Question

How do you use the distributive property to find $20 \times 12?$

Answer 1

Hint: As we know that distributive property simply states that “ multiplication distributed over addition”. It applies to the multiplication of the number with the sum or difference of two numbers. It holds true for multiplication over addition and subtraction. The distributive property can be written as $a(b + c) = ab + bc$.

Complete step by step answer:
As per the above question we have $20 \times 12$. In this question, we will first break down any number in the form of the sum of two different numbers and bring it to the general form of distributive formula.
So we can write $12$ as $10 + 2$. The new expression is $20\left( {10 + 2} \right)$.
 We know that distributive property is given as $a(b + c) = ab + bc$. On comparing it with the above expression, we have $a = 20,b = 10$ and $c = 2$.
So by applying the distributive property we can write the expression as $20(10 + 2) = 20 \times 10 + 20 \times 2$.
 On further solving it gives the value $200 + 40 = 240$.

Hence the required answer is $240.$

Note: Before solving this kind of question we must know the algebraic properties in order to solve easily. We should also take the proper care of positive and negative signs of the different terms while carrying out the multiplication. We should always try to break down the numbers in the easier form so that we can make the multiplication easier. It is also called to apply the distributive property to solve a product mentally.