Distributive property for 144 divided by 8

Distributive property for 144 divided by 8

The Correct Answer and Explanation is :

The correct answer is: 18

The distributive property is a fundamental principle in mathematics that states that when you multiply a number by a sum, you can distribute the multiplication across each addend in the sum. While it’s commonly used for multiplication, we can also apply its principles to division by rewriting the division problem.

Let’s examine ( 144 \div 8 ) using the distributive property by breaking down the number 144 into simpler components. We can express 144 as a sum of two numbers: 80 and 64. Thus, we can rewrite the division problem as follows:

[
144 \div 8 = (80 + 64) \div 8
]

Next, we can apply the distributive property:

[
(80 + 64) \div 8 = 80 \div 8 + 64 \div 8
]

Now, we can calculate each part separately:

1. Calculating ( 80 \div 8 ):
   [
   80 \div 8 = 10
   ]
2. Calculating ( 64 \div 8 ):
   [
   64 \div 8 = 8
   ]

Now, we can combine these results:

[
80 \div 8 + 64 \div 8 = 10 + 8 = 18
]

Thus, we find that ( 144 \div 8 = 18 ).

This method showcases how the distributive property allows us to simplify the division of larger numbers by breaking them down into more manageable components. Instead of performing a single division operation, we can utilize addition, which can be easier to handle mentally or on paper, especially with larger numbers. This flexibility in manipulating numbers is a powerful tool in arithmetic, demonstrating the interconnectedness of addition and multiplication/division. Understanding and applying the distributive property enhances computational efficiency and strengthens number sense.