Multi-Digit Multiplication

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Answer Key & Explanations

Multi-Digit Multiplication · Grade 5 · Worksheet 2

1. 1,847 × 63 = ? Answer: 116361 Solution: Multiply 1,847 by the ones digit of 63, which is 3. 1,847 × 3 = 5,541 Multiply 1,847 by the tens digit of 63, which is 6 (representing 60). 1,847 × 60 = 110,820 Add the two partial products together.
   Full step-by-step solution

   Step 1: Multiply 1,847 by the ones digit of 63, which is 3. 1,847 × 3 = 5,541 Step 2: Multiply 1,847 by the tens digit of 63, which is 6 (representing 60). 1,847 × 60 = 110,820 Step 3: Add the two partial products together. 5,541 + 110,820 = 116,361 The final answer is 116,361.

2. Mason is designing a rectangular mural on a coordinate grid where each unit represents 1 foot. The mural's corners are at coordinates (82, 37), (82, 247), (432, 247), and (432, 37). What is the area of the mural in square feet? Answer: 73500 Solution: Find the length by subtracting the x-coordinates of two points on the same horizontal side: 432 - 82 = 350 feet.
   Full step-by-step solution

   Step 1: Find the length by subtracting the x-coordinates of two points on the same horizontal side: 432 - 82 = 350 feet. Step 2: Find the width by subtracting the y-coordinates of two points on the same vertical side: 247 - 37 = 210 feet. Step 3: Calculate the area using the formula: Area = length x width = 350 x 210. Step 4: Multiply: 350 x 200 = 70,000; 350 x 10 = 3,500; 70,000 + 3,500 = 73,500 square feet. The area of the mural is 73,500 square feet.

3. 1,856 × 73 = ? Answer: 135488 Solution: Multiply 1,856 by 3 (units digit of 73) 1,856 × 3 = 5,568 Multiply 1,856 by 70 (tens digit of 73) 1,856 × 70 = 129,920 5,568 + 129,920 = 135,488 The answer is 135,488.
   Full step-by-step solution

   Step 1: Multiply 1,856 by 3 (units digit of 73) 1,856 × 3 = 5,568 Step 2: Multiply 1,856 by 70 (tens digit of 73) 1,856 × 70 = 129,920 Step 3: Add the partial products 5,568 + 129,920 = 135,488 The answer is 135,488.

4. A school is organizing a field trip and needs to transport 328 students. Each school bus can carry 46 students. How many buses are needed to transport all the students? Answer: 8 Solution: We have 328 students, and each bus can carry 46 students. We need to find how many buses are needed to transport all students. Divide the total number of students by the capacity of one bus.
   Full step-by-step solution

   Step 1: Understand the problem. We have 328 students, and each bus can carry 46 students. We need to find how many buses are needed to transport all students. Step 2: Divide the total number of students by the capacity of one bus. 328 ÷ 46 = ? Step 3: Perform the division. 46 × 7 = 322 328 − 322 = 6 So 328 ÷ 46 = 7 remainder 6. Step 4: Interpret the result. 7 full buses will carry 322 students, but there are 6 students left over. These 6 students also need a bus, so we need one more bus for them. Step 5: Total buses needed. 7 buses + 1 extra bus = 8 buses. Final answer: 8 buses are needed to transport all 328 students.

5. A rectangular solar panel array is drawn on a coordinate grid where each unit represents 1 centimeter. The array has corners at coordinates (125, 80), (125, 240), (385, 240), and (385, 80). What is the area of the solar panel array in square centimeters? Answer: 41600 Solution: Find the length of the rectangle by calculating the horizontal distance between the x-coordinates. The x-coordinates are 125 and 385, so length = 385 - 125 = 260 centimeters.
   Full step-by-step solution

   Step 1: Find the length of the rectangle by calculating the horizontal distance between the x-coordinates. The x-coordinates are 125 and 385, so length = 385 - 125 = 260 centimeters. Step 2: Find the width of the rectangle by calculating the vertical distance between the y-coordinates. The y-coordinates are 80 and 240, so width = 240 - 80 = 160 centimeters. Step 3: Calculate the area using the formula: area = length × width. Area = 260 × 160 = 41600 square centimeters. The area of the solar panel array is 41600 square centimeters.

6. 3,456 × 89 = ? Answer: 307584 Solution: Multiply 3,456 by the ones digit of 89, which is 9. 3,456 × 9 = 31,104 Multiply 3,456 by the tens digit of 89, which is 8 (representing 80). 3,456 × 80 = 276,480 Add the two partial products together.
   Full step-by-step solution

   Step 1: Multiply 3,456 by the ones digit of 89, which is 9. 3,456 × 9 = 31,104 Step 2: Multiply 3,456 by the tens digit of 89, which is 8 (representing 80). 3,456 × 80 = 276,480 Step 3: Add the two partial products together. 31,104 + 276,480 = 307,584 The final answer is 307,584.

7. 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.

8. Mere is designing a rectangular mural on a coordinate grid where each unit represents 1 centimeter. The mural's corners are at coordinates (140, 60), (140, 330), (560, 330), and (560, 60). What is the area of the mural in square centimeters? Answer: 113400 Solution: Find the length of the mural by calculating the horizontal distance between the x-coordinates. The x-coordinates are 140 and 560, so length = 560 - 140 = 420 centimeters.
   Full step-by-step solution

   Step 1: Find the length of the mural by calculating the horizontal distance between the x-coordinates. The x-coordinates are 140 and 560, so length = 560 - 140 = 420 centimeters. Step 2: Find the width of the mural by calculating the vertical distance between the y-coordinates. The y-coordinates are 60 and 330, so width = 330 - 60 = 270 centimeters. Step 3: Calculate the area using the formula: Area = length × width. Area = 420 × 270. First, multiply 420 × 200 = 84,000. Then, multiply 420 × 70 = 29,400. Add them together: 84,000 + 29,400 = 113,400 square centimeters. The area of the mural is 113,400 square centimeters.

9. A rectangular garden is drawn on a grid where each unit square represents 1 square meter. The garden has corners 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 corners are at (2,1) and (8,1). The length is 8 - 2 = 6 meters.
   Full step-by-step solution

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