seegongsik
Grade 4 (age 9-10)

grade 4 Multi-digit Multiplication

To multiply a three-digit number by a two-digit number, split the numbers by place value, multiply the parts and add the results. For 234 × 16, split 234 into 200, 30 and 4 and 16 into 10 and 6; that turns the problem into six small products, each just a basic fact with some zeros. The column method is a short way to write the same work: find 234 × 6 and 234 × 10 separately, then add them with the places lined up. Change the two numbers to see each partial product written in its rectangle of the area model, and the two rows and the answer of the column method change too.

How Do We Multiply Big Numbers?

🏗️ Split It, Then Multiply
①234 is 200 + 30 + 4, and 16 is 10 + 6
②Split into small products like 200 × 10 and 30 × 6, each one is easy to find
③Adding all the small products gives 234 × 16 = 3744

The Area Model

234
16
💡 Reading the Area Model
①Across the top, the larger number is split into hundreds, tens and ones; down the side, the multiplier is split into tens and ones
②Each small rectangle's area is the product of its two parts, a partial product
③All the partial products add up to the area of the whole rectangle, which is the product of the two numbers
④Below the picture you can see the sum of the partial products and the answer

The Column Method

📝 Steps of the Column Method
①First multiply the larger number by the ones digit of the multiplier
②On the next row, write the product for the tens digit; you are multiplying by tens, so it ends in 0
③Add the two rows with the places lined up to get the answer
④For 234 × 16, add 1404 and 2340 to get 3744

Summary

Splitting the Multiplier
234 × 16 = 234 × 10 + 234 × 6
Split the multiplier into tens and ones, multiply each, then add
Area Model
(200 + 30 + 4) × (10 + 6) = sum of six partial products
Shows multiplication as the area of a rectangle cut into small parts
Column Method
(product for the ones) + (product for the tens) = answer
Line up the places and add
🎯 Summary
①Multiply big numbers by splitting them by place value, multiplying the parts and adding
②In the area model, each small rectangle is one partial product
③The column method adds the row for the ones digit and the row for the tens digit
④The row for the tens digit is lined up one place to the left
⑤Estimating the size of the answer first makes mistakes easier to catch

Examples and Unit Test

Example 1
Find 234 × 16 by splitting the multiplier.
1
Split 16 into 10 and 6: 234 × 16 = 234 × 10 + 234 × 6.
2
234 × 10 = 2340 and 234 × 6 = 1404, so 2340 + 1404 = 3744.
▸ 3744
Estimating 234 as about 200 and 16 as about 20 gives about 4000, so 3744 is a sensible size.
Example 2
Use the area model to find 23 × 14.
1
Split 23 into 20 and 3 and 14 into 10 and 4; that makes four partial products.
2
20 × 10 + 20 × 4 + 3 × 10 + 3 × 4 = 200 + 80 + 30 + 12 = 322.
▸ 322
When both numbers are split, the number of partial products is the number of parts of one times the number of parts of the other.
Unit Test
What is 123 × 3?
①339
②369
③366
④393
▸ ② 369
1
Split 123 into 100, 20 and 3: 100 × 3 + 20 × 3 + 3 × 3.
2
300 + 60 + 9 = 369.
← Previous
Large Numbers
Next →
Fraction Addition & Subtraction

Last updated