Distributive property of 12×7=
The Correct Answer and Explanation is :
The correct answer is: 84
The distributive property states that for any numbers ( a ), ( b ), and ( c ), the equation ( a(b + c) = ab + ac ) holds true. This property allows us to break down complex multiplication problems into simpler parts.
To apply the distributive property to the multiplication of ( 12 \times 7 ), we can express 12 in a form that makes the multiplication easier. We can break down 12 into two simpler components, for instance, ( 10 + 2 ). Thus, we can rewrite the original multiplication as follows:
[
12 \times 7 = (10 + 2) \times 7
]
Now, using the distributive property, we distribute ( 7 ) across both ( 10 ) and ( 2 ):
[
(10 + 2) \times 7 = 10 \times 7 + 2 \times 7
]
Calculating each part gives:
[
10 \times 7 = 70
]
[
2 \times 7 = 14
]
Now we can add the two results together:
[
70 + 14 = 84
]
Therefore, ( 12 \times 7 = 84 ).
The distributive property is particularly useful in mental math and simplifying computations, especially when dealing with larger numbers. By breaking down numbers into smaller, more manageable parts, we can perform calculations more easily and accurately. It also emphasizes the relationship between addition and multiplication, illustrating how the two operations can work together.
In summary, the distributive property not only simplifies calculations like ( 12 \times 7 ) but also reinforces foundational arithmetic principles. It is a versatile tool that can be applied in various mathematical contexts, making it an essential concept for learners of all ages.