96 divided by 6 in distributive property
The Correct Answer and Explanation is:
To solve ( 96 \div 6 ) using the distributive property, we can break the number 96 into smaller, more manageable parts and then divide each part by 6. This process makes use of the distributive property of multiplication over addition or subtraction, which states that:
[
a(b + c) = ab + ac
]
In the context of division, the distributive property works similarly: you can split the dividend into parts, divide each part by the divisor, and then sum the results.
Step-by-Step Breakdown Using the Distributive Property:
- Start by breaking 96 into two smaller numbers:
We can break 96 into 60 and 36, because 60 + 36 = 96. These numbers are easier to divide by 6. [
96 = 60 + 36
] - Apply division to each part:
Now, apply the division to each of the two parts separately. Since we are dividing by 6, we divide both 60 and 36 by 6. [
\frac{96}{6} = \frac{60}{6} + \frac{36}{6}
] - Divide each part:
- ( \frac{60}{6} = 10 )
- ( \frac{36}{6} = 6 )
- Add the results:
Now, add the two results together: [
10 + 6 = 16
]
Thus, ( 96 \div 6 = 16 ).
Explanation:
The distributive property helps simplify division by breaking up larger numbers into smaller, more manageable components. Instead of directly dividing 96 by 6, we split 96 into 60 and 36, both of which are easier to divide by 6. After dividing each part separately and then adding the results, we arrive at the final answer.
This method can be especially helpful in mental math or when dealing with larger numbers. It illustrates how the distributive property can make complex division problems simpler by dividing the number into smaller, easier-to-handle parts.