B.1 Multiply whole numbers

Multiply whole numbers

Key notes :

Understanding Multiplication

Definition: Multiplication is the process of adding a number to itself a certain number of times. Multiplication is a math operation used to find the total when you have equal groups.

It is a repeated addition.
➤ Example: 4 × 3 means 4 added 3 times → 4 + 4 + 4 = 12

Terminology:

Multiplicand: The number being multiplied.
Multiplier: The number by which the multiplicand is multiplied.
Product: The result of the multiplication.

Basic Properties of Multiplication

Commutative Property: The order of factors does not change the product.

Example: 3×4=4×3

Associative Property: The grouping of factors does not change the product.

Example: (2×3)×4=2×(3×4)

Distributive Property: Multiplying a number by a sum is the same as doing each multiplication separately.

Identity Property: Any number multiplied by 1 remains the same.

Example: 5×1=5

Zero Property: Any number multiplied by 0 is 0.

Example: 6×0=0

Multiplication Techniques

Times Tables: Memorizing multiplication tables helps in quick calculation.

Repeated Addition: Understanding that multiplication is repeated addition.

Example: 4×3=4+4+4=12

Skip Counting: Counting by numbers other than 1 to find the product.

Example: Skip counting by 5s to find 5×4 : 5, 10, 15, 20.

Area Model: Breaking numbers into parts, multiplying each part, and then adding them.

Example: To multiply 23 by 5, break 23 into 20 and 3: (20×5)+(3×5)=100+15=115 (20 \times 5) + (3 \times 5) = 100 + 15 = 115(20×5)+(3×5)=100+15=115.

Simple Multiplication Techniques for Large Numbers

Multiplying Large Numbers (2-digit × 2-digit)

Example: 34 × 12

     34
    ×12
  _______
      68   ← 34 × 2 (ones place)
+   340   ← 34 × 1 (tens place; shift one place to left)
  _______
     408

Answer: 408

Break Down the Numbers (Distributive Property)

Splitting Numbers into Parts: Break large numbers into smaller, more manageable parts, multiply each part separately, and then add the results

Area Model (Box Method)

Column Method (Standard Algorithm)

The Column Method, also known as the Standard Algorithm, is a step-by-step method of multiplying multi-digit numbers, writing each part in columns and adding partial products.

🧮 Steps to Use the Column Method

Let’s multiply: 326 × 4

326
× 4

1304

Step-by-Step Multiplication: Write the numbers in columns, multiply each digit, starting from the rightmost digit, and add the partial products.

✅ Steps:

Multiply 4 × 6 = 24 → Write 4, carry 2
Multiply 4 × 2 = 8 → Add carry 2 → 8 + 2 = 10, write 0, carry 1
Multiply 4 × 3 = 12 → Add carry 1 → 12 + 1 = 13
Final answer: 1304

4. Lattice Method

Drawing a Grid: Draw a grid, split numbers into their individual digits, and multiply each digit, writing the results in the corresponding grid squares. Add the results along the diagonals.