Multiplication Properties

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Answer Key & Explanations

Multiplication Properties · Grade 3 · Worksheet 2

1. A rectangular playground is drawn on a grid where each square represents 1 square meter. The playground is 24 meters long and 18 meters wide. What is the total area of the playground in square meters? Answer: 432 Solution: The area of a rectangle is found by multiplying its length by its width. The playground's length is 24 meters and its width is 18 meters. Multiply 24 × 18.
   Full step-by-step solution

   Step 1: The area of a rectangle is found by multiplying its length by its width. Step 2: The playground's length is 24 meters and its width is 18 meters. Step 3: Multiply 24 × 18. Step 4: First, multiply 24 × 10 = 240. Step 5: Then, multiply 24 × 8 = 192. Step 6: Add the two results: 240 + 192 = 432. Step 7: The total area is 432 square meters.

2. Emma is planting flowers in her garden. She has 6 rows of flowers, and each row has 15 flowers. How many flowers does Emma have in total? Answer: 90 Solution: Emma has 6 rows of flowers. Each row has 15 flowers. To find the total number of flowers, multiply the number of rows by the number of flowers in each row: 6 × 15.
   Full step-by-step solution

   Step 1: Emma has 6 rows of flowers. Step 2: Each row has 15 flowers. Step 3: To find the total number of flowers, multiply the number of rows by the number of flowers in each row: 6 × 15. Step 4: Calculate 6 × 15 = 90. The answer is 90.

3. 64 × 25 = ? Answer: 1600 Solution: We need to multiply 64 by 25. Notice that 25 is the same as 100 ÷ 4. First, multiply 64 × 100 = 6400.
   Full step-by-step solution

   Step 1: We need to multiply 64 by 25. Step 2: Notice that 25 is the same as 100 ÷ 4. Step 3: First, multiply 64 × 100 = 6400. Step 4: Now, divide that result by 4: 6400 ÷ 4 = 1600. Step 5: Therefore, 64 × 25 = 1600. The answer is 1600.

4. 24 × 15 = ? Answer: 360 Solution: Break 15 into easier numbers to multiply. 15 is the same as 10 + 5. So, 24 × 15 = 24 × (10 + 5).
   Full step-by-step solution

   Let's solve 24 × 15 step by step. Step 1: Break 15 into easier numbers to multiply. 15 is the same as 10 + 5. So, 24 × 15 = 24 × (10 + 5). Step 2: Use the distributive property. Multiply 24 by 10 and 24 by 5 separately, then add the results. First, 24 × 10 = 240. Second, 24 × 5 = 120. Step 3: Add the two results. 240 + 120 = 360. Therefore, 24 × 15 = 360.

5. 72 × 50 = ? Answer: 3600 Solution: Start with 72 × 50 Multiply 72 × 5 = 360 Since we multiplied by 5 instead of 50, we need to multiply by 10 to get the correct result 360 × 10 = 3600 Therefore, 72 × 50 = 3600 The answer is 3600.
   Full step-by-step solution

   Step 1: Start with 72 × 50 Step 2: Multiply 72 × 5 = 360 Step 3: Since we multiplied by 5 instead of 50, we need to multiply by 10 to get the correct result Step 4: 360 × 10 = 3600 Step 5: Therefore, 72 × 50 = 3600 The answer is 3600.

6. A farmer has 24 apple trees in each row of her orchard. If there are 35 rows of apple trees, how many apple trees are there in total? Answer: 840 Solution: We are told that the farmer has 24 apple trees in each row, and there are 35 rows in total. To find the total number of apple trees, we multiply the number of trees per row by the number of rows.
   Full step-by-step solution

   We are told that the farmer has 24 apple trees in each row, and there are 35 rows in total. To find the total number of apple trees, we multiply the number of trees per row by the number of rows. Step 1: Write the multiplication expression. Total trees = trees per row × number of rows Total trees = 24 × 35 Step 2: Break down 35 into 30 + 5 for easier mental calculation. 24 × 35 = 24 × (30 + 5) Step 3: Use the distributive property: multiply 24 by 30 and 24 by 5, then add. First, 24 × 30: 24 × 3 = 72, so 24 × 30 = 720. Step 4: Now, 24 × 5: 20 × 5 = 100, and 4 × 5 = 20, so 100 + 20 = 120. Step 5: Add the two results: 720 + 120 = 840. Step 6: Conclusion: There are 840 apple trees in total.

7. A rectangular garden is planted with tomato plants arranged in 12 rows. Each row contains 15 plants. How many tomato plants are in the garden total? Answer: 180 Solution: We are told the garden has tomato plants arranged in 12 rows, and each row contains 15 plants. The total number of plants is the number of rows multiplied by the number of plants in each row. Write the multiplication.
   Full step-by-step solution

   We are told the garden has tomato plants arranged in 12 rows, and each row contains 15 plants. Step 1: Understand the problem. The total number of plants is the number of rows multiplied by the number of plants in each row. Step 2: Write the multiplication. Total plants = 12 rows × 15 plants per row Step 3: Perform the multiplication. First, multiply 12 by 15. We can break it down: 12 × 15 = 12 × (10 + 5) = (12 × 10) + (12 × 5) Step 4: Calculate each part. 12 × 10 = 120 12 × 5 = 60 Step 5: Add the results. 120 + 60 = 180 Step 6: Conclusion. So, the total number of tomato plants in the garden is 180.