Multi-Digit Multiplication

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Answer Key & Explanations

Multi-Digit Multiplication · Grade 5 · Worksheet 2

1. 2.5 × 0.4 = ? Answer: 1 Solution: Multiply the numbers as if they were whole numbers: 25 × 4 = 100 Count the decimal places in the original numbers: 2.5 has 1 decimal place, 0.4 has 1 decimal place Total decimal places = 1 + 1 = 2 Place the decimal point in the product: 100 becomes 1.00 1.00 simplifies to 1 The answer is 1.
   Full step-by-step solution

   Step 1: Multiply the numbers as if they were whole numbers: 25 × 4 = 100 Step 2: Count the decimal places in the original numbers: 2.5 has 1 decimal place, 0.4 has 1 decimal place Step 3: Total decimal places = 1 + 1 = 2 Step 4: Place the decimal point in the product: 100 becomes 1.00 Step 5: 1.00 simplifies to 1 The answer is 1.

2. A community center is organizing a charity run. They need to provide water bottles for 648 participants. If each case contains 24 water bottles, how many cases should they order to have enough for everyone? Answer: 27 Solution: Identify the total number of participants: 648 Identify the number of water bottles per case: 24 Divide the total participants by the number of bottles per case to find the number of cases needed: 648 ÷ 24 Perform the division: 24 × 27 = 648 Therefore, they need 27 cases.
   Full step-by-step solution

   Step 1: Identify the total number of participants: 648 Step 2: Identify the number of water bottles per case: 24 Step 3: Divide the total participants by the number of bottles per case to find the number of cases needed: 648 ÷ 24 Step 4: Perform the division: 24 × 27 = 648 Step 5: Therefore, they need 27 cases. The answer is 27.

3. A community center is organizing a summer reading program. They want to give each of the 48 participating children a reading kit that contains 15 books. How many books does the community center need to prepare for all the reading kits? Answer: 720 Solution: Identify the number of children: 48 Identify the number of books per kit: 15 Multiply to find the total number of books: 48 × 15 Calculate 48 × 10 = 480 Calculate 48 × 5 = 240 Add the partial products: 480 + 240 = 720 The answer is 720.
   Full step-by-step solution

   Step 1: Identify the number of children: 48 Step 2: Identify the number of books per kit: 15 Step 3: Multiply to find the total number of books: 48 × 15 Step 4: Calculate 48 × 10 = 480 Step 5: Calculate 48 × 5 = 240 Step 6: Add the partial products: 480 + 240 = 720 The answer is 720.

4. A community center is organizing a charity run and needs to provide water bottles for all participants. They have 48 cases of water, and each case contains 24 bottles. How many water bottles do they have in total? Answer: 1152 Solution: Identify the number of cases: 48 Identify the number of bottles per case: 24 Multiply to find the total number of bottles: 48 × 24 Break down the multiplication: 48 × 20 = 960 and 48 × 4 = 192 Add the partial products: 960 + 192 = 1152 The total number of water bottles is 1152.
   Full step-by-step solution

   Step 1: Identify the number of cases: 48 Step 2: Identify the number of bottles per case: 24 Step 3: Multiply to find the total number of bottles: 48 × 24 Step 4: Break down the multiplication: 48 × 20 = 960 and 48 × 4 = 192 Step 5: Add the partial products: 960 + 192 = 1152 Step 6: The total number of water bottles is 1152.

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. 1,247 × 68 = ? Answer: 84796 Solution: Multiply 1,247 by the ones digit of 68, which is 8. 1,247 × 8 = 9,976 Multiply 1,247 by the tens digit of 68, which is 6 (representing 60). 1,247 × 60 = 74,820 Add the two partial products together.
   Full step-by-step solution

   Step 1: Multiply 1,247 by the ones digit of 68, which is 8. 1,247 × 8 = 9,976 Step 2: Multiply 1,247 by the tens digit of 68, which is 6 (representing 60). 1,247 × 60 = 74,820 Step 3: Add the two partial products together. 9,976 + 74,820 = 84,796 The final answer is 84,796.

7. 2,345 × 78 = ? Answer: 182910 Solution: Multiply 2,345 by the ones digit of 78, which is 8. 2,345 × 8 = 18,760 Multiply 2,345 by the tens digit of 78, which is 7 (representing 70). 2,345 × 70 = 164,150 Add the two partial products together.
   Full step-by-step solution

   Step 1: Multiply 2,345 by the ones digit of 78, which is 8. 2,345 × 8 = 18,760 Step 2: Multiply 2,345 by the tens digit of 78, which is 7 (representing 70). 2,345 × 70 = 164,150 Step 3: Add the two partial products together. 18,760 + 164,150 = 182,910 The final answer is 182,910.

8. A community garden is planting tomato seedlings in rows. Each seedling needs 0.75 square feet of space, and each garden bed has an area of 168 square feet. How many tomato seedlings can be planted in one garden bed? Answer: 224 Solution: Identify what we're solving for: number of seedlings = total area ÷ area per seedling Total area = 168 square feet Area per seedling = 0.75 square feet Calculate: 168 ÷ 0.75 To divide by a decimal, multiply both numbers by 100: 16800 ÷ 75 75 × 224 = 16800 Therefore, 168 ÷ 0.75 = 224 The answer…
   Full step-by-step solution

   Step 1: Identify what we're solving for: number of seedlings = total area ÷ area per seedling Step 2: Total area = 168 square feet Step 3: Area per seedling = 0.75 square feet Step 4: Calculate: 168 ÷ 0.75 Step 5: To divide by a decimal, multiply both numbers by 100: 16800 ÷ 75 Step 6: 75 × 224 = 16800 Step 7: Therefore, 168 ÷ 0.75 = 224 The answer is 224 seedlings.

9. A farmer harvested 725 pounds of apples from each of his 36 apple trees. How many pounds of apples did he harvest in total? Answer: 26100 Solution: We need to multiply 725 by 36 First, multiply 725 by 30: 725 × 30 = 21,750 Next, multiply 725 by 6: 725 × 6 = 4,350 Add the two results together: 21,750 + 4,350 = 26,100 The farmer harvested 26,100 pounds of apples in total The answer is 26100.
   Full step-by-step solution

   Step 1: We need to multiply 725 by 36 Step 2: First, multiply 725 by 30: 725 × 30 = 21,750 Step 3: Next, multiply 725 by 6: 725 × 6 = 4,350 Step 4: Add the two results together: 21,750 + 4,350 = 26,100 Step 5: The farmer harvested 26,100 pounds of apples in total The answer is 26100.