Lesson 6: Use Partial Products to Multiply by 2-Digit Numbers

Property

When you multiply two 2-digit numbers, the four partial products you calculate correspond to the areas of the four smaller rectangles in an area model.
For factors decomposed as $(a+b)$ and $(c+d)$, the four partial products are $a \times c$, $a \times d$, $b \times c$, and $b \times d$.

Examples

Property

To multiply two 2-digit numbers, you can break the problem into four simpler multiplication problems. Multiply the ones and tens of the first number by the ones of the second number. Then, multiply the ones and tens of the first number by the tens of the second number.

Examples

• Find the product of $47 \times 35$.

• Find the product of $28 \times 14$.

• Find the product of $56 \times 72$.

Explanation

This method uses place value to multiply. You find four "partial products" by multiplying each digit of one factor by each digit of the other, paying close attention to their place values. For example, when multiplying by the tens digit, you are multiplying by a multiple of 10, not just the digit itself. After finding all four partial products, you add them together to get the final answer.