## Multiply by Two-Digit Numbers

When multiplying a one-digit number by a multiple of 10, 100, or 1,000, the Associative Property makes it easier to complete the multiplication mentally.

Examples:

= (3 × 8) × 10

= 24 × 10

= 240

= (9 × 2) × 100

= 18 × 100

= 1,800

= (5 × 6) × 1,000

= 30 × 1,000

= 30,000

Such multiplications can be extended to include multiplying a multiple of 10 by a multiple of 10 or 100. In this process both the Associative and Commutative properties are used.

Examples:

= (3 × 10) × (8 × 10)

= 3 × (10 × 8) × 10

= 3 × (8 × 10) × 10

= (3 × 8) × (10 × 10)

= 24 × 100

= 2,400

= (9 × 10) × (2 × 100)

= 9 × (10 × 2) × 100

= 9 × (2 × 10) × 100

= (9 × 2) × (10 × 100)

= 18 × 1,000

= 18,000

These products can be found by first multiplying the leading digits and then writing the total number of zeros in the factors after that product.

Examples:

Think: 3 × 8 = 24. There are 2 zeros.

Write: 2,400

Think: 9 × 2 = 18. There are 3 zeros.

Write: 18,000

**Estimating Products**

When estimating products involving a one-digit factor and a multidigit factor, round the multidigit factor to the nearest multiple of 10, 100, or 1,000 with only one nonzero digit. Then multiply.

Examples:

Round:

Multiply:

7 × 8,000

(7 × 8) × 1,000

56,000

Round:

Multiply:

5 × $40

(5 × $4) × 10

$200

**Teaching Model 7.2:** Estimate Products