Multiplying Three-Digit by Two-Digit Numbers
Multiplying three-digit by two-digit numbers is a Grade 5 math skill in enVision Mathematics, Chapter 3: Fluently Multiply Multi-Digit Whole Numbers. Using the standard algorithm, students find two partial products—multiplying the top 3-digit number by the ones digit and then by the tens digit (shifted one place left)—and add them for the final product. Zero digits in the top number require careful placeholder handling.
Key Concepts
Property To multiply a 3 digit number containing a zero by a 2 digit number, use the standard algorithm. First, find the partial product by multiplying the top number by the ones digit of the bottom number. Then, find the second partial product by multiplying the top number by the tens digit, placing a zero in the ones place. Finally, add the two partial products to find the final product.
Examples Find the product of $309 \times 42$: $$ \begin{array}{r r r r r} & & & 3 & 0 & 9 \\ \times & & & & 4 & 2 \\ \hline & & & 6 & 1 & 8 \\ + & 1 & 2 & 3 & 6 &0 \\ \hline & 1 & 2 & 9 & 7 &8 \\ \end{array} $$ Find the product of $704 \times 56$: $$ \begin{array}{r r r r r} & & & 7 & 0 & 4 \\ \times & & & & 5 & 6 \\ \hline & & 4 & 2 & 2 & 4 \\ + & 3 & 5 & 2 & 0 &0 \\ \hline & 3 & 9 & 4 & 2 &4 \\ \end{array} $$.
Find the product of $430 \times 56$: $$.
Common Questions
How do you multiply a 3-digit number by a 2-digit number?
Multiply the top number by the ones digit to get the first partial product. Multiply the top number by the tens digit (writing the result shifted one place left) to get the second. Add both partial products.
How do you handle a zero digit in a 3-digit multiplication?
Multiply as normal. A zero digit contributes 0 to that place value. For example, 304 x 6 = 1,824 (3x6 in hundreds, 0x6 in tens, 4x6 in ones).
What is 234 x 47?
234 x 7 = 1,638 (ones partial product). 234 x 40 = 9,360 (tens partial product). Sum: 1,638 + 9,360 = 10,998.
Where is 3-digit by 2-digit multiplication taught in enVision Grade 5?
Chapter 3: Fluently Multiply Multi-Digit Whole Numbers in enVision Mathematics, Grade 5.
Why do you shift the second partial product one place to the left?
The tens digit represents tens (a value 10 times larger), so its partial product belongs one place further left in the place value chart.