This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
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5: 1. Fill in the blanks. a) 134 × 245 = 245 × 134 b) 8 × 2513 × 125 = (8 × 125) × 2513 = 1000 × 2513 = 2513000 (This is an example, already filled) c) 519 × 3105 = 3105 × 519 d) 8175 × 6213 = 8175 × 6213 e) 1 × 8367 = 8367 f) 0 × 93653 = 0 g) 27 × (121 + 23) = (27 × 121) + (27 × 23) h) 119 × (100 + 17) = (119 × 100) + (119 × 17) 2. Write the product without actually multiplying. a) 6323 × 10 = 63230 b) 2799 × 10 = 27990 c) 4215 × 100 = 421500 d) 3612 × 100 = 361200 e) 2530 × 1000 = 2530000 f) 4795 × 1000 = 4795000 3. Find the products. a) 3058 × 40 Step 1: Multiply 3058 by 4. 3058 × 4 = 12232 Step 2: Add the zero from 40. 12232 × 10 = 122320 The product is 122320. b) 1978 × 300 Step 1: Multiply 1978 by 3. 1978 × 3 = 5934 Step 2: Add the two zeros from 300. 5934 × 100 = 593400 The product is 593400. c) 7200 × 500 Step 1: Multiply 72 by 5. 72 × 5 = 360 Step 2: Add the four zeros (two from 7200 and two from 500). 360 × 10000 = 3600000 The product is 3600000. d) 800 × 6000 Step 1: Multiply 8 by 6. 8 × 6 = 48 Step 2: Add the five zeros (two from 800 and three from 6000). 48 × 100000 = 4800000 The product is 4800000. 4. Find the products using suitable arrangements. a) 2 × 1768 × 50 Step 1: Group 2 and 50. (2 × 50) × 1768 Step 2: Multiply the grouped numbers, then by 1768. 100 × 1768 = 176800 The product is 176800. b) 4 × 927 × 25 Step 1: Group 4 and 25. (4 × 25) × 927 Step 2: Multiply the grouped numbers, then by 927. 100 × 927 = 92700 The product is 92700. c) 8 × 291 × 125 Step 1: Group 8 and 125. (8 × 125) × 291 Step 2: Multiply the grouped numbers, then by 291. 1000 × 291 = 291000 The product is 291000. d) 625 × 16 × 57 Step 1: Group 625 and 16. (625 × 16) × 57 Step 2: Multiply 625 × 16. 625 × 16 = 10000 Step 3: Multiply the result by 57. 10000 × 57 = 570000 The product is 570000. e) 25 × 80 × 17 Step 1: Group 25 and 80. (25 × 80) × 17 Step 2: Multiply 25 × 80. 25 × 80 = 2000 Step 3: Multiply the result by 17. 2000 × 17 = 34000 The product is 34000. f) 125 × 40 × 8 Step 1: Group 125 and 8. (125 × 8) × 40 Step 2: Multiply the grouped numbers, then by 40. 1000 × 40 = 40000 The product is 40000. That's 2 down. 3 left today — send the next one.