Multiply 2- and 3-Digit Numbers
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What you will learn
- 1Multiply a 2-digit number by a 1-digit number using the column method
- 2Multiply a 3-digit number by a 1-digit number using the column method
- 3Apply regrouping (carrying) correctly when multiplying
- 4Estimate multiplication products to check reasonableness
Mini Lesson
The column method (also called long multiplication) keeps digits aligned by place value so that ones, tens, and hundreds are multiplied separately and then combined. Regrouping — carrying the extra tens digit into the next column — makes this method work for any size of number.
Column Method: 2-Digit × 1-Digit
- 47 × 6: write 47 on top and the 1-digit multiplier 6 below the ones column, with a horizontal line underneath.
- Multiply the ones digit first: 7 × 6 = 42. Write 2 in the ones place; carry the 4 above the tens column.
- Multiply the tens digit: 4 × 6 = 24. Add the carried 4: 24 + 4 = 28. Write 28 to the left of the 2.
- Read the answer: 282.
Column Method: 3-Digit × 1-Digit
- 234 × 5: multiply ones first: 4 × 5 = 20. Write 0, carry 2.
- Multiply tens: 3 × 5 = 15. Add carried 2: 17. Write 7, carry 1.
- Multiply hundreds: 2 × 5 = 10. Add carried 1: 11. Write 11.
- Answer: 1,170.
Estimating First
- Round the 2- or 3-digit number to the nearest ten or hundred.
- 47 × 6: round 47 to 50 → 50 × 6 = 300. Exact answer 282 is close to 300. ✓
- 234 × 5: round 234 to 200 → 200 × 5 = 1,000. Exact 1,170 is in the right range. ✓
- If your exact answer is far from your estimate, check your regrouping.
Words to know
Multiply
To find the total when groups of equal size are added
e.g. Multiply 6 × 47 to find the total of six 47s.
Column method
A way to write a multiplication so the place values line up
e.g. I used the column method to multiply 234 × 5.
Regroup
To carry an extra ten into the next place value
e.g. I regrouped 42 as 4 tens and 2 ones.
Product
The answer to a multiplication problem
e.g. The product of 47 and 6 is 282.
Carry
The extra digit moved to the next column when regrouping
e.g. I carry the 4 above the tens column.
Tip: always estimate first by rounding, then use the column method. If your exact answer is far from the estimate, recheck your carries.
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