Question

Find the product of largest 5-digit number and largest 3-digit number using distributive law.

Answer 1

Hint: In mathematics, the distributive property of binary operations generalizes the distributive law from Boolean algebra and elementary algebra. The distributive property lets you multiply a sum by multiplying each addend separately and then add the products.

Complete step-by-step answer:
Now, from the question,
Largest possible 5-digit number = 99999
And, largest possible 3-digit number = 999
Now according to distributive law,
$99999 \times (1000 - 1)$
$(99999 \times 1000) - (99999 \times 1)$
99899001 , which is the required answer of the question.
Thus, we have used distributive law for solving the above question.

Note: Commutative law – the commutative law states that we can swap numbers over and still get the same result (a + b = b + a)
Associative law – the associative law states that it doesn’t matter that how we group the numbers
 (a + b) + c = a + (b + c)
More on distributive
Given a set S and two binary operators $ * $ and + on S, the operation $ * $:
 is left distributive over + if, given any elements x, y and z of S,
$x * (y + z) = (x * y) + (x * z)$,
Is right distributive over + if, given elements x, y and z of S,
$(y + z) * x = (y * x) + (z * x)$, and
Is distributive over + if it is left and right distributive.
The operators used for example in this section are those of the usual addition (+) and multiplication (.)
If the operation denoted . is not commutative there is a distinction between left-distributivity and right-distributivity:
$a.(b \pm c) = a.b \pm a.c$ (left-distributive)
$(a \pm b).c = a.c \pm b.c$ (right-distributive)
In either case, the distributive property can be described in words as:
To multiply a sum (or difference) by a factor, each summand (or minuend and subtrahend) is multiplied by this factor and the resulting products are added (or subtracted). If the operation under parentheses (in this case, the multiplication) is commutative, then left-distributivity implies right-distributivity and vice versa, and one talks simply of distributivity.