Multiply by two-digit numbers - 3-digit x 2-digit
Theory
To multiply a three-digit number by a two-digit number, find a partial product for the ones and one for the tens (with a zero placeholder), then add them. The method matches two-by-two with one extra column.
A three-digit number is multiplied by a two-digit multiplier using the same two-row method.
The first partial product comes from the ones digit; the second from the tens digit, with a zero placeholder.
Adding the two partial products gives the answer. There is just one more column than a two-by-two.
Two rows of multiplying across three digits, then one addition.
| Step | Multiply | Partial product |
|---|---|---|
| Ones | \(346\times5\) | \(1730\) |
| Tens | \(346\times20\) | \(6920\) |
| Add | \(1730+6920\) | \(8650\) |
How to multiply three digits by two digits
- Multiply the three-digit number by the ones digit.
- Write a zero, then multiply by the tens digit.
- Line up the two partial products by place value.
- Add them for the final answer.
\(468\) then \(2340\).
| \(234 \times 12\) | \(=\) | \(2808\) |
\(1730\) then \(6920\).
| \(346 \times 25\) | \(=\) | \(8650\) |
\(500\) then \(1250\).
| \(125 \times 14\) | \(=\) | \(1750\) |
| \(145 \times 32\) | \(=\) | \(4640\) |
The total is $4640.
Common pitfalls
Frequently asked questions
How do you multiply a three-digit number by a two-digit number?
Multiply the three-digit number by the ones digit, then by the tens digit with a zero placeholder, and add the two partial products. \(346\times25=1730+6920=8650\).
Why is there a zero in the second partial product?
The tens digit stands for tens, so multiplying by it gives a number of tens. The zero in the ones place keeps the digits in their correct columns.
Is this different from two-digit by two-digit?
No, the method is the same. There is just one more column to multiply in each row.
How can I check my answer?
Estimate by rounding: \(346\times25\) is about \(350\times25=8750\), close to \(8650\).
What if a row needs several carries?
Carry each time a product reaches ten, writing the carried digit above the next column and adding it in. Keep track of every carry.