Multiply Using Four Partial Products
Multiply Using Four Partial Products is a Grade 4 math skill in enVision Mathematics, Chapter 4: Use Strategies and Properties to Multiply by 2-Digit Numbers. Students multiply two 2-digit numbers by decomposing each into tens and ones, finding four partial products, and summing them for the final answer.
Key Concepts
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 $47 \times 35$. $$ \begin{array}{r} &&&4&7 \\ &&\times & 3&5 \\ \hline &&&3&5 & \leftarrow 5 \times 7 \\ &&2&0&0 & \leftarrow 5 \times 40 \\ &&2&1&0 & \leftarrow 30 \times 7 \\ +&1&2&0&0 & \leftarrow 30 \times 40 \\ \hline &1&6&4&5 \end{array} $$ Find the product of $28 \times 14$. $$ \begin{array}{r} &&2&8 \\ &\times & 1&4 \\ \hline &&3&2& \leftarrow 4 \times 8 \\ &&8&0& \leftarrow 4 \times 20 \\ &&8&0 & \leftarrow 10 \times 8 \\ +&2&0&0 & \leftarrow 10 \times 20 \\ \hline &3&9&2 \end{array} $$ Find the product of $56 \times 72$. $$ \begin{array}{r} &&&5&6 \\ &&\times & 7&2 \\ \hline &&&1&2 & \leftarrow 2 \times 6 \\ &&1&0&0 & \leftarrow 2 \times 50 \\ &&4&2&0 & \leftarrow 70 \times 6 \\ +&3&5&0&0 & \leftarrow 70 \times 50 \\ \hline &4&0&3&2 \end{array} $$.
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.
Common Questions
How do you multiply using four partial products?
Decompose each 2-digit factor into tens and ones. Find all four combinations: tens times tens, tens times ones, ones times tens, ones times ones. Add all four products.
What is the formula for four partial products?
For (a+b) times (c+d), the four partial products are a times c, a times d, b times c, and b times d. Add all four for the total product.
What is an example of multiplying with four partial products?
For 37 times 24, decompose as (30+7) times (20+4): 30 times 20 equals 600, 30 times 4 equals 120, 7 times 20 equals 140, 7 times 4 equals 28. Total: 888.
How is multiplying with four partial products connected to the area model?
Each partial product corresponds to one of four rectangles in the area model. The sum of their areas equals the total product.
What chapter covers four partial products in enVision Grade 4?
Multiplying using four partial products is covered in Chapter 4: Use Strategies and Properties to Multiply by 2-Digit Numbers in enVision Mathematics Grade 4.