Multiplication Identities - STD 9 - Page 66.2 EM

Two Digit Multiplication Method

Visual & Algebraic Explanation

Problem

Given below is a method to find the product of two 2-digit numbers. Check it for other numbers and explain why it works using algebra.

First Number

36

3 tens + 6 units

Second Number

28

2 tens + 8 units

Method

1.

Multiply units digits:

6 × 8 = 48

2.

Cross multiply and add, then × 10:

(3×8) + (6×2) = 36 → 36 × 10 = 360

3.

Multiply tens digits, then × 100:

3 × 2 = 6 → 6 × 100 = 600

4.

Add all:

600 + 360 + 48 = 1008

Algebraic Proof

Let the first number = 10a + b

Let the second number = 10c + d

Product = (10a + b)(10c + d) = 100ac + 10ad + 10bc + bd

This can be grouped as:

• 100 × (a × c)

• 10 × [(a × d) + (b × c)]

• (b × d)

This is exactly the method shown above!