## 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.

Examples: 3 × 80 = 3 × (8 × 10)
= (3 × 8) × 10
= 24 × 10
= 240
9 × 200 = 9 × (2 × 100)
= (9 × 2) × 100
= 18 × 100
= 1,800
5 × 6,000 = 5 × (6 × 1,000)
= (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

When two addends are multiplied by a factor, the product is the same as if each addend were multiplied by the factor and the products were added.
(2 + 3) × 4 = (2 × 4) + (3 × 4)
(a + b) × c = (a × c) + (b × c)
Example: 356 × 7 = (300 + 50 + 6) × 7
= (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