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‌‌Find‌ ‌$285\times‌ ‌98$‌ ‌using‌ ‌distributive‌ ‌property?‌ ‌

Last updated date: 24th Jul 2024
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Hint: In this problem we have to calculate the product of the two given numbers by using the distribution law of multiplication. Distribution law of multiplication says that “If $a$, $b$, $c$ are the three number then the result of $a\left( b\pm c \right)$ will be $ab\pm ac$”. To use the distributive property, we need to convert any one of the numbers as a sum or difference of two numbers such that our multiplication or calculation will become easier. In the given problem we have the numbers $285$, $98$. From both the given numbers when we write $98$ as $100-2$, then our calculation will be easier. So, we are going to the number $98$ as $100-2$ and use the distributive property to get the result.

Complete step by step solution:
Given $285\times 98$.
In the above expression we have the numbers $285$, $98$. We are going to write the number $98$ as $100-2$ in order to use the distributive property. Hence the given value will be
$\Rightarrow 285\times 98=285\left( 100-2 \right)$
From the distribution law of the multiplication, we can write $a\left( b-c \right)=ab-ac$. From this we can write the above value as
$\Rightarrow 285\times 98=285\times 100-285\times 2$
Simplifying the above equation, then we will get
  & \Rightarrow 285\times 98=28500-570 \\
 & \Rightarrow 285\times 98=27930 \\
Hence the result of the given value $285\times 98$ is $27930$.

Note: In this above solution we have written $98$ as $100-2$. There are several possibilities to solve this problem. We can use $98=90+8$, $285=290-5$, $285=280+5$ etc. All these substitutions are not easy as $98=100-2$ in calculations. So, we have used $98=100-2$ only for better and easy simplification.