# Multiplying numbers by one digit and two-digit numbers

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## 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

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

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

## Working with two-digit numbers

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

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### Question 1/5

1. What is a good strategy for working out written multiplication calculations?

 Multiply the numbers by 10 to make them larger Work with the largest place value columns first Work with the lowest place value columns first Divide the numbers by 10 to make them smaller

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