Question

1. each small square in the graph paper represents 1 square unit. which expression is closest to the area of the rectangle, in square units? a. ( 5\frac{1}{2} \times 4\frac{1}{4} ) b. ( 4\frac{1}{2} \times 3\frac{1}{4} ) c. ( 4 \times 3 ) d. ( 5 \times 4 )

Explanation:

Step1: Analyze the rectangle's dimensions

From the graph, the length of the rectangle is close to 4.5 (or \(4\frac{1}{2}\)) and the width is close to 3.25 (or \(3\frac{1}{4}\))? Wait, no, looking at the options, let's re - check. Wait, the handwritten note has 5 and 3, but the options: Let's see the rectangle in the grid. Let's count the number of squares along length and width. If we look at the options, option B is \(4\frac{1}{2}\times3\frac{1}{4}\), option A is \(5\frac{1}{2}\times4\frac{1}{4}\), option C is \(4\times3\), option D is \(5\times4\). Wait, maybe the length is around \(4\frac{1}{2}\) (4.5) and width around \(3\frac{1}{4}\) (3.25). Let's calculate each option:

• Option A: \(5\frac{1}{2}\times4\frac{1}{4}=\frac{11}{2}\times\frac{17}{4}=\frac{187}{8} = 23.375\)
• Option B: \(4\frac{1}{2}\times3\frac{1}{4}=\frac{9}{2}\times\frac{13}{4}=\frac{117}{8}=14.625\)
• Option C: \(4\times3 = 12\)
• Option D: \(5\times4=20\)

Wait, maybe my initial analysis is wrong. Wait, the rectangle in the grid: let's count the number of squares. The length (horizontal) seems to be 4.5 (since it's between 4 and 5, closer to 4.5) and width (vertical) is 3.25 (between 3 and 4, closer to 3.25). But let's check the options again. Wait, maybe the length is 4.5 (\(4\frac{1}{2}\)) and width is 3.25 (\(3\frac{1}{4}\)), so option B. But wait, maybe the grid: each small square is 1 unit. Let's see the rectangle: the horizontal side: from the grid, if we count the number of squares, maybe 4.5 (like 4 and a half squares) and vertical side 3.25 (3 and a quarter squares). So the area is length × width. So \(4\frac{1}{2}\times3\frac{1}{4}\) which is option B. Wait, but let's check the other options. Option C is 12, option D is 20, option A is 23.375, option B is 14.625. If the actual area (by counting squares) is, say, if the rectangle is 4.5 units long and 3.25 units wide, then option B is the closest.

Wait, maybe I made a mistake in the grid. Let's look at the image again. The rectangle is drawn on the grid. The horizontal direction: how many squares? Let's see the numbers written: 5 and 3. Wait, the handwritten note has 5×3 = 15. But the options: let's recalculate the options:

Option A: \(5\frac{1}{2}\times4\frac{1}{4}=\frac{11}{2}\times\frac{17}{4}=\frac{187}{8}=23.375\)

Option B: \(4\frac{1}{2}\times3\frac{1}{4}=\frac{9}{2}\times\frac{13}{4}=\frac{117}{8}=14.625\)

Option C: \(4\times3 = 12\)

Option D: \(5\times4 = 20\)

If the actual area is around, say, 15 (from 5×3), then which is closest? 14.625 (option B) is closer to 15 than 12 (option C) or 20 (option D) or 23.375 (option A). So option B.

Step2: Compare the calculated values with the expected area

We calculated the values of each option. The expected area (from the grid, maybe around 15) is closest to the value of option B (\(4\frac{1}{2}\times3\frac{1}{4}=14.625\)) compared to the other options.

Answer:

B. \(4\frac{1}{2}\times3\frac{1}{4}\)