Use multiplication and distributive property to find the quotient.
72 divided by 4?
The Correct Answer and Explanation is :
To find the quotient of ( 72 \div 4 ) using multiplication and the distributive property, we can approach the problem by breaking down the dividend (72) into manageable parts that are easier to divide.
Step 1: Understand the Division
The operation ( 72 \div 4 ) asks how many times 4 can fit into 72. We can think of 72 as a sum of numbers that can be easily divided by 4.
Step 2: Use the Distributive Property
We can express 72 as the sum of two numbers that are both divisible by 4. For instance, we can split 72 into ( 64 ) and ( 8 ):
[
72 = 64 + 8
]
Step 3: Apply the Distributive Property
Now, we can rewrite our division problem using the distributive property:
[
72 \div 4 = (64 + 8) \div 4
]
By the distributive property, we can separate this into two parts:
[
(64 \div 4) + (8 \div 4)
]
Step 4: Calculate Each Part
Now we can perform the division on each part:
- ( 64 \div 4 = 16 )
- ( 8 \div 4 = 2 )
Step 5: Add the Results
Now, we combine the results:
[
16 + 2 = 18
]
Conclusion
Thus, the quotient of ( 72 \div 4 ) is ( 18 ).
Summary of the Method
In this approach, we utilized the distributive property to break down a complex division into simpler parts. By expressing ( 72 ) as ( 64 + 8 ), we transformed the problem into two easier divisions. This method not only helps in obtaining the answer but also deepens the understanding of how numbers interact with division, particularly in terms of how they can be decomposed into smaller, manageable components. Understanding this principle is beneficial for tackling more complex arithmetic and aids in mental math.