## Multiply by 1-Digit Numbers

**Multiplication With Multiples of 10, 100, and 1,000**

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

= (3 × 8) × 10

= 24 × 10

= 240

= (9 × 2) × 100

= 18 × 100

= 1,800

= (5 × 6) × 1,000

= 30 × 1,000

= 30,000

**The Multiplication Algorithm**

Multiplication of a multidigit number by a one-digit number can be completed by using the Distributive Property with the expanded form of the multidigit number.

**Distributive Property of Multiplication Over Addition**

(a + b) × c = (a × c) + (b × c)

= (300 × 7) + (50 × 7) + (6 × 7)

= 2,100 + 350 + 42

= 2,492

This process can also be completed in a vertical arrangement as

The standard multiplication algorithm uses the steps shown in each method above but records the results in a more compact way.

**Teaching Model 21.1:** Multiply Multiples of 10, 100, and 1,000