharing Model

Visual Understanding

To divide 3/4 by 4, we need to split 3/4 into 4 equal parts. Think of it as "How much does each person get when we share 3/4 equally among 4 people?"

3/4
÷
4

Split 3/4 into 4 equal parts

Step 1: Divide the Numerator

Keep the denominator the same, divide the numerator by 4

Step 2: Calculate

3 ÷ 4 = 3/4, but we need 3/4 ÷ 4 = 3/(4×4) = 3/16

Understanding the Result

3/4 ÷ 4 = 3/16

Each friend gets 3/16 kg of fruit salad

Answer: Each friend receives 3/16 kilograms of fruit salad!

Method 2: Reciprocal Multiplication

The Key Insight

Dividing by a whole number is the same as multiplying by its reciprocal (1 over that number):

a/b ÷ c = a/b × 1/c

For 3/4 ÷ 4:

  • • 3/4 ÷ 4 = 3/4 × 1/4
  • • 3/4 × 1/4 = (3×1)/(4×4)
  • • = 3/16

General Rule:

  • • a/b ÷ c = a/(b×c)
  • • Or: a/b ÷ c = a/b × 1/c
  • • Both methods give the same result

Common Error & Correction

Common Mistake

Many students make this error when dividing fractions by integers:

❌ 2/3 ÷ 3 = 2/1 (WRONG!)

This is incorrect!

Why It's Wrong:

You can't just "cancel out" the 3s. Division doesn't work that way!

Correct Method:

2/3 ÷ 3 = 2/(3×3) = 2/9

Model Verification

Let's verify the correct answer using a visual model:

Start with 2/3:

Divide into 3 equal parts:

Each part = 2/9

Correct Answer: 2/3 ÷ 3 = 2/9

Practice Problems

Problem 1: Pizza Sharing

You have 5/8 of a pizza and want to share it equally among 2 friends. How much pizza does each friend get?

5/8 ÷ 2 = 5/(8×2) = 5/16

Answer: Each friend gets 5/16 of the pizza.

More Practice

Calculate: 7/9 ÷ 3

7/9 ÷ 3 = 7/(9×3) = 7/27

Calculate: 4/5 ÷ 2

4/5 ÷ 2 = 4/(5×2) = 4/10 = 2/5

Key Takeaways

Algorithm Steps

  • •Keep the numerator the same
  • •Multiply the denominator by the divisor
  • •Simplify the result if possible
  • •Use fair sharing to visualize

Remember

  • •Division means "fair sharing"
  • •Don't cancel out numbers incorrectly
  • •Use models to verify your answers
  • •Practice with real-world examples
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