Question

use tools jeeran is making a rectangular banner for school. the dimensions of the banner are \\(1\frac{1}{2}\\) yards by \\(1\frac{3}{4}\\) yards. what is the area of the banner? use the visual model to show the area. then write an equation to model the problem.

Explanation:

Step1: Convert mixed numbers to fractions

Convert $1\frac{1}{2}$ to $\frac{3}{2}$ and $1\frac{3}{4}$ to $\frac{7}{4}$.

Step2: Apply area formula for rectangle

Area = length $\times$ width, so calculate $\frac{3}{2} \times \frac{7}{4}$.

Step3: Multiply numerators and denominators

$\frac{3 \times 7}{2 \times 4} = \frac{21}{8}$

Step4: Convert to mixed number

$\frac{21}{8} = 2\frac{5}{8}$

Answer:

The area of the banner is $2\frac{5}{8}$ square yards. The equation modeling the problem is $1\frac{1}{2} \times 1\frac{3}{4} = 2\frac{5}{8}$.

For the visual model (the given rectangle divided into 4 smaller rectangles):

• Divide the length side into $1 + \frac{1}{2}$ and the width side into $1 + \frac{3}{4}$.
• The four smaller rectangles have areas: $1 \times 1 = 1$, $1 \times \frac{3}{4} = \frac{3}{4}$, $\frac{1}{2} \times 1 = \frac{1}{2}$, $\frac{1}{2} \times \frac{3}{4} = \frac{3}{8}$.
• Summing these: $1 + \frac{3}{4} + \frac{1}{2} + \frac{3}{8} = \frac{8}{8} + \frac{6}{8} + \frac{4}{8} + \frac{3}{8} = \frac{21}{8} = 2\frac{5}{8}$, which matches the calculated area.