Write Expressions

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Answer Key & Explanations

Write Expressions · Grade 5 · Worksheet 2

1. Noah is designing a rectangular playground that is divided into three equal rectangular sections. Each section measures 18 meters by 12 meters. Write a numerical expression that represents the total area of the entire playground, then calculate the total area. Answer: 648 Solution: Find the area of one rectangular section. Area of a rectangle = length x width = 18 m x 12 m = 216 square meters. Since there are 3 equal sections, multiply the area of one section by 3: 3 x 216.
   Full step-by-step solution

   Step 1: Find the area of one rectangular section. Area of a rectangle = length x width = 18 m x 12 m = 216 square meters. Step 2: Since there are 3 equal sections, multiply the area of one section by 3: 3 x 216. Step 3: Calculate 3 x 216: 200 x 3 = 600, 16 x 3 = 48, then 600 + 48 = 648. Step 4: The numerical expression is 3 x (18 x 12). Step 5: Verify: 18 x 12 = 216, then 3 x 216 = 648. The total area of the playground is 648 square meters.

2. Liam is building a rectangular garden box that is 2.4 meters long and 1.5 meters wide. He wants to surround it with a decorative border. How many meters of border does Liam need to go around the entire garden box? Answer: 7.8 Solution: To find the total length of the decorative border needed to go around the entire rectangular garden box, we need to calculate the perimeter of the rectangle. Recall the formula for the perimeter of a rectangle. The perimeter P is given by: P = 2 * (length + width) Identify the given measurements…
   Full step-by-step solution

   To find the total length of the decorative border needed to go around the entire rectangular garden box, we need to calculate the perimeter of the rectangle. Step 1: Recall the formula for the perimeter of a rectangle. The perimeter P is given by: P = 2 * (length + width) Step 2: Identify the given measurements from the problem. Length of the garden box = 2.4 meters Width of the garden box = 1.5 meters Step 3: Substitute the given values into the perimeter formula. P = 2 * (2.4 + 1.5) Step 4: Perform the addition inside the parentheses. 2.4 + 1.5 = 3.9 Step 5: Multiply the result by 2. P = 2 * 3.9 = 7.8 Step 6: State the final answer with the correct unit. Liam needs 7.8 meters of border to go around the entire garden box.

3. Liam is building a rectangular garden bed that is 3.75 meters long and 2.4 meters wide. He wants to put a decorative border around the entire garden. How many meters of border material does Liam need to buy? Answer: 12.3 Solution: To find the total length of border material needed, we need to calculate the perimeter of the rectangular garden bed. Identify the formula for the perimeter of a rectangle. The perimeter P of a rectangle is given by the formula: P = 2 * (length + width) Write down the given measurements.
   Full step-by-step solution

   To find the total length of border material needed, we need to calculate the perimeter of the rectangular garden bed. Step 1: Identify the formula for the perimeter of a rectangle. The perimeter P of a rectangle is given by the formula: P = 2 * (length + width) Step 2: Write down the given measurements. Length of the garden = 3.75 meters Width of the garden = 2.4 meters Step 3: Substitute the given values into the formula. P = 2 * (3.75 + 2.4) Step 4: Perform the addition inside the parentheses. First, add the length and width. 3.75 + 2.4 = 6.15 Step 5: Multiply the result by 2. P = 2 * 6.15 P = 12.30 Step 6: Write the final answer. Since 12.30 meters is the same as 12.3 meters, Liam needs to buy 12.3 meters of border material. Therefore, the final answer is 12.3.