Multiplying with regrouping
Multiplying with regrouping (carrying over) is a Grade 4 skill in Saxon Math Intermediate 4 (Chapter 5). When multiplying produces a two-digit number in any column, write the ones digit below the line and carry the tens digit to the next column. For 24 x 8: multiply ones (4 x 8 = 32), write 2 carry 3, then multiply tens (8 x 2 = 16) and add carried 3 to get 19. The most common error is adding the carried digit before multiplying instead of after.
Key Concepts
Property When multiplying the ones place results in a two digit number, we don't write both digits down. Write the second digit (the ones) below the line and carry the first digit (the tens) above the tens column. Then, multiply the tens digit and remember to add the number you carried over to find the final product.
Example To solve $18 \times 4$: First, $8 \times 4 = 32$. Write down the 2 and carry the 3. Then, $4 \times 1 = 4$, plus the carried 3 is 7. The answer is 72. To solve $47 \times 6$: First, $7 \times 6 = 42$. Write down the 2 and carry the 4. Then, $6 \times 4 = 24$, plus the carried 4 is 28. The answer is 282. To solve $56 \times 7$: First, $6 \times 7 = 42$. Write down the 2 and carry the 4. Then, $7 \times 5 = 35$, plus the carried 4 is 39. The answer is 392.
Explanation Think of it like a trade up game! When you get 10 or more ones, you can't keep them all there. You trade 10 ones for a ten, carry it over, and add it in after multiplying.
Common Questions
What is regrouping in multiplication?
When multiplying a digit produces a two-digit result (like 4 x 8 = 32), you write the ones digit (2) below the line and carry the tens digit (3) to the top of the next column to be added after the next multiplication.
How do you multiply 24 x 8 with regrouping?
Multiply ones: 4 x 8 = 32. Write 2, carry 3. Multiply tens: 8 x 2 = 16. Add carried 3: 16 + 3 = 19. Write 19. Answer: 192.
How do you multiply 47 x 6 with regrouping?
Multiply ones: 7 x 6 = 42. Write 2, carry 4. Multiply tens: 6 x 4 = 24. Add carried 4: 24 + 4 = 28. Write 28. Answer: 282.
What is the most common regrouping error?
Adding the carried digit before multiplying. For 24 x 8: after carrying 3, some students do 2 + 3 = 5 then 8 x 5 = 40 instead of the correct 8 x 2 = 16 then 16 + 3 = 19. Always multiply first, then add the carried digit.
How do you multiply 56 x 7 with regrouping?
Ones: 7 x 6 = 42. Write 2, carry 4. Tens: 7 x 5 = 35. Add carried 4: 35 + 4 = 39. Write 39. Answer: 392.