Multiplying Two-Digit Numbers, Part 2
Grade 4 students master multiplying two-digit numbers in Saxon Math Intermediate 4 Chapter 5 by learning to regroup (carry) when partial products reach 10 or more. In 58 × 4: multiply ones (8 × 4 = 32), write the 2 and carry the 3 to the tens column; multiply tens (5 × 4 = 20), add the carried 3 to get 23; final answer is 232. The critical rule: always multiply first, then add the carried number—never add the carry before multiplying.
Key Concepts
New Concept We write the second digit below the line in the ones column and write the first digit above the tens column.
What’s next Now, you will apply this regrouping method to solve multiplication problems, including those involving money and estimation.
Common Questions
What is regrouping (carrying) in multiplication?
When you multiply two digits and get a two-digit product, you write the ones digit in your answer and carry the tens digit to the next column. For example, 8 × 4 = 32; write 2, carry 3.
What is the step-by-step method for multiplying a two-digit number by a one-digit number?
Step 1: Multiply the ones digit (e.g., 8 × 4 = 32). Write the ones digit (2) and carry the tens digit (3). Step 2: Multiply the tens digit (5 × 4 = 20). Step 3: Add the carried number (20 + 3 = 23). Final answer: 232.
What is the most common mistake when carrying in multiplication?
Adding the carried number before multiplying instead of after. For 58 × 4, some students do 5 + 3 = 8, then 8 × 4 = 32, which is incorrect. Always multiply the column first, then add the carry.
How do you multiply 47 × 9 using the standard method?
Ones: 9 × 7 = 63. Write 3, carry 6. Tens: 9 × 4 = 36. Add carried 6: 36 + 6 = 42. Write 42 next to the 3. Answer: 423.
Why do we start multiplication from the ones place?
Starting from the ones place ensures that any regrouped (carried) value from the ones column is properly added into the tens column calculation. The process flows right to left, building the answer one column at a time.
What are real-world uses for two-digit multiplication?
Calculating the total cost of multiple items, finding distances traveled at a constant speed, computing area of small rectangles, and totaling groups of equal quantities all require two-digit multiplication.