Multiplication Properties

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Answer Key & Explanations

Multiplication Properties · Grade 3 · Worksheet 1

1. 125 × 8 = ? Answer: 1000 Solution: Step 1: Start with 125 × 8 Step 2: Break it down: 125 × 8 = (100 × 8) + (25 × 8) Step 3: Calculate 100 × 8 = 800 Step 4: Calculate 25 × 8 = 200 Step 5: Add the results: 800 + 200 = 1000 Step 6: Verify: 125 × 8 = 1000 The answer is 1000.
   Full step-by-step solution

   Step 1: Start with 125 × 8 Step 2: Break it down: 125 × 8 = (100 × 8) + (25 × 8) Step 3: Calculate 100 × 8 = 800 Step 4: Calculate 25 × 8 = 200 Step 5: Add the results: 800 + 200 = 1000 Step 6: Verify: 125 × 8 = 1000 The answer is 1000.

2. A farmer has 24 rows of apple trees. Each row has 15 trees. How many apple trees does the farmer have in total? Answer: 360 Solution: The farmer has 24 rows of apple trees. Each row has 15 trees. To find the total number of trees, we need to multiply the number of rows by the number of trees in each row.
   Full step-by-step solution

   Step 1: Understand the problem. The farmer has 24 rows of apple trees. Each row has 15 trees. To find the total number of trees, we need to multiply the number of rows by the number of trees in each row. Step 2: Write the multiplication expression. Total trees = Number of rows × Trees per row Total trees = 24 × 15 Step 3: Break down the multiplication for easier calculation. We can split 15 into 10 + 5. So, 24 × 15 = 24 × (10 + 5) Step 4: Multiply 24 by 10 and 24 by 5 separately. 24 × 10 = 240 24 × 5 = 120 Step 5: Add the two results. 240 + 120 = 360 Step 6: State the final answer. The farmer has 360 apple trees in total.

3. 5 × (3 × 6) = (5 × 3) × ? Answer: 6 Solution: We have 5 × (3 × 6) on the left side. The associative property says we can change the grouping: (5 × 3) × 6. Check: 5 × (3 × 6) = 5 × 18 = 90, and (5 × 3) × 6 = 15 × 6 = 90.
   Full step-by-step solution

   Step 1: We have 5 × (3 × 6) on the left side. Step 2: The associative property says we can change the grouping: (5 × 3) × 6. Step 3: So the missing number is 6. Step 4: Check: 5 × (3 × 6) = 5 × 18 = 90, and (5 × 3) × 6 = 15 × 6 = 90. Both equal 90. The answer is 6.

4. A rectangular garden is planted with flowers arranged in 15 rows. Each row contains 24 flowers. If you visualize this arrangement as a rectangular array, how many flowers are in the garden total? Answer: 360 Solution: The garden has 15 rows of flowers Each row contains 24 flowers To find the total number of flowers, multiply the number of rows by the number of flowers in each row 15 × 24 = 360 The total number of flowers is 360
   Full step-by-step solution

   Step 1: The garden has 15 rows of flowers Step 2: Each row contains 24 flowers Step 3: To find the total number of flowers, multiply the number of rows by the number of flowers in each row Step 4: 15 × 24 = 360 Step 5: The total number of flowers is 360

5. 72 × 4 = ? Answer: 288 Solution: Break 72 into 70 and 2 Multiply 70 × 4 = 280 Multiply 2 × 4 = 8 Add the results: 280 + 8 = 288 Therefore, 72 × 4 = 288
   Full step-by-step solution

   Step 1: Break 72 into 70 and 2 Step 2: Multiply 70 × 4 = 280 Step 3: Multiply 2 × 4 = 8 Step 4: Add the results: 280 + 8 = 288 Step 5: Therefore, 72 × 4 = 288

6. A rectangular classroom floor is covered with square tiles. The tiles are arranged in 24 rows, and each row has 36 tiles. If you visualize this tile pattern as a rectangular array, how many tiles cover the entire classroom floor? Answer: 864 Solution: The classroom has 24 rows of tiles Each row contains 36 tiles To find the total number of tiles, multiply the number of rows by the number of tiles in each row 24 × 36 = ?
   Full step-by-step solution

   Step 1: The classroom has 24 rows of tiles Step 2: Each row contains 36 tiles Step 3: To find the total number of tiles, multiply the number of rows by the number of tiles in each row Step 4: 24 × 36 = ? Step 5: First, multiply 24 × 30 = 720 Step 6: Then, multiply 24 × 6 = 144 Step 7: Add the two results: 720 + 144 = 864 Step 8: The total number of tiles is 864

7. A school is organizing a field day and needs juice boxes for all the students. There are 18 classes participating, and each class has 24 students. If every student gets one juice box, how many juice boxes does the school need to order? Answer: 432 Solution: Identify the number of groups (classes) and the number in each group (students per class). There are 18 classes with 24 students each.
   Full step-by-step solution

   Step 1: Identify the number of groups (classes) and the number in each group (students per class). There are 18 classes with 24 students each. Step 2: To find the total number of juice boxes, multiply the number of classes by the number of students in each class. Step 3: Calculate 18 × 24. Step 4: Break it down: 18 × 20 = 360, and 18 × 4 = 72. Step 5: Add the partial products: 360 + 72 = 432. The school needs to order 432 juice boxes.

8. 64 × 12 = ? Answer: 768 Solution: Break 12 into 10 and 2. So, 64 × 12 = 64 × (10 + 2). Multiply 64 by 10: 64 × 10 = 640.
   Full step-by-step solution

   Step 1: Break 12 into 10 and 2. So, 64 × 12 = 64 × (10 + 2). Step 2: Multiply 64 by 10: 64 × 10 = 640. Step 3: Multiply 64 by 2: 64 × 2 = 128. Step 4: Add the two results: 640 + 128 = 768. The answer is 768.

9. A school is organizing a field trip to the zoo. Each school bus can carry 48 students. If 12 buses are needed for the trip, how many students can go to the zoo in total? Answer: 576 Solution: Each bus carries 48 students There are 12 buses Multiply the number of students per bus by the number of buses: 48 × 12 Calculate 48 × 10 = 480 Calculate 48 × 2 = 96 Add the partial products: 480 + 96 = 576 The total number of students is 576.
   Full step-by-step solution

   Step 1: Each bus carries 48 students Step 2: There are 12 buses Step 3: Multiply the number of students per bus by the number of buses: 48 × 12 Step 4: Calculate 48 × 10 = 480 Step 5: Calculate 48 × 2 = 96 Step 6: Add the partial products: 480 + 96 = 576 Step 7: The total number of students is 576.