Multi-digit multiplication handles big numbers by splitting them by place value and multiplying step by step.
Break 234 into 200, 30, and 4, multiply each piece, and add them up, and a hard-looking product becomes easy.
You use it to find the total price of several items or to measure an area.
On this page you change the numbers with sliders and watch how the partial products build up to the answer.
How to multiply big numbers?
🏗️ Split it up to multiply easily!
①Split 234 into 200 + 30 + 4
②Multiply each part, then add them up
③This is called the area model
Understand with the Area Model
234
16
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Multiplication shown by splitting into place values (area model)
💡 Principle of the Area Model
①Split the big number into hundreds, tens, ones
②Multiply each part separately (partial products)
③Sum all partial products = final answer!
Calculate with Long Multiplication
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The long-multiplication process
📝 Long Multiplication Order
①Start with the ones place
②Tens-place product shifts one column left
③Line up and add → answer
Summary
Distributive Law
234 × 16 = 234 × 10 + 234 × 6
Split the multiplier, multiply each, then add
Area Model
(200+30+4) × (10+6) = sum of partial products
Visualize multiplication as a rectangle's area
Long Multiplication
Ones-product + Tens-product (×10) = answer
Align by place, multiply, then add in turn
🎯 Key Points
①Calculate big multiplications by splitting
②Distributive law: split, multiply, combine
③Long multiplication: aligning places matters
④Carry to the next place when needed
⑤The area model reduces mistakes
Examples and Unit Test
Example 1
Use the distributive law to calculate 234 × 16.
1
Split the multiplier 16 into 10 and 6: 234 × 10 + 234 × 6.