Extending multiplication to larger numbers

 

When we looked at the 10 times tables, we discussed how important place value is because each column in the place value table is $10$10 times larger than the previous one.

$10$10 units make a ten, $10$10 tens make a hundred, $10$10 hundreds make a thousand and so on.

Let's build on that knowledge and discuss how we can use it to multiply larger numbers.

 

 

 

What is $6\times7$6×7?

As we know our multiplication fact of $6\times7$6×7 is $42$42.

We can use this to answer questions like $6\times70$6×70, or $6\times700$6×700 or even $60\times70$60×70. 

Let's see how.

$6\times70$6×70

$6\times70$6×70 is the same as $6\times\left(7\times10\right)$6×(7×10) which we can write as $6\times7\times10$6×7×10

As multiplication is commutative, we can complete this multiplication in any order we like, so as we know $6\times7$6×7 is $42$42, then the final multiplication is by $10$10 which is a final easy step. 

$6\times7\times10=42\times10=420$6×7×10=42×10=420

 

$6\times700$6×700

The same process can be applied to $6\times700.$6×700.

Rewrite (or imagine)	$6\times700$6×700	$=$=	$6\times7\times100$6×7×100
Do the $6\times7$6×7 component		$=$=	$42\times100$42×100
Then the multiplication of $100$100		$=$=	$4200$4200

 

$60\times70$60×70

Rewrite (or imagine)	$60\times70$60×70	$=$=	$6\times10\times7\times10$6×10×7×10
Regroup the multiplication by $10$10's		$=$=	$6\times7\times100$6×7×100
Do the $6\times7$6×7 component		$=$=	$42\times100$42×100
Complete the multiplication		$=$=	$4200$4200

 

Worked Examples

Question 1

 

Question 2

 

Question 3