Decimal Multiplication

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Answer Key & Explanations

Decimal Multiplication · Grade 5 · Worksheet 2

1. Liam is building a bookshelf and needs to cut 4 pieces of wood that are each 2.75 meters long. How many meters of wood does Liam need in total? Answer: 11 Solution: Liam needs to cut 4 pieces of wood, and each piece is 2.75 meters long. To find the total meters of wood needed, we multiply the number of pieces by the length of each piece. Write the multiplication expression.
   Full step-by-step solution

   Liam needs to cut 4 pieces of wood, and each piece is 2.75 meters long. To find the total meters of wood needed, we multiply the number of pieces by the length of each piece. Step 1: Write the multiplication expression. Total wood = 4 × 2.75 Step 2: Multiply 4 by 2.75. First, multiply 4 by 2: 4 × 2 = 8 Then, multiply 4 by 0.75: 4 × 0.75 = 3 Now add the results: 8 + 3 = 11 Alternatively, you can think of 2.75 as 2 + 3/4. 4 × 2 = 8 4 × (3/4) = 12/4 = 3 8 + 3 = 11 Step 3: Conclusion. Liam needs 11 meters of wood in total.

2. 6.28 × 35 = ? Answer: 219.80 Solution: Multiply 6.28 × 35 as if they were whole numbers: 628 × 35 628 × 30 = 18,840 628 × 5 = 3,140 Add the partial products: 18,840 + 3,140 = 21,980 Since 6.28 has two decimal places, the product must also have two decimal places Place the decimal point two places from the right: 219.80 The answer is…
   Full step-by-step solution

   Step 1: Multiply 6.28 × 35 as if they were whole numbers: 628 × 35 Step 2: 628 × 30 = 18,840 Step 3: 628 × 5 = 3,140 Step 4: Add the partial products: 18,840 + 3,140 = 21,980 Step 5: Since 6.28 has two decimal places, the product must also have two decimal places Step 6: Place the decimal point two places from the right: 219.80 The answer is 219.80.

3. Ava is making friendship bracelets for her class. Each bracelet requires 0.85 meters of string. If she needs to make bracelets for all 24 students in her class, how many meters of string does Ava need in total? Answer: 20.4 Solution: Each bracelet requires 0.85 meters of string. Ava needs to make 24 bracelets.
   Full step-by-step solution

   Step 1: Each bracelet requires 0.85 meters of string. Step 2: Ava needs to make 24 bracelets. Step 3: Multiply the length per bracelet by the number of bracelets: 0.85 × 24 Step 4: Calculate 0.85 × 20 = 17 Step 5: Calculate 0.85 × 4 = 3.4 Step 6: Add the partial products: 17 + 3.4 = 20.4 Step 7: Ava needs 20.4 meters of string in total.

4. 4.25 × 6 = ? Answer: 25.5 Solution: Write the multiplication: 4.25 × 6 Multiply the whole number part: 4 × 6 = 24 Multiply the decimal part: 0.25 × 6 = 1.5 Add the results: 24 + 1.5 = 25.5 Place the decimal point in the answer: 25.5 The final answer is 25.5.
   Full step-by-step solution

   Step 1: Write the multiplication: 4.25 × 6 Step 2: Multiply the whole number part: 4 × 6 = 24 Step 3: Multiply the decimal part: 0.25 × 6 = 1.5 Step 4: Add the results: 24 + 1.5 = 25.5 Step 5: Place the decimal point in the answer: 25.5 The final answer is 25.5.

5. A rectangular garden is drawn on a coordinate plane with corners at (2.5, 1), (8.5, 1), (8.5, 4), and (2.5, 4). Each unit represents 1 meter. What is the area of the garden in square meters? Answer: 18 Solution: Identify the coordinates of the rectangle. A = (2.5, 1) B = (8.5, 1) C = (8.5, 4) D = (2.5, 4) Determine the length of the horizontal side. Points A and B are on the same horizontal line (y = 1).
   Full step-by-step solution

   Let's find the area step by step. Step 1: Identify the coordinates of the rectangle. The corners are: A = (2.5, 1) B = (8.5, 1) C = (8.5, 4) D = (2.5, 4) Step 2: Determine the length of the horizontal side. Points A and B are on the same horizontal line (y = 1). Length AB = 8.5 - 2.5 = 6.0 meters. Step 3: Determine the length of the vertical side. Points A and D are on the same vertical line (x = 2.5). Height AD = 4 - 1 = 3.0 meters. Step 4: Calculate the area of the rectangle. Area = length × width = 6.0 × 3.0 = 18.0 square meters. Step 5: Conclusion. The area of the garden is 18 square meters.

