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.
ScanSolve AI Answer
1. 1. Calculate the following pairs: a) (328 ÷ 4) ÷ 2 and 328 ÷ (4 ÷ 2) For (328 ÷ 4) ÷ 2: Step 1: Calculate the expression in the first parenthesis. 328 ÷ 4 = 82 Step 2: Divide the result by 2. 82 ÷ 2 = 41 The first expression equals 41. For 328 ÷ (4 ÷ 2): Step 1: Calculate the expression in the second parenthesis. 4 ÷ 2 = 2 Step 2: Divide 328 by the result. 328 ÷ 2 = 164 The second expression equals 164. b) 144 ÷ (6 ÷ 3) and (144 ÷ 6) ÷ 3 For 144 ÷ (6 ÷ 3): Step 1: Calculate the expression in the first parenthesis. 6 ÷ 3 = 2 Step 2: Divide 144 by the result. 144 ÷ 2 = 72 The first expression equals 72. For (144 ÷ 6) ÷ 3: Step 1: Calculate the expression in the second parenthesis. 144 ÷ 6 = 24 Step 2: Divide the result by 3. 24 ÷ 3 = 8 The second expression equals 8. 2. Divide these numbers by 4. Check your answers by multiplying. a) 118 ÷ 4 Step 1: Perform the division. 118 ÷ 4 = 29 remainder 2 Step 2: Check the answer by multiplying. 29 × 4 + 2 = 116 + 2 = 118 The answer is 29 remainder 2. b) 85 ÷ 4 Step 1: Perform the division. 85 ÷ 4 = 21 remainder 1 Step 2: Check the answer by multiplying. 21 × 4 + 1 = 84 + 1 = 85 The answer is 21 remainder 1. c) 261 ÷ 4 Step 1: Perform the division. 261 ÷ 4 = 65 remainder 1 Step 2: Check the answer by multiplying. 65 × 4 + 1 = 260 + 1 = 261 The answer is 65 remainder 1. 3. Divide these numbers by 9. Use rounding to decide whether the answers are reasonable. a) 475 ÷ 9 Step 1: Perform the division. 475 ÷ 9 = 52 remainder 7 Step 2: Round 475 to the nearest multiple of 9. 475 ≈ 450. Step 3: Estimate the division. 450 ÷ 9 = 50 The answer 52 is close to the estimate 50, so it is reasonable. b) 234 ÷ 9 Step 1: Perform the division. 234 ÷ 9 = 26 Step 2: Round 234 to the nearest multiple of 9. 234 ≈ 230 (not a multiple of 9). 234 ≈ 270 (multiple of 9). Or 234 ≈ 225 (multiple of 9). Let's use 234 ≈ 230. Step 3: Estimate the division. 230 ÷ 9 ≈ 25.5 The answer 26 is close to the estimate 25.5, so it is reasonable. c) 701 ÷ 9 Step 1: Perform the division. 701 ÷ 9 = 77 remainder 8 Step 2: Round 701 to the nearest multiple of 9. 701 ≈ 720. Step 3: Estimate the division. 720 ÷ 9 = 80 The answer 77 is close to the estimate 80, so it is reasonable. d) 511 ÷ 9 Step 1: Perform the division. 511 ÷ 9 = 56 remainder 7 Step 2: Round 511 to the nearest multiple of 9. 511 ≈ 540. Step 3: Estimate the division. 540 ÷ 9 = 60 The answer 56 is close to the estimate 60, so it is reasonable. 4. Fill in the missing numbers: a) 630 ÷ = 7 To find the missing number, divide 630 by 7. 630 ÷ 7 = 90 The missing number is 90. b) 560 ÷ = 7 To find the missing number, divide 560 by 7. 560 ÷ 7 = 80 The missing number is 80. c) 720 ÷ = 60 To find the missing number, divide 720 by 60. 720 ÷ 60 = 12 The missing number is 12. d) 360 ÷ = 9 To find the missing number, divide 360 by 9. 360 ÷ 9 = 40 The missing number is 40. That's 2 down. 3 left today — send the next one.