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 times larger than the previous one.

$$10 units make a ten, $$10 tens make a hundred, $$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 $$6×7?

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

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

Let's see how.

$$6×70

$$6×70 is the same as $$6×(7×10) which we can write as $$6×7×10

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

$$6×7×10=42×10=420

 

$$6×700

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

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

 

$$60×70

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

 

Worked Examples

Question 1

 

Question 2

 

Question 3