Question

Find the following product by using suitable properties $1938 \times 99$

Answer 1

Hint: Here we are asked to apply the appropriate property to find the product of$1938 \times 99$
We shall use the distributive property here. The distributive property’s work is to divide the operations so that we are able to solve the problem easily.
To use the distributive property, we need to look at the operation. Here, the operation will be minus. We have a formula for applying the distributive property for both addition and subtraction. Since the operation is subtraction, we shall apply the following formula.
Formula to be used:
\[a \times (b - c) = a \times b - a \times c\]

Complete step by step answer:
We are asked to apply some property to find the product of$1938 \times 99$
We shall use the distributive property here.
$1938 \times 99 = 1938 \times \left( {100 - 1} \right)$ (Here we split the number so that we can able to apply the distributive property)
                   $ = 1938 \times 100 - 1938 \times 1$(Here, we applied the distributive property)
                   \[ = 193800-1938\]
         \[ = 191862\]
Additional information:
        We often have three important properties of numbers: they are commutative property, associative property, and distributive property. The distributive property is the most often used property in mathematics and it is also called the distributive law of multiplication. The distributive property’s work is to divide the operations so that we are able to solve the problem easily.

Note: If we did not ask to apply the property, we can multiply the given numbers in the usual method. Since we are asked to apply the suitable property, we used the distributive property. The distributive property’s work is to divide the operations so that we are able to solve the problem easily.
      Also, if the operation is addition, we need to apply the formula of the distributive property\[a \times (b + c) = a \times b + a \times c\]