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.
(a × b) × c = (a × c) + (b × c)
= (300 × 8) + (60 × 8) + (2 × 8)
= 2,400 + 480 + 16
= 2,896
This process can also be completed in a vertical arrangement as follows.
The standard multiplication algorithm uses the steps shown in each method above, but records the results in a more compact way.
To multiply a multidigit number by a two-digit number, the algorithm is expanded.
Think: 28 × 362 = (20 × 362) + (8 × 362)
Teaching Model 6.4: Multiply Two-Digit Numbers by One-Digit Numbers