Multi-Digit Multiplication
Grade 4 · Math · Study Guide
Learn how to multiply large numbers using place value and the standard algorithm.
Multi-digit multiplication builds on what you know about multiplying single digits. When you multiply a multi-digit number, you use place value to break the problem into smaller parts.
The standard algorithm works by multiplying each digit of one number by each digit of the other number, keeping track of place value. For example, when you multiply 23 × 4, you first multiply 3 × 4 = 12 (write 2, carry the 1), then multiply 2 × 4 = 8, and add the carried 1 to get 9. So 23 × 4 = 92.
For two two-digit numbers like 23 × 14, you multiply 23 × 4 = 92, then multiply 23 × 10 = 230, and add the results: 92 + 230 = 322. The key is to add a zero placeholder when you multiply by the tens digit.
Estimation is a powerful tool to check your work. Round each number to the nearest ten or hundred before multiplying. If 23 × 14 ≈ 20 × 10 = 200, your answer of 322 is in the right ballpark.
Key terms
- Product
- The answer you get when you multiply two or more numbers together.
- Factor
- Each of the numbers being multiplied together in a multiplication problem.
- Place value
- The value of a digit based on its position in a number (ones, tens, hundreds, etc.).
- Regrouping
- Carrying a value to the next place when a digit's value is 10 or more.
- Partial product
- One of the smaller multiplication results you add together to find the final product.
- Estimation
- Finding an approximate answer by rounding numbers before calculating.
Flashcards
- 23 × 4
- 92 — multiply 3 × 4 = 12 (write 2, carry 1), then 2 × 4 + 1 = 9
- Partial product
- A smaller product found by multiplying by one digit at a time; you add all partial products to get the final answer
- Zero placeholder
- A 0 written in the ones place when multiplying by the tens digit to keep place value correct
- 34 × 10
- 340 — multiplying by 10 shifts all digits one place to the left
- Regrouping in multiplication
- When a product of two digits is 10 or more, carry the tens digit to the next column
- Estimate 47 × 8
- About 400 — round 47 to 50, then 50 × 8 = 400
- 25 × 12
- 300 — partial products: 25 × 2 = 50 and 25 × 10 = 250; 50 + 250 = 300
- Checking multiplication with estimation
- Round factors to the nearest ten, multiply, and compare to your actual answer to spot big errors
Questions
What is 34 × 5?
- 160
- 165
- 170
- 175
Show answer
Answer: 170
34 × 5: multiply 4 × 5 = 20 (write 0, carry 2), then 3 × 5 + 2 = 17. Result: 170.
When multiplying 46 × 3, you multiply 6 × 3 = 18. You write down the 8 and _____ the 1 to the tens column.
Show answer
Answer: carry
When a digit product is 10 or more, you write the ones digit and carry the tens digit to the next column.
When multiplying 52 × 13, you need to add a zero placeholder before writing the second partial product.
Show answer
Answer: True
When multiplying by the tens digit (1 in 13), you write a 0 in the ones place first to show you are multiplying by 10, not 1.
What is 27 × 12?
- 314
- 324
- 334
- 344
Show answer
Answer: 324
27 × 12: 27 × 2 = 54 and 27 × 10 = 270; 54 + 270 = 324.
A good estimate for 48 × 6 is 50 × 6 = _____.
Show answer
Answer: 300
Round 48 to 50. 50 × 6 = 300. The actual answer is 288, so 300 is a close estimate.
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