# Multiplying numbers by one digit and two-digit numbers

## Multiplication

Multiplication is really just a process of **repeated addition**.

4 = 3 lots of 4 (or 4 + 4 + 4) = 12

This **array** shows 3 rows of 4.

Multiplication requires knowledge of the **times tables**.

The word **product** is used to represent the result of multiplication: factor x factor = product

## Strategies for mental multiplication

To work out multiplication calculations **mentally**, it is easiest to work with the **largest place value columns first**, followed by the other columns.

Example:

472 x 6 = (400 x 6) + (70 x 6) + (2 x 6)

= 2 400 + 420 + 12

= 2 832

## Written multiplication (short form)

In written multiplication problems, we work with the **lowest place value columns first** and then work progressively higher. It is important to keep your place value columns clear and neat. It will often be necessary to trade a (tens) digit as you go along.

Example:

**Step 1:** (Units column) 6 x 2 = 12 2 recorded in Units

1 (ten) traded to Tens

**Step 2:** (Tens column) 6 x 7 (+ 1 traded) = 43 3 recorded in Tens

4 (tens) traded to Hundreds

**Step 3:** (Hundreds column) 6 x 4 (+ 4 traded) = 28 8 recorded in Hundreds

2 (tens) traded to Thousands

**Answer:** 2 832

## Written multiplication (extended forms)

**Answer:** 2 832

## Working with two-digit numbers

The above example should not be confused with the algorithm used when the multiplication involves two **multi-digit factors**.

**Answer:** 8 424