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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
            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


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Question 1/5

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

Divide the numbers by 10 to make them smaller

Work with the largest place value columns first

Multiply the numbers by 10 to make them larger

Work with the lowest place value columns first

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