Area Model Multiplication is a visual technique used to simplify multiplying larger numbers by breaking them down into smaller, more manageable parts based on their place values. This method uses a rectangular grid, where each section represents a partial product of the multiplication.
Table of Content
What is Area Model Multiplication?
Area Model Multiplication is a visual method used to multiply numbers, particularly helpful in breaking down complex multiplication problems into smaller, more manageable parts. It is often taught in elementary schools to help students understand the concept of multiplication and the distributive property.
Steps for Area Model Multiplication
Steps to calculate multiplication using are model are:
Step 1: Break down each number into its place values. For example, if multiplying 23 by 15, you'd break them down as 20 + 3 and 10 + 5.
Step 2: Draw a rectangle and divide it into sections based on the place values. For example, a rectangle for 23 × 15 would have four sections: 20 × 10, 20 × 5, 3 × 10, and 3 × 5.
Step 3: Multiply the numbers in each section.
Step 4: Add all the products together to get the final answer.
Let's consider example for better understanding.
Example: If you want to multiply 23 by 15:
Solution:
- Break them down: 23 = 20 + 3 and 15 = 10 + 5.
- Draw a rectangle divided into four smaller rectangles.
- Label each rectangle with the appropriate multiplication:
- Top left: 20 × 10 = 200
- Top right: 20 × 5 = 100
- Bottom left: 3 × 10 = 30
- Bottom right: 3 × 5 = 15
- Add the products: 200 + 100 + 30 + 15 = 345.
So, 23 × 15 = 345.
Area Model Multiplication: Solved Problems
Problem 1: Multiply 12 by 14.
Solution:
- Break down: 12=10+2 and 14=10+4
- Area Model:
- 10×10=100
- 10×4=40
- 2×10=20
- 2×4=8
- Add: 100+40+20+8=168
Answer: 12×14=168
Problem 2: Multiply 23 by 35.
Solution:
- Break down: 23=20+3 and 35=30+5
- Area Model:
- 20×30=600
- 20×5=100
- 3×30=90
- 3×5=15
- Add: 600+100+90+15=805
Answer: 23×35=805
Problem 3: Multiply 16 by 27.
Solution:
- Break down: 16=10+6 and 27=20+7
- Area Model:
- 10×20=200
- 10×7=70
- 6×20=120
- 6×7=42
- Add: 200+70+120+42=432
Answer: 16×27=432
Problem 4: Multiply 34 by 22.
Solution:
- Break down: 34=30+4 and 22=20+2
- Area Model:
- 30×20=600
- 30×2=60
- 4×20=80
- 4×2=8
- Add: 600+60+80+8=748
Answer: 34×22=748
Problem 5: Multiply 45 by 19.
Solution:
- Break down: 45=40+5 and 19=10+9
- Area Model:
- 40×10=400
- 40×9=360
- 5×10=50
- 5×9=45
- Add: 400+360+50+45=855
Answer: 45×19=855
Problem 6: Multiply 21 by 33.
Solution:
- Break down: 21=20+1 and 33=30+3
- Area Model:
- 20×30=600
- 20×3=60
- 1×30=30
- 1×3=3
- Add: 600+60+30+3=693
Answer: 21×33=693
Problem 7: Multiply 52 by 18.
Solution:
- Break down: 52=50+2 and 18=10+8
- Area Model:
- 50×10=500
- 50×8=400
- 2×10=20
- 2×8=16
- Add: 500+400+20+16=936
Answer: 52×18=936
Worksheet: Area Model Multiplication
Q1: Multiply 17 by 23.
Q2: Multiply 25 by 36.
Q3: Multiply 48 by 29.
Q4: Multiply 31 by 42.
Q5: Multiply 63 by 54.
Q6: Multiply 39 by 27.
Q7: Multiply 55 by 33.
Q8: Multiply 47 by 32.
Q9: Multiply 24 by 45.
Q10: Multiply 19 by 28.
Read More,