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# Use the properties of the whole number and simplify $50\times 102$ .

Last updated date: 14th Jul 2024
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Hint: For solving these problems, we need to have a clear understanding about the concept of whole numbers and their various properties. Using the properties of multiplication, we can easily solve $50\times 102$ and get to the correct answer.

$0,11,25,36,999,1200,\text{ }etc.$
The sum and product of two whole numbers will be the same whatever the order they are added or multiplied in is called the commutative property of addition and multiplication, i.e., if x and y are two whole numbers, then $x+y=y+x$ and $x\times y\text{ }=\text{ }y\times x$ .
Associative property states that when whole numbers are being added or multiplied as a set, they can be grouped in any order, and the result will be the same, i.e. if x, y and z are whole numbers then $x+\left( y+z \right)=\left( x+y \right)\text{+}z$ and $x\times \left( y\times z \right)=\left( x\times y \right)\times z$ .
$x\times \left( y+z \right)=\left( x\times y \right)+\left( x\times z \right)$
$\Rightarrow 50\times 102=50\times \left( 100+2 \right)=50\times 100+50\times 2=5000+100=5100$
Hence, by employing the properties of whole numbers we get that the answer to the given question is $5100$ .