You're looking at an example of
division using the Area Model, which is a visual and conceptual way to break down division problems — especially helpful for understanding how larger numbers can be divided by breaking them into smaller, friendlier parts.
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🎯 The Problem:
Find 96 ÷ 4
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##
✔ Step-by-Step Solution Using the Area Model:
Step 1: Understand the Area Model
In the area model for division:
- The
dividend (96) is the total
area of a rectangle.
- The
divisor (4) is one
side length of the rectangle.
- The
quotient is the unknown side length — what we’re solving for.
So, imagine a rectangle with:
- Height = 4
- Area = 96
- We need to find the width → that’s 96 ÷ 4.
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Step 2: Break the Dividend into Friendly Parts
Instead of dividing 96 all at once, we
decompose 96 into two numbers that are easier to divide by 4.
The example breaks 96 into:
>
80 + 16
Why these numbers?
- Both 80 and 16 are divisible by 4.
- 80 is a multiple of 10, so it’s easy to work with.
- 16 is also small and divisible by 4.
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Step 3: Divide Each Part by 4
Now divide each part separately:
-
80 ÷ 4 = 20
-
16 ÷ 4 = 4
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Step 4: Add the Results
Add the two quotients together:
>
20 + 4 = 24
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✔ Final Answer:
>
96 ÷ 4 = 24
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## 📐 Visual Interpretation (Area Model Diagram)
The rectangle with area 96 and height 4 is split into two smaller rectangles:
- One with area 80 → width = 20
- One with area 16 → width = 4
Total width = 20 + 4 =
24
This matches the total area:
>
4 × 24 = 96 ✔️
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## 💡 Why This Method Works
This method uses the
Distributive Property of Division:
>
(a + b) ÷ c = (a ÷ c) + (b ÷ c)
So:
>
96 ÷ 4 = (80 + 16) ÷ 4 = (80 ÷ 4) + (16 ÷ 4) = 20 + 4 = 24
It’s a powerful strategy for mental math and building number sense!
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##
✔ Summary
| Step | Action |
|------|--------|
| 1 | Decompose 96 → 80 + 16 |
| 2 | Divide each part by 4 → 80÷4=20, 16÷4=4 |
| 3 | Add results → 20 + 4 = 24 |
| 4 | Verify: 4 × 24 = 96 ✔️ |
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✔ Answer: 96 ÷ 4 = 24
Let me know if you’d like to try another problem using this method!
Parent Tip: Review the logic above to help your child master the concept of area model division worksheet.
