What is a partial-products algorithm. For example 87*65=? How do you do it and show your work?
Here is how Chicago Math does it:
87
x65
multiply 80 x 60.....4800
multiply 7 x 60..... 420
multiply 5 x 80.......400
multlply 5 x 7 ........35
add the products.
A partial-products algorithm is a method used to multiply two numbers by breaking them down into smaller, more manageable parts and computing their products separately. This approach is commonly taught in some math curriculums, such as the Chicago Math method.
To apply the partial-products algorithm to the multiplication problem 87 * 65, you would follow these steps:
Step 1: Write down the two numbers, one below the other, aligning the digits according to their place values:
87
x65
Step 2: Break down each number into its place value components and calculate the products for each combination:
Multiply 80 by 60, which equals 4,800.
Multiply 7 by 60, which equals 420.
Multiply 5 by 80, which equals 400.
Multiply 5 by 7, which equals 35.
Step 3: Add up all the products:
4,800 + 420 + 400 + 35 = 5,655
Therefore, 87 multiplied by 65 equals 5,655.
Using the partial-products algorithm allows you to break down the multiplication into smaller, more manageable calculations, making it easier to solve the problem.