Question

Find \[15 \times 68\] using distributive property.

Answer 1

Hint: In this particular question split one of the number, into sum or difference of two different numbers and then apply distributive property which states that \[a \times \left( {b - c} \right) = a \times b - a \times c\] to find the solution of the problem.

Complete step-by-step answer:
According to the definition of distributive property, which states that the value of product of a number and difference of two numbers is calculated by multiplying each minuend and subtrahend with the number and then subtracting the products.
In mathematical terms, if x, y and z are the two numbers then \[y \times \left( {x - z} \right) = y \times x - y \times z\]
Where x and z are the minuend and subtrahend because the number y is multiplied by each x and y, and then the difference of the products is calculated on the RHS of the above equation.
So, now let us first spit one of the numbers in the given equation into the sum or difference of two numbers.
Let us write 68 as (70 – 2)
\[ \Rightarrow 15 \times 68 = 15 \times \left( {70 - 2} \right)\] (1)
So, now let us solve the above equation 1 by using distributive property by multiplying each number 70 and 2 by 15 and then calculating the difference.
\[ \Rightarrow 15 \times 68 = 15 \times 70 - 15 \times 2\]
Now solving the above equation.
\[ \Rightarrow 15 \times 68 = 1050 - 30 = 1020\]
Hence, \[15 \times 68 = 1020\]

Note:Whenever we face such types of questions the key concept is to recall the formula for the distributive property. In general, the distributive property of multiplication of integers is divided into two categories: over addition and over subtraction. Like if a, b and c are three integers then from distributive property of multiplication of integers over addition \[a \times \left( {b + c} \right) = a \times b + a \times c\] and from distributive property of multiplication of integers over subtraction \[a \times \left( {b - c} \right) = a \times b - a \times c\]. In the above equation we can also split the number 68 into a sum of two numbers as (60 + 8) after that