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
Here are the calculations: 1. Calculate the following with box method: a) 864 ÷ 24 Step 1: Set up the division. r 00 \\ 24 ) 864 \\ Step 2: Determine how many times 24 goes into 864. We can start by finding a multiple of 24 that is close to 864. 24 × 30 = 720. Subtract 720 from 864. r 30 \\ 24 ) 864 \\ 720 \\ 144 \\ Step 3: Determine how many times 24 goes into the remainder, 144. 24 × 6 = 144. Subtract 144 from 144. r 30 + 6 \\ 24 ) 864 \\ 720 \\ 144 \\ 144 \\ 0 \\ Step 4: Add the partial quotients. 30 + 6 = 36. The remainder is 0. The answer is 36. b) 945 ÷ 27 Step 1: Set up the division. r 00 \\ 27 ) 945 \\ Step 2: Determine how many times 27 goes into 945. 27 × 30 = 810. Subtract 810 from 945. r 30 \\ 27 ) 945 \\ 810 \\ 135 \\ Step 3: Determine how many times 27 goes into the remainder, 135. 27 × 5 = 135. Subtract 135 from 135. r 30 + 5 \\ 27 ) 945 \\ 810 \\ 135 \\ 135 \\ 0 \\ Step 4: Add the partial quotients. 30 + 5 = 35. The remainder is 0. The answer is 35. c) 108 ÷ 12 Step 1: Set up the division. r 0 \\ 12 ) 108 \\ Step 2: Determine how many times 12 goes into 108. 12 × 9 = 108. Subtract 108 from 108. r 9 \\ 12 ) 108 \\ 108 \\ 0 \\ The remainder is 0. The answer is 9. 2. Estimate 782 ÷ 20 Step 1: Round 782 to the nearest hundred that is easily divisible by 20. 782 is close to 800. Step 2: Perform the division with the rounded number. 800 ÷ 20 Step 3: Simplify the division. 800 ÷ 20 = 40 The estimate is 40. That's 2 down. 3 left today — send the next one.