The Standard Algorithm for Multiplication
The standard algorithm for multiplication involves multiplying each digit of the bottom factor by the entire top factor, creating partial products that must be aligned by place value, then adding all partial products to get the final answer. This Grade 5 math skill from Eureka Math Chapter 8 covers the standard algorithm for multi-digit whole number multiplication.
Key Concepts
The standard algorithm for multiplication is a procedure for multiplying numbers by breaking the problem into partial products.
You multiply the top factor by each digit of the bottom factor, one at a time from right to left, and then add the resulting partial products together.
Common Questions
What is the standard algorithm for multiplication?
The standard algorithm involves multiplying the top number by each digit of the bottom number from right to left, creating partial products, then adding all partial products together to find the final answer.
Why are placeholder zeros used in the standard algorithm?
Placeholder zeros align each partial product correctly according to its place value. When multiplying by the tens digit, for example, you add a zero to shift the partial product one place to the left.
What is a partial product?
A partial product is the result of multiplying the entire top number by just one digit of the bottom number, and the final product is the sum of all partial products.
How do you multiply 427 times 35 using the standard algorithm?
Multiply 427 times 5 to get 2135, then multiply 427 times 3 (the tens digit) to get 1281, written as 12810. Add 2135 plus 12810 to get 14945.