Question

Find the product of $8739\times 102$ using distributive property.

Answer 1

Hint: In this question, we are given two numbers and we have to find the product of them using distributive property. Distributive property helps us in ease the calculations. As we can see, both 8739 and 102 are large numbers and their multiplication is difficult, so we will use distributive property for easing our calculations. We will split 102 into 100 and 2 and then use distributive property. Distributive property is given by:
\[a\times \left( b+c \right)=\left( a\times b \right)+\left( a\times c \right)\]
Where, a, b, c are any three numbers.

Complete step by step answer:
We are given numbers as 8739 and 102. We have to find their product. To ease our calculations, we will first split one of the numbers and then use distributive property to find the product. As we can see, splitting 8739 will do us no good, that is, it will not ease our calculations. So, let us split 102 as 100+2. Since, multiplication of any number by 100 and 2 is easy, we will use it to find products.
Now, we get $8739\times 102$ as $8739\times \left( 100+2 \right)$.
As we know, \[a\times \left( b+c \right)=\left( a\times b \right)+\left( a\times c \right)\] by distributive property. Hence, applying it on above numbers we get:
\[8739\times \left( 100+2 \right)=\left( 8739\times 100 \right)+\left( 8739\times 2 \right)\]
Solving $\left( 8739\times 100 \right)\text{ and }\left( 8739\times 2 \right)$ separately we get:
\[\left( 8739\times 100=873900 \right)\text{ and }\left( 8739\times 2=17478 \right)\]
Adding both of them we get:
\[\Rightarrow 873900+17478=891378\]
Thus, we have performed operations as under:
\[\begin{align}
  & 8739\times 102=8739\times \left( 100+2 \right)=\left( 8739\times 100 \right)+\left( 8739\times 2 \right) \\
 & \Rightarrow 873900+17478 \\
 & \Rightarrow 891378 \\
\end{align}\]

Hence, product of 8739 and 102 is 891378.

Note: Students can perform normal calculations to verify their answer. For using distributive property students should only split the number which will ease the calculation. We can see splitting 8739 to 8000 and 739, multiplication is still difficult which is why we split 102 to 100 and 2 as multiplication of any number by 100 or 2 is easy. If we were given number as 98, we could also use difference of 100 and 2 and use distributive property as:
\[a\times \left( b-c \right)=\left( a\times b \right)-\left( a\times c \right)\]
Keep in mind the order should not get changed.