Question

How do you use the distributive property to rewrite and evaluate $6\left( 525 \right)$?

Answer 1

Hint: We will first understand the concept of left distribution law and right distribution law. And, then we will use it to evaluate $6\left( 525 \right)$. At first, we will expand 525 and write it as $\left( 525 \right)=\left( 500+20+5 \right)$ and thus we have evaluate $6\left( 525 \right)=6\left( 500+20+5 \right)$ and then we will use the left distribution property and take 6 inside the bracket and multiply it with each terms and then add them.

Complete answer:
We will first understand the concept of distributive property. Distributive property means to ‘distribute’ or divide something and give a part or share of something. Here, we have to distribute the multiplication terms over addition. There are two distributive properties, first one is left distributive property and right distributive property.
Left distributive property is given as: $a\left( b+c \right)=ab+ac$
Right distributive property is given as: $\left( b+c \right)a=ba+ca$
Since, we have to use distributive property to evaluate $6\left( 525 \right)$.
We will first expand 525 and write it as $\left( 525 \right)=\left( 500+20+5 \right)$.
$\Rightarrow 6\left( 525 \right)=6\left( 500+20+5 \right)$
Now, we will use the left distributive property and distribute 6 over expanded terms.
$\Rightarrow 6\left( 525 \right)=6\left( 500 \right)+6\left( 20 \right)+6\left( 5 \right)$
Now, we will simplify the above expression to obtain an answer.
$\Rightarrow 6\left( 525 \right)=3000+120+30$
$\Rightarrow 6\left( 525 \right)=3150$
Hence, the value of $6\left( 525 \right)$ using the distributive property is 3150.
This is our required solution.

Note: Students are required to remember the distributive property and use then accordingly. Also note that even if division is inverse of multiplication the distributive law only holds true in case of division, when the dividend is distributed or broken down.