# What is the value of 555 $\times$ 193 – 555 $\times$ 93 ?(a) 555,931(b) 1,210,321(c) 53,912(d) 55,500

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Hint: To solve this question in no time we can use elementary property of multiplication called ‘Removing a common factor’ which states that If we are given an expression as $(a\times b)+(a\times c)$ then it can also be expressed as $a\times (b+c)$ by taking $a$ common from the given expression.

We will apply an elementary property of multiplication to solve this problem called ‘Removing a common factor’ but before that we’ll learn the ‘Distributive property’ of multiplication,
Distributive property: The multiplication of a number by a sum is equal to the sum of the multiplications of this number by each one of the amounts to be added.
According to the distributive property a $\times$ (b + c) will be equal to a $\times$ b + a $\times$ c.
Now ‘Removing a common factor’ property of multiplication,
Removing a common factor: This is the inverse property of the distributive property. If various addends have a common factor, we can transform the sum into a product by taking out this factor.
It states that if we are given an expression as $(a\times b)+(a\times c)$ then it can also be expressed as $a\times (b+c)$ .
Given question can be simplified using ‘Removing a common factor’ property,
Applying the above mentioned property we get,
$555\times 193-555\times 93=(555\times 193)-(555\times 93)$
We applied the brackets to the given equation following the basic rule of DMAS which states that in mathematical equations division should be done first followed by multiplication and then addition and subtraction.
$555\times 193-555\times 93=555\times (193-93)$
\begin{align} & 555\times 193-555\times 93=555\times (100) \\ & 555\times 193-555\times 93=555,00 \\ \end{align}
So, the correct answer is “Option D”.

Note: we can also solve this question by simple calculations like in equation a $\times$ b - a $\times$ c first, calculate a $\times$ b and then a $\times$ c, after that subtract second from first but don’t do this in that way it’ll consume a lot of time. Hence it is preferred to do in the way it’s shown.
And always remember to satisfy the rule of DMAS while calculations.