Multiplying Two-Digit Numbers, Part 1
Grade 4 students learn to multiply two-digit numbers using the partial products method in Saxon Math Intermediate 4. Multiplying 21 times 3 means multiplying the ones digit first (3 times 1 = 3), then the tens digit (3 times 20 = 60), then adding: 3 + 60 = 63. For 28 times 5, multiply the ones: 5 times 8 = 40, write 0 and carry 4; then 5 times 2 = 10, add the 4 to get 14. The answer is 140. A very common error is forgetting to add the carried digit when multiplying the tens. This Chapter 5 skill bridges single-digit multiplication to multi-digit algorithms.
Key Concepts
New Concept Instead of finding $21 + 21 + 21$, we will solve this problem by multiplying 21 by 3.
What’s next Next, you’ll master a mental math shortcut and a pencil and paper method for multiplying two digit numbers.
Common Questions
How do you multiply a two-digit number by a one-digit number?
Multiply the bottom number by the ones digit of the top number first. If the product is 10 or more, write the ones digit and carry the tens digit. Then multiply the bottom number by the tens digit and add any carry. Combine for the final answer.
What is 28 times 5 using the standard algorithm?
Multiply 5 times 8 = 40. Write 0 and carry 4. Multiply 5 times 2 = 10, add the carried 4 to get 14. Write 14. The complete answer is 140.
Why is multiplication faster than repeated addition?
Instead of writing 21 plus 21 plus 21 = 63, multiplying 21 times 3 gives 63 directly. As numbers get larger, repeated addition becomes impractical, while the multiplication algorithm stays the same.
What is the most common mistake when multiplying two-digit numbers?
Forgetting to add the carried digit. After multiplying the tens digit, students must add the number they carried from the ones step. In 28 times 5, after computing 5 times 2 = 10, the carry of 4 must be added to get 14.
What Saxon Math chapter introduces two-digit multiplication?
Multiplying two-digit numbers is introduced in Saxon Math Intermediate 4, Chapter 5 (Lessons 41-50), as the first step toward multi-digit multiplication algorithms.