Multiplying Three-Digit Numbers
Grade 4 students extend multiplication to three-digit numbers in Saxon Math Intermediate 4. The algorithm moves from ones to tens to hundreds, carrying at each step. Multiplying 175 by 5: 5 times 5 = 25 (write 5, carry 2); 5 times 7 = 35 plus 2 = 37 (write 7, carry 3); 5 times 1 = 5 plus 3 = 8. The answer is 875. A library with 175 shelves holding 5 books each has 875 books total. The most common error is forgetting to add the carry after each multiplication step. This Chapter 6 skill is the prerequisite for multiplying multi-digit numbers by two-digit multipliers.
Key Concepts
New Concept When we multiply a three digit number using pencil and paper, we multiply the ones digit first. Then we multiply the tens digit. Then we multiply the hundreds digit.
What’s next Next, you'll use this process to solve multiplication problems with three digit numbers, including those involving money and carrying.
Common Questions
How do you multiply a three-digit number by a one-digit number?
Start at the ones place and multiply, carrying when the product is 10 or more. Move to the tens place, multiply, and add the carry. Then move to the hundreds place and repeat. Write the full product from the last multiplication onward.
What is 175 times 5?
Step 1: 5 times 5 = 25. Write 5, carry 2. Step 2: 5 times 7 = 35, add carry 2 = 37. Write 7, carry 3. Step 3: 5 times 1 = 5, add carry 3 = 8. Write 8. Answer: 875.
What is the most common mistake in three-digit multiplication?
Forgetting to add the carried digit before moving to the next step. After computing 5 times 7 = 35, you must add the 2 that was carried from the ones step to get 37, not just write 35.
How does carrying work in three-digit multiplication?
When a partial product is 10 or more, write the ones digit in the answer row and place the tens digit as a small carry above the next column. Include this carry in the next multiplication step.
What Saxon Math chapter covers multiplying three-digit numbers?
Multiplying three-digit numbers is covered in Saxon Math Intermediate 4, Chapter 6 (Lessons 51-60), building toward multiplication with larger numbers.