The partial product method of multiplication is a method that allows us to multiply two numbers quickly in our heads by decomposing each number as a sum of two numbers. This method is most useful when we are dealing with small numbers having two or three digits. The disadvantage of this method is that it is not very suitable when we wish to multiply two large numbers.

**Steps for Partial Product Multiplication:**

- Write each of the two numbers as a sum of units and tens. For example, 23 = 20 + 3.
- Use the distributive property of multiplication to expand the brackets.
- Calculate each product and add the resulting numbers to get the final answer.

Let us try to understand this method by looking at some examples.

**Example 1:**

Suppose you want to calculate: 33 \times 11.

** Step 1**: We write each number as a sum of two simpler numbers as follows: 33 =30 + 3. 11 =10 + 1.

** Step 2**: Apply the distributive property and expand the brackets: \begin{align*}33 \times 11 &= (30 + 3)(10 + 1) \\ &= 30 \times (10 + 1) + 3 \times (10 + 1) \\ &= (30 \times 10) + (30 \times 1) + (3 \times 10) + (3 \times 1)\end{align*}

** Step 3**: Add up the resulting numbers: \begin{align*}33 \times 11 &= (30 \times 10) + (30 \times 1) + (3 \times 10) + (3 \times 1) \\ &= 300 + 30 +30 + 3 \\ &= 363. \end{align*}

So the final answer is 33 \times 11 = 363 .

**Example 2:**

Calculate the product 47 \times 86 .

\begin{align*}47 \times 86 &= (40 + 7)(80 + 6) \\ &= 40 \times (80 + 6) + 7 \times (80 + 6) \\ &= (40 \times 80) + (40 \times 6) + (7 \times 80) + (7 \times 6) \\ &= 3200 + 240 + 560 + 42 \\ &= 4042. \end{align*}**Example 3:**

Calculate the product 327 \times 16 using the partial multiplication method.

\begin{align*}327 \times 16 &= (300 + 20 + 7)(10 + 6) \\ &= 300 \times (10 + 6) + 20 \times (10 + 6) + 7 \times (10 + 6) \\ &= (300 \times 10) + (300 \times 6) + (20 \times 10) + (20 \times 6) + (7 \times 10) + (7 \times 6) \\ &= 3000 + 1800 + 200 + 120 + 70 + 42 \\ &= 5232. \end{align*}So the final answer is 327 \times 16 = 5232 .