Multi-Digit Multiplication

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Answer Key & Explanations

Multi-Digit Multiplication · Grade 5 · Worksheet 3

1. A rectangular garden is drawn on a grid where each unit square represents 1 square meter. The garden has vertices at coordinates (2, 1), (8, 1), (8, 5), and (2, 5). What is the area of the garden in square meters? Answer: 24 Solution: Identify the length from the x-coordinates. The bottom vertices are at (2,1) and (8,1). The difference in x-coordinates is 8 - 2 = 6.
   Full step-by-step solution

   Step 1: Identify the length from the x-coordinates. The bottom vertices are at (2,1) and (8,1). The difference in x-coordinates is 8 - 2 = 6. So the length is 6 meters. Step 2: Identify the width from the y-coordinates. The left vertices are at (2,1) and (2,5). The difference in y-coordinates is 5 - 1 = 4. So the width is 4 meters. Step 3: Calculate the area using the formula: area = length × width. Step 4: Multiply: 6 × 4 = 24. The area of the garden is 24 square meters.

2. A rectangular swimming pool is drawn on a coordinate grid where each unit represents 1 meter. The pool has vertices at coordinates (3, 2), (15, 2), (15, 8), and (3, 8). What is the area of the pool in square meters? Answer: 72 Solution: Find the length of the rectangle by calculating the horizontal distance between the x-coordinates: 15 - 3 = 12 meters Find the width of the rectangle by calculating the vertical distance between the y-coordinates: 8 - 2 = 6 meters Calculate the area using the formula: area = length × width Area…
   Full step-by-step solution

   Step 1: Find the length of the rectangle by calculating the horizontal distance between the x-coordinates: 15 - 3 = 12 meters Step 2: Find the width of the rectangle by calculating the vertical distance between the y-coordinates: 8 - 2 = 6 meters Step 3: Calculate the area using the formula: area = length × width Step 4: Area = 12 × 6 = 72 square meters The answer is 72.

3. 2.5 × 3.4 = ? Answer: 8.5 Solution: Multiply 2.5 × 3.4 as if they were whole numbers: 25 × 34 25 × 30 = 750 25 × 4 = 100 750 + 100 = 850 Count the decimal places: 2.5 has 1 decimal place, 3.4 has 1 decimal place, so total decimal places = 2 Place the decimal point in 850 to get 2 decimal places: 8.50 Simplify: 8.50 = 8.5 The…
   Full step-by-step solution

   Step 1: Multiply 2.5 × 3.4 as if they were whole numbers: 25 × 34 Step 2: 25 × 30 = 750 Step 3: 25 × 4 = 100 Step 4: 750 + 100 = 850 Step 5: Count the decimal places: 2.5 has 1 decimal place, 3.4 has 1 decimal place, so total decimal places = 2 Step 6: Place the decimal point in 850 to get 2 decimal places: 8.50 Step 7: Simplify: 8.50 = 8.5 The answer is 8.5.

4. Ben is packing eggs for the farmers market. Each carton holds 317 eggs, and Ben filled 27 cartons. How many eggs did Ben pack in total? Answer: 8559 Solution: Find the number of eggs per carton: 317. Find the number of cartons: 27. Multiply: 317 × 27 = 8559.
   Full step-by-step solution

   Step 1: Find the number of eggs per carton: 317. Step 2: Find the number of cartons: 27. Step 3: Multiply: 317 × 27 = 8559. The answer is 8559 eggs.

5. 847 × 56 = ? Answer: 47432 Solution: Multiply 847 by the ones digit of 56, which is 6. 847 × 6 = 5,082 Multiply 847 by the tens digit of 56, which is 5 (representing 50). 847 × 50 = 42,350 Add the two partial products together.
   Full step-by-step solution

   Step 1: Multiply 847 by the ones digit of 56, which is 6. 847 × 6 = 5,082 Step 2: Multiply 847 by the tens digit of 56, which is 5 (representing 50). 847 × 50 = 42,350 Step 3: Add the two partial products together. 5,082 + 42,350 = 47,432 The final answer is 47,432.

6. A rectangular prism is drawn with dimensions 12 cm by 8 cm by 5 cm. What is the volume of this prism in cubic centimeters? Answer: 480 Solution: The formula for volume of a rectangular prism is length × width × height Multiply the length and width: 12 × 8 = 96 Multiply that result by the height: 96 × 5 = 480 The volume is 480 cubic centimeters Final answer: 480
   Full step-by-step solution

   Step 1: The formula for volume of a rectangular prism is length × width × height Step 2: Multiply the length and width: 12 × 8 = 96 Step 3: Multiply that result by the height: 96 × 5 = 480 Step 4: The volume is 480 cubic centimeters Step 5: Final answer: 480

7. 1,729 × 85 = ? Answer: 146965 Solution: Multiply 1,729 by the ones digit of 85, which is 5. 1,729 × 5 = 8,645 Multiply 1,729 by the tens digit of 85, which is 8 (representing 80). 1,729 × 80 = 138,320 Add the two partial products together.
   Full step-by-step solution

   Step 1: Multiply 1,729 by the ones digit of 85, which is 5. 1,729 × 5 = 8,645 Step 2: Multiply 1,729 by the tens digit of 85, which is 8 (representing 80). 1,729 × 80 = 138,320 Step 3: Add the two partial products together. 8,645 + 138,320 = 146,965 The final answer is 146,965.

8. 789 × 56 = ? Answer: 44184 Solution: Multiply 789 by the ones digit of 56, which is 6. 789 × 6 = 4,734 Multiply 789 by the tens digit of 56, which is 5 (representing 50). 789 × 50 = 39,450 Add the two partial products together.
   Full step-by-step solution

   Step 1: Multiply 789 by the ones digit of 56, which is 6. 789 × 6 = 4,734 Step 2: Multiply 789 by the tens digit of 56, which is 5 (representing 50). 789 × 50 = 39,450 Step 3: Add the two partial products together. 4,734 + 39,450 = 44,184 The final answer is 44,184.