Multiplying Multi-Digit Numbers
Multiplying multi-digit numbers is a Grade 5 math skill in enVision Mathematics, Chapter 3: Fluently Multiply Multi-Digit Whole Numbers. Students multiply the top factor by each digit of the bottom factor one at a time (right to left), generating partial products, then add all partial products together for the final answer. This is the standard multi-digit multiplication algorithm.
Key Concepts
Property To multiply multi digit numbers, multiply the top number by each digit of the bottom number, one at a time, from right to left. These intermediate results are called partial products. The final product is the sum of the partial products.
Examples To calculate $86 \times 42$: $$.
\begin{array}{r r r r} & & & 8 & 6 \\ \times & & & 2 & 4 \\ \hline & & 3 & 4& 4 \\ + & 1 & 7 & 2 &0 \\ \hline & 2 & 0 & 6& 4 \\ \end{array} $$ To calculate $527 \times 35$: $$ \begin{array}{r r r r r} & & & 5 & 2 & 7 \\ \times & & & & 3 & 5 \\ \hline & & 2 & 6 & 3& 5 \\ + & 1 & 5 & 8 & 1& 0 \\ \hline & 1 & 8 & 4 & 4& 5 \\ \end{array} $$ To calculate $1677\times 18$: $$.
Common Questions
How do you multiply multi-digit numbers?
Multiply the top number by the ones digit of the bottom number, then by the tens digit (shifting one place left), and so on. Add all partial products for the final answer.
What are partial products in multi-digit multiplication?
Partial products are the intermediate results when you multiply the top factor by each digit of the bottom factor separately before adding them together.
How do you multiply 234 x 56?
Multiply 234 x 6 = 1,404, then multiply 234 x 50 = 11,700. Add: 1,404 + 11,700 = 13,104.
Where is multi-digit multiplication taught in enVision Grade 5?
Chapter 3: Fluently Multiply Multi-Digit Whole Numbers in enVision Mathematics, Grade 5.
Why do you shift one place left when multiplying by the tens digit?
Each digit position represents a different power of 10. Multiplying by the tens digit means multiplying by a value 10 times larger, so the result shifts one column to the left.