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

Example 2

What is $$64\times3$$?​

Split $$64$$ into tens and ones.

$$64=60+4$$

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

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

Add the parts together.

$$180+12=\underline{192}$$

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.

​$$80-4=\underline{76}$$