6. Emma is making friendship bracelets for her classmates. Each bracelet requires 0.35 meters of colorful yarn. If Emma needs to make bracelets for 12 classmates, how many meters of yarn does she need in total? Answer: 4.2 Solution: Each bracelet requires 0.35 meters of yarn Emma needs to make 12 bracelets Multiply the yarn per bracelet by the number of bracelets: 0.35 × 12 First multiply 35 × 12 = 420 Since 0.35 has two decimal places, move the decimal point two places to the left: 420 becomes 4.20 4.20 is the same as 4.2…
   Full step-by-step solution

   Step 1: Each bracelet requires 0.35 meters of yarn Step 2: Emma needs to make 12 bracelets Step 3: Multiply the yarn per bracelet by the number of bracelets: 0.35 × 12 Step 4: First multiply 35 × 12 = 420 Step 5: Since 0.35 has two decimal places, move the decimal point two places to the left: 420 becomes 4.20 Step 6: 4.20 is the same as 4.2 Step 7: Emma needs 4.2 meters of yarn total

7. Emma is making friendship bracelets for her classmates. She needs 0.85 meters of string for each bracelet. If she wants to make 12 bracelets, how many meters of string does Emma need in total? Answer: 10.2 Solution: Each bracelet requires 0.85 meters of string Emma needs to make 12 bracelets Multiply the string per bracelet by the number of bracelets: 0.85 × 12 Calculate 0.85 × 10 = 8.5 Calculate 0.85 × 2 = 1.7 Add the results: 8.5 + 1.7 = 10.2 Emma needs 10.2 meters of string in total.
   Full step-by-step solution

   Step 1: Each bracelet requires 0.85 meters of string Step 2: Emma needs to make 12 bracelets Step 3: Multiply the string per bracelet by the number of bracelets: 0.85 × 12 Step 4: Calculate 0.85 × 10 = 8.5 Step 5: Calculate 0.85 × 2 = 1.7 Step 6: Add the results: 8.5 + 1.7 = 10.2 Emma needs 10.2 meters of string in total.

8. 4.82 × 25 = ? Answer: 120.5 Solution: Multiply 4.82 by 25 as if they were whole numbers: 482 × 25 482 × 20 = 9,640 482 × 5 = 2,410 Add the partial products: 9,640 + 2,410 = 12,050 Since 4.82 has two decimal places, the product must also have two decimal places Place the decimal point two places from the right: 120.50, which…
   Full step-by-step solution

   Step 1: Multiply 4.82 by 25 as if they were whole numbers: 482 × 25 Step 2: 482 × 20 = 9,640 Step 3: 482 × 5 = 2,410 Step 4: Add the partial products: 9,640 + 2,410 = 12,050 Step 5: Since 4.82 has two decimal places, the product must also have two decimal places Step 6: Place the decimal point two places from the right: 120.50, which simplifies to 120.5 The answer is 120.5.

9. 2.75 × 8 = ? Answer: 22 Solution: 2.75 means 2 whole parts and 75 hundredths. So 2.75 = 2 + 0.75. Break the multiplication into parts.
   Full step-by-step solution

   Let's solve 2.75 × 8 step-by-step. Step 1: Understand the decimal. 2.75 means 2 whole parts and 75 hundredths. So 2.75 = 2 + 0.75. Step 2: Break the multiplication into parts. 2.75 × 8 = (2 + 0.75) × 8. Step 3: Use the distributive property. (2 × 8) + (0.75 × 8). Step 4: Multiply the whole number part. 2 × 8 = 16. Step 5: Multiply the decimal part. 0.75 means 75/100, so 0.75 × 8 = (75/100) × 8. First, 75 × 8 = 600. Then divide by 100: 600 / 100 = 6. Step 6: Add the two results. 16 + 6 = 22. Final answer: 22.