Decimal Multiplication

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Answer Key & Explanations

Decimal Multiplication · Grade 5 · Worksheet 2

1. 6.48 × 23 = ? Answer: 149.04 Solution: Multiply 6.48 × 23 as if they were whole numbers: 648 × 23 648 × 20 = 12,960 648 × 3 = 1,944 Add the partial products: 12,960 + 1,944 = 14,904 Since 6.48 has two decimal places, the product must also have two decimal places Place the decimal point two places from the right: 149.04 The answer is…
   Full step-by-step solution

   Step 1: Multiply 6.48 × 23 as if they were whole numbers: 648 × 23 Step 2: 648 × 20 = 12,960 Step 3: 648 × 3 = 1,944 Step 4: Add the partial products: 12,960 + 1,944 = 14,904 Step 5: Since 6.48 has two decimal places, the product must also have two decimal places Step 6: Place the decimal point two places from the right: 149.04 The answer is 149.04.

2. A farmer harvested 750 kilograms of apples from one orchard. If each kilogram of apples sells for $3.25, how much money will the farmer earn from selling all the apples? Answer: 2437.50 Solution: The farmer has 750 kilograms of apples. Each kilogram sells for $3.25. We need to find the total money earned by selling all the apples.
   Full step-by-step solution

   Step 1: Understand the problem The farmer has 750 kilograms of apples. Each kilogram sells for $3.25. We need to find the total money earned by selling all the apples. Step 2: Set up the calculation Total money = (Number of kilograms) × (Price per kilogram) Total money = 750 × 3.25 Step 3: Break down the multiplication We can multiply 750 by 3.25 by first thinking of 3.25 as 3 + 0.25. Step 4: Multiply 750 by 3 750 × 3 = 2250 Step 5: Multiply 750 by 0.25 0.25 is the same as 1/4, so: 750 × (1/4) = 750 ÷ 4 = 187.5 Step 6: Add the two results 2250 + 187.5 = 2437.5 Step 7: Write the final answer in money format 2437.5 is the same as 2437.50 when dealing with dollars and cents. Final Answer: 2437.50

3. 8.42 × 23 = ? Answer: 193.66 Solution: Multiply 8.42 by 23 as if they were whole numbers: 842 × 23 842 × 20 = 16,840 842 × 3 = 2,526 Add the partial products: 16,840 + 2,526 = 19,366 Since 8.42 has two decimal places, the product must also have two decimal places Place the decimal point two places from the right: 193.66 The answer is…
   Full step-by-step solution

   Step 1: Multiply 8.42 by 23 as if they were whole numbers: 842 × 23 Step 2: 842 × 20 = 16,840 Step 3: 842 × 3 = 2,526 Step 4: Add the partial products: 16,840 + 2,526 = 19,366 Step 5: Since 8.42 has two decimal places, the product must also have two decimal places Step 6: Place the decimal point two places from the right: 193.66 The answer is 193.66.

4. Liam is building a rectangular garden bed that is 2.5 meters long and 1.8 meters wide. He needs to buy enough soil to fill the entire bed to a depth of 0.3 meters. How many cubic meters of soil does Liam need? Answer: 1.35 Solution: To find the volume of soil needed, we calculate the volume of the rectangular garden bed using the formula: Volume = length × width × height Here, the height is the depth of soil. Write down the given measurements.
   Full step-by-step solution

   To find the volume of soil needed, we calculate the volume of the rectangular garden bed using the formula: Volume = length × width × height Here, the height is the depth of soil. Step 1: Write down the given measurements. Length = 2.5 meters Width = 1.8 meters Depth = 0.3 meters Step 2: Multiply the length and width to find the base area. Base area = 2.5 × 1.8 First, multiply 2.5 × 1.8. 2.5 × 1 = 2.5 2.5 × 0.8 = 2.0 Add them: 2.5 + 2.0 = 4.5 So, base area = 4.5 square meters. Step 3: Multiply the base area by the depth to find the volume. Volume = 4.5 × 0.3 4.5 × 0.3 = 1.35 Step 4: State the final answer. Liam needs 1.35 cubic meters of soil.

5. Aroha is designing a rectangular mural on a coordinate grid. The corners of the mural are at (0, 0), (12.5, 0), (12.5, 9.6), and (0, 9.6). Each unit on the grid represents 1 meter. Aroha wants to paint the entire mural with special paint. One can of paint covers 15 square meters. How many cans of paint does Aroha need to buy? Answer: 8 Solution: Find the length of the rectangle by subtracting the x-coordinates: 12.5 - 0 = 12.5 meters. Find the width of the rectangle by subtracting the y-coordinates: 9.6 - 0 = 9.6 meters. Calculate the area: 12.5 × 9.6.
   Full step-by-step solution

   Step 1: Find the length of the rectangle by subtracting the x-coordinates: 12.5 - 0 = 12.5 meters. Step 2: Find the width of the rectangle by subtracting the y-coordinates: 9.6 - 0 = 9.6 meters. Step 3: Calculate the area: 12.5 × 9.6. Step 4: Multiply: 12.5 × 9 = 112.5, and 12.5 × 0.6 = 7.5. Add: 112.5 + 7.5 = 120 square meters. Step 5: Each can covers 15 square meters. Divide: 120 ÷ 15 = 8. Step 6: Since 120 is exactly divisible by 15, Aroha needs exactly 8 cans. The answer is 8.

6. 7.35 × 15 = ? Answer: 110.25 Solution: Multiply 735 × 15 735 × 10 = 7350 735 × 5 = 3675 Add the partial products: 7350 + 3675 = 11025 Since 7.35 has two decimal places, the product must also have two decimal places Place the decimal point: 11025 becomes 110.25 The answer is 110.25.
   Full step-by-step solution

   Step 1: Multiply 735 × 15 Step 2: 735 × 10 = 7350 Step 3: 735 × 5 = 3675 Step 4: Add the partial products: 7350 + 3675 = 11025 Step 5: Since 7.35 has two decimal places, the product must also have two decimal places Step 6: Place the decimal point: 11025 becomes 110.25 The answer is 110.25.

7. Ethan is filling water bottles for a soccer game. Each bottle holds 32 liters of water. Ethan fills 6 bottles. How many liters of water does Ethan use? Answer: 192 Solution: Find how much water is in one bottle: 32 liters. Multiply by the number of bottles: 32 × 6 = 192. Ethan uses 192 liters of water.
   Full step-by-step solution

   Step 1: Find how much water is in one bottle: 32 liters. Step 2: Multiply by the number of bottles: 32 × 6 = 192. Ethan uses 192 liters of water.