Question

7\\(\frac{1}{8}\\) m, 4 m. number sentence: \\(\boldsymbol{7\frac{1}{8} \times 4 = 28\frac{4}{8}}\\). area: \\(\boldsymbol{28\frac{4}{8}}\\)

Explanation:

Step1: Convert mixed number to improper fraction

The length is \( 7\frac{1}{8} \) m. Convert it to an improper fraction: \( 7\frac{1}{8}=\frac{7\times8 + 1}{8}=\frac{57}{8} \) m.

Step2: Calculate the area of the rectangle

The formula for the area of a rectangle is \( A = l\times w \), where \( l \) is the length and \( w \) is the width. Here, \( l=\frac{57}{8} \) m and \( w = 4 \) m. So, \( A=\frac{57}{8}\times4 \).
Simplify the calculation: \( \frac{57}{8}\times4=\frac{57\times4}{8}=\frac{57}{2}=28\frac{1}{2} \) (or we can also calculate it as \( 7\frac{1}{8}\times4=(7 + \frac{1}{8})\times4=7\times4+\frac{1}{8}\times4 = 28+\frac{4}{8}=28+\frac{1}{2}=28\frac{1}{2} \) square meters). The original number sentence had a mistake in the fraction part after multiplication, \( \frac{4}{8} \) simplifies to \( \frac{1}{2} \).

Answer:

Number Sentence: \( 7\frac{1}{8}\times4 = 28\frac{1}{2} \)
Area: \( 28\frac{1}{2} \) square meters (or \( \frac{57}{2} \) square meters)