Question

Match the following:

• A. $3582$
• B. $299$
• C. $7147$
• D. $248$

Answer 1

Let's use the product of sum property here to simplify the sums given.
$A.8\times (20+5+6)$
Using the property of products of sum:

$\Rightarrow 8\times (20+5+6)=8\times 20+8\times 5+8\times 6$
$\Rightarrow 8\times (20+5+6)=160+40+48$
$\Rightarrow 8\times (20+5+6)=248$

$B.(6+8+9)\times 13$
Using the commutative property of multiplication:
$\Rightarrow (6+8+9)\times 13=13\times (6+8+9)$
And, using the property of sum of products:

$\Rightarrow 13\times (6+8+9)=13\times 6+13\times 8+13\times 9$
$\Rightarrow 13\times (6+8+9)=78+104+117$
$\Rightarrow 13\times (6+8+9)=299$

$C.9\times 398$
Here, we can either find the product using the long multiplication method or by using product of sums.
For product of sums we can write $398=300+90+8$
And, hence the product becomes
$9\times (300+90+8)$
And, using the product of sums:

$\Rightarrow 9\times (300+90+8)=9\times 300+9\times 90+9\times 8$
$\Rightarrow 9\times 300+9\times 90+9\times 8=2700+810+72$
$\Rightarrow 9\times 300+9\times 90+9\times 8=3582$
$\Rightarrow 9\times 398=3582$

D. $7\times 1021$
Let's use the product of sums method here.
For that, we can write $1021=1000+20+1$
So, the product becomes: $7\times (1000+20+1)$
Now, using the product of sums method:

$\Rightarrow 7\times (1000+20+1)=7\times 1000+7\times 20+7\times 1$
$\Rightarrow 7\times 1000+7\times 20+7\times 1=7000+140+7$
​​​​​​$\Rightarrow 7\times 1000+7\times 20+7\times 1=7147$
$\Rightarrow 7\times 1021=7147$