Multiplication patterns over increasing place values

Understanding Place Values

• Units (Ones): The digit’s value is based on its position in the number, such as 1, 10, 100, etc.
• Tens: Multiplying numbers in the tens place, e.g., 20, 30.
• Hundreds: Multiplying numbers in the hundreds place, e.g., 100, 200.

Patterns in Multiplication

Multiplying by 10: Each time you multiply by 10, the digits shift one place to the left. For example:

• 3×10=30
• 3×100=300

Multiplying by 100: Each time you multiply by 100, the digits shift two places to the left. For example:

• 4×100=400
• 4×1000=4000

Patterns in Multiplying Larger Numbers

• Multiplying by 2, 3, 4, etc.: Patterns in products of larger numbers are observed by noticing how the product increases with each multiplier. For example:

• 5×20=100
• 5×30=150

Pattern: The product increases by 50 for each increase of 10 in the multiplier.

Using Place Value to Simplify Multiplication

Breaking Down Numbers: When multiplying large numbers, break them down into smaller place values:

23 × 4

Break down 23 into 20+3:

( 20 × 4 ) + ( 3 × 4 ) = 80 + 12 = 92

Exploring Multiplication Patterns

Patterns in Multiplying by 5: Products always end in 0 or 5. For example:

• 5×4=20
• 5×7=35

Patterns in Multiplying by 9: The sum of the digits in the product always equals 9. For example:

9 × 3 = 27 ( 2 + 7 = 9 )

9 × 4 = 36 ( 3 + 6 = 9 )

Learn with an example

Let’s practice!🖊️