2:40 PM Tue Feb 25 \( 36 \% \) \( \square \) \[ \square \] Chat M Me Can you do the same thing but with distributive property please Im begging you x Gauth AI Answer: 30 Explanation: The distributive property states that \( a(b+c)=a b+a c \). We can use this to solve \( 12 \times 2 \frac{1}{2} \) by breaking down the mixed number. \( 2 \frac{1}{2} \) can be rewritten as \( 2+\frac{1}{2} \). Then, applying the distributive property: Expl \( 12 \times \) \[ 12 \times\left(2+\frac{1}{2}\right)=(12 \times 2)+\left(12 \times \frac{1}{2}\right)=24+6=30 \] \( 12 \times \) Therefore, \( 12 \times 2 \frac{1}{2}=30 \). We've essentially distributed the multiplication of 12 across the sum of 2 and \( 1 / 2 \). Ask Gauth AI follow-up... Ask Gauth AI follow-up...

Let's solve the problem using the distributive property step by step. ### Problem We want to calculate \( 12 \times 2 \frac{1}{2} \) using the distributive property. ### Step 1: Convert the Mixed Number First, we need to convert the mixed number \( 2 \frac{1}{2} \) into an improper fraction or a sum of whole and fractional parts. \[ 2 \frac{1}{2} = 2 + \frac{1}{2} \] ### Step 2: Apply the Distributive Property Now, we can apply the distributive property, which states that \( a(b+c) = ab + ac \). In our case, \( a = 12 \), \( b = 2 \), and \( c = \frac{1}{2} \). \[ 12 \times (2 + \frac{1}{2}) = (12 \times 2) + (12 \times \frac{1}{2}) \] ### Step 3: Perform the Calculations Now, we will calculate each part: 1. Calculate \( 12 \times 2 \): \[ 12 \times 2 = 24 \] 2. Calculate \( 12 \times \frac{1}{2} \): \[ 12 \times \frac{1}{2} = 6 \] ### Step 4: Add the Results Now, we add the results from the two calculations: \[ 24 + 6 = 30 \] ### Conclusion Therefore, using the distributive property, we find that: \[ 12 \times 2 \frac{1}{2} = 30 \] This demonstrates how the distributive property can be used to simplify multiplication involving mixed numbers.