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Multiplying a 2-digit number by a 1-digit number

Tutor: Alice

# Multiplying a 2-digit number by a 1-digit number

## ​​In a nutshell

There are lots of different ways to multiply a two-digit number by a one-digit number, using both mental methods and written methods.

## Mental methods

Any method that can be done in your head without writing down working out is a mental method. Different mental methods can be used depending on the question.

### Breaking down

Numbers can be broken down into simpler calculations.

##### Example 1

What is $5\times40$?

Break $40$ down.

$40=4\times10$

Work out new calculation.

\begin {aligned} 5\times4\times10&=20\times10\\&=\underline{200}\end {aligned}

​​

Tip: Remember, to multiply by any multiple of ten, first times by the number in the tens column, then times by ten.

### Partitioning

#### Procedure

 1 Split the two-digit number into tens and ones. 2 Multiply the tens and ones by the one digit number separately. 3 Add the multiplied parts together.

##### Example 2

What is $64\times3$?​

Split $64$ into tens and ones.

$64=60+4$

Multiply both $60$ and $4$ by $3$ separately.

\begin {aligned}60\times3&=10\times6\times3\\&=10\times18\\&=180\\4\times3&=12\end{aligned}

$180+12=\underline{192}$

### Taking away

In some cases it may be simpler to multiply by a larger number close to the two-digit number and then take away lots of the one-digit number.

##### Example 3

What is $19\times4$

Instead, work out $20\times4$.

\begin {aligned}10\times2\times4&=10\times8\\&=80\end {aligned}​​

This is equivalent to $20$ lots of four. To work out $19$ lots of four, take one lot of four away.

$80-4=\underline{76}$

## FAQs - Frequently Asked Questions

### How do I multiply a two-digit number by a one-digit number in my head?

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