EXT: Mixed Multiplications 2,4,8

We've already looked at our 2 times tables, our 4 times tables and our 8 times tables. Now we're going to look at the really cool relationship between these three sets of multiplication tables.

Let's start by watching this video:

 

x 2: Double

Multiplying a number by $2$2 is the same as doubling that number. For example, "double $5$5" would be the same as saying "$5\times2$5×2." This means that instead of $1$1 group of five, there are now $2$2 groups of five.

When we double the number of stars, we can write this mathematically as $5+5$5+5 or $5\times2$5×2 and our answer will be the same: $10$10!

 

x 4: Double, Double

What happens when we double the $2$2 groups in the last picture? Now we have $4$4 groups of $5$5! 

We know that in $2$2 groups there are $10$10 stars. So since we have doubled the number of groups, we need to double our answer. This means there are now $20$20 stars! 

Now we know $4$4 groups of $5$5 stars or $4\times5=20$4×5=20.

So multiplying a number by $4$4 is the same as doubling the number and then doubling the answer.

Another example 

What is $4\times7$4×7?

Think: Let's use the double, double strategy!

Do:

$2\times7$2×7	$=$=	$14$14	(This is $2$2 groups of $7$7)
$2\times14$2×14	$=$=	$28$28	(We've doubled our number of groups to $4$4)
So:
$4\times7$4×7	$=$=	$28$28

 

x 8: Double, Double, Double

Let's double the number of groups again. $4+4=8$4+4=8, so now we have $8$8 groups of $5$5 stars. Now we have $2$2 groups of $20$20, which means that there are $40$40 stars in total.

So now we know that $8$8 groups of $5$5 or $8\times5=40$8×5=40.

Example

What is $8\times3$8×3?

Think: This time we are going to use a double, double, double strategy.

$2\times3$2×3	$=$=	$6$6	(This is $2$2 groups of $3$3)
$2\times6$2×6	$=$=	$12$12	($2\times6$2×6 is the same as $4\times3$4×3)
$2\times12$2×12	$=$=	$24$24	(We've doubled our answer for a third time)
So:
$8\times3$8×3	$=$=	$24$24