Question

1. write a simplified expression for the area of the rectangle. 12x - 6 in 6 1/4 in

Explanation:

Step1: Convert mixed number to improper fraction

The width is \(6\frac{1}{4}=\frac{6\times4 + 1}{4}=\frac{25}{4}\)

Step2: Use the area formula for a rectangle \(A=\text{length}\times\text{width}\)

\(A=(12x - 6)\times\frac{25}{4}\)

Step3: Apply the distributive property \(a(b + c)=ab+ac\)

\(A = 12x\times\frac{25}{4}-6\times\frac{25}{4}\)

Step4: Simplify each term

For \(12x\times\frac{25}{4}\), \(\frac{12x\times25}{4}=75x\)
For \(6\times\frac{25}{4}\), \(\frac{6\times25}{4}=\frac{150}{4}=\frac{75}{2}\)

Answer:

\(75x-\frac{75}{2}\) square inches