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Use the properties of the whole number and simplify \[50\times 102\] .

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Last updated date: 14th Jul 2024
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Answer
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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.

Complete step by step answer:
The whole numbers are the part of the number system in which it includes all the positive integers from zero to infinity. These numbers exist in the number line. Hence, they are all real numbers. We can say, all the whole numbers are real numbers, but not all the real numbers are whole numbers. The complete set of natural numbers along with zero are called whole numbers. The examples are:
\[0,11,25,36,999,1200,\text{ }etc.\]
The properties of whole numbers are based on arithmetic operations such as addition, subtraction, division and multiplication. Two whole numbers if added or multiplied will give a whole number itself. Subtraction of two whole numbers may not result in whole numbers, i.e., it can be an integer too. Also, division of two whole numbers results in getting a fraction in some cases.
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 \[x\times \left( y\times z \right)=\left( x\times y \right)\times z\] .
Distributive property of multiplication over the addition of whole numbers is:
\[x\times \left( y+z \right)=\left( x\times y \right)+\left( x\times z \right)\]
Employing this property to solve 50×102 we get that
$\Rightarrow 50\times 102=50\times \left( 100+2 \right)=50\times 100+50\times 2=5000+100=5100$
Hence, by employing the properties of whole numbers we get that the answer to the given question is $5100$ .

Note: These types of problems are pretty easy to solve, but one needs to be careful otherwise small misjudgements can lead to a totally different answer. We need to carefully employ the properties of whole numbers to get to the correct answer and not get confused between the properties as well.