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: 33 x 11.
Suppose you want to calculate: 33 x 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:
33 x 11 = (30 +3) x (10 +1) = 30 x (10 +1) + 3 x (10 +1).
33 x 11 = 30 x 10 + 30 x 1 + 3 x 10 + 3 x 1.
Step 3: Add up the resulting numbers:
33 x 11 = 300 + 30 + 30 + 3 = 363.
So the final answer is 33 x 11 = 363
Example 2: Calculate the product 47 x 86.
47 x 86 = (40 + 7) x (80 + 6) = 40 x (80 + 6) + 7 x (80 + 6)
= (40 x 80) + (40 x 6) + (7 x 80) + (7 x 6)
= 3200 + 240 + 560 + 42 = 4042.
Example 3: Calculate the product 327 x 16 using the partial multiplication method.
327 x 16 = (300 + 20 + 7) x (10 + 6)
= 300 x (10 + 6) + 20 x (10 + 6) + 7 x (10 + 6)
= (300 x 10) + (300 x 6) + (20 x 10) + (20 x 6) + (7 x 10) + (7 x 6)
= 3000 + 1800 + 200 + 120 + 70 + 42 = 5232.
