Multi-Digit Multiplication

Multiplication and Place Value#

Multiplication is one of the four fundamental operations in mathematics, and in Grade 4 you will extend your multiplication skills to work with much larger numbers — up to four-digit numbers. The key to multiplying large numbers is understanding place value.

What Is Place Value?#

Every digit in a number has a place value based on its position. In the number 3,472:

• 3 is in the thousands place → value: 3,000
• 4 is in the hundreds place → value: 400
• 7 is in the tens place → value: 70
• 2 is in the ones place → value: 2

Connecting Multiplication to Place Value#

When you multiply a large number, you are really multiplying each digit by its place value and adding the results. For example, 3 × 2,000 is the same as 3 × 2 × 1,000 = 6,000.

This understanding is the foundation for all multi-digit multiplication strategies.

Mental Math with Multiplication#

Using place value, you can solve many problems mentally:

• 4 × 300 → Think: 4 × 3 = 12, then × 100 = 1,200
• 6 × 5,000 → Think: 6 × 5 = 30, then × 1,000 = 30,000
• 7 × 80 → Think: 7 × 8 = 56, then × 10 = 560

Properties of Multiplication#

Commutative property: 4 × 6 = 6 × 4 (order dösn't change the product)

Associative property: (2 × 3) × 4 = 2 × (3 × 4) (grouping dösn't change the product)

Distributive property: 3 × (4 + 2) = (3 × 4) + (3 × 2) = 12 + 6 = 18

The distributive property is especially important for multi-digit multiplication — it allows you to break apart a factor, multiply each part, and add the results. This is the foundation of the area model and partial products strategies.