65×7 in distributive property
The Correct Answer and Explanation is :
The correct answer is: 455
To solve ( 65 \times 7 ) using the distributive property, we can break down the number ( 65 ) into more manageable parts. The distributive property states that ( a(b + c) = ab + ac ). Here’s how we can apply this property:
- Break down the number: We can express ( 65 ) as ( 60 + 5 ). This allows us to distribute ( 7 ) to both parts of the sum. [
65 \times 7 = (60 + 5) \times 7
] - Distribute ( 7 ): Next, we apply the distributive property: [
(60 + 5) \times 7 = 60 \times 7 + 5 \times 7
] - Calculate each part:
- First, calculate ( 60 \times 7 ):
[
60 \times 7 = 420
] - Next, calculate ( 5 \times 7 ):
[
5 \times 7 = 35
]
- Combine the results: Now, we add the two products together:
[
420 + 35 = 455
]
So, the answer to ( 65 \times 7 ) is ( 455 ).
Explanation of the Distributive Property
The distributive property is a fundamental concept in arithmetic that allows us to simplify multiplication involving addition. By breaking a larger number into smaller, easier-to-handle parts, we can perform calculations that are often simpler and less prone to errors. This technique is particularly useful in mental math, where we might not have a calculator handy.
In our example, we chose to break ( 65 ) into ( 60 ) and ( 5 ) because ( 60 ) is a multiple of ( 10 ), making ( 60 \times 7 ) straightforward. By distributing ( 7 ) across both parts, we leverage our understanding of basic multiplication facts to arrive at the total more efficiently. This method not only aids in calculation but also deepens our understanding of how numbers relate to one another. Thus, the distributive property serves as a powerful tool in arithmetic and algebra, helping to simplify problems and enhance computational fluency.