Teaching Models

Multiply by One-Digit Numbers

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 it would be 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: 362 × 8 = (300 + 60 + 2) × 8
= (300 × 8) + (60 × 8) + (2 × 8)
= 2,400 + 480 + 16
= 2,896

This process can also be completed in a vertical arrangement as follows.

Vertical example

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

Annotated 362x8

To multiply a multidigit number by a two-digit number, the algorithm is expanded.
Think: 28 × 362 = (20 × 362) + (8 × 362)

Vertical example 28x362

Teaching Model 6.4: Multiply Two-Digit Numbers by One-Digit Numbers


Houghton Mifflin Math Grade 4