Question

Q5. Find the product of the greatest 3- digit number and the greatest 2-digit
number . ( use distributive property )

Answer 1

Answer:

(i) greatest number of three digits = 999

and smallest number of five digits = 10000

Required product = 999 × 10000 = 9990000

(ii) greatest number of four digits = 9999

and the greatest number of three digits = 999

Required product = 9999 × 999

= 9999 × (1000-1)

= 9999 × 1000 - 9999 × 1 (using distributivity)

= (10000 - 1) × 1000 - (10000 - 1) × 1

= 10000 × 1000 - 1 × 1000 - 10000 + 1]

= 10000001 - 11000

= 9989001

Answer 2

Solution

Step ①, Finding the numbers

The first greatest 4-digit number is $10^{3}$. The greatest 3-digit number is smaller by 1, so the 3-digit number is $10^{3}-1$.

In the same manner, the greatest 2-digit number is $10^{2}-1$.

Step ②, Finding the product

$\text{(Given Number)}$

$=(10^{3}-1)\times (10^{2}-1)$

$=10^{3}(10^{2}-1)-1(10^{2}-1)\ \text{(Distributive Property)}$

$=10^{5}-10^{3}-10^{2}+1\ \text{(Expansion)}$

$=(10^{5}+1)-(10^{3}+10^{2})\ \text{(Commutative Property)}$

$=100001-1100$

$=\boxed{98901}$

This is the required answer.

Learn More

Commutative property: $a+b=b+a$

Associative property: $a+(b+c)=(a+b)+c$

Distributive property: $a(b+c)=ac+bc$

Identity property (Addition): $a+0=a$

Identity property (Multiplication): $a\times 1=a$