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
Welcome back Lethabo — missed you this week. 1. Use rounding to the nearest 10 to estimate the answers: a) 31 + 78 Step 1: Round each number to the nearest 10. 31 ≈ 30 78 ≈ 80 Step 2: Add the rounded numbers. 30 + 80 = 110 The estimated answer is 110. b) 137 - 56 Step 1: Round each number to the nearest 10. 137 ≈ 140 56 ≈ 60 Step 2: Subtract the rounded numbers. 140 - 60 = 80 The estimated answer is 80. 2. Use rounding to the nearest 100 to estimate the answers: a) 589 - 213 Step 1: Round each number to the nearest 100. 589 ≈ 600 213 ≈ 200 Step 2: Subtract the rounded numbers. 600 - 200 = 400 The estimated answer is 400. b) 621 + 273 Step 1: Round each number to the nearest 100. 621 ≈ 600 273 ≈ 300 Step 2: Add the rounded numbers. 600 + 300 = 900 The estimated answer is 900. 3. Anna must add 583 and 294. Help her by filling in the missing numbers: Step 1: Decompose the numbers into hundreds, tens, and ones. 583 + 294 = 500 + 80 + 3 + 200 + 90 + 4 Step 2: Group the hundreds, tens, and ones together. = 500 + 200 + 80 + 90 + 3 + 4 Step 3: Add the grouped numbers. = 700 + 170 + 7 Step 4: Add the results. = 877 The completed calculation is: 583 + 294 = 500 + 80 + 3 + 200 + 90 + 4 = 500 + 200 + 80 + 90 + 3 + 4 = 700 + 170 + 7 = 877 4. Calculate the answers, then use the opposite operation to check: a) 189 - 47 Step 1: Calculate the difference. 189 - 47 = 142 Step 2: Check using the opposite operation (addition). 142 + 47 = 189 The answer is 142. b) 632 + 179 Step 1: Calculate the sum. 632 + 179 = 811 Step 2: Check using the opposite operation (subtraction). 811 - 179 = 632 The answer is 811. 5. Mrs Mafaya's eggs: Step 1: Calculate the total number of eggs Mrs Mafaya had initially. 103 (white eggs) + 58 (brown eggs) = 161 eggs Step 2: Subtract the number of eggs left from the total initial eggs to find how many were given away. 161 (total eggs) - 49 (eggs left) = 112 eggs Mrs Mafaya gave away 112 eggs. 6. Flow diagram: The flow diagram shows: Input → × 5 → Output → +3 → Final Output The question implies the rule is × 5 then +3. a) Write the rule for this flow diagram in words. The rule is: Multiply the input number by 5, then add 3. b) Use the flow diagram to fill in the missing values in the table: Step 1: Apply the rule (n × 5) + 3 for each input number. • For input 1: (1 × 5) + 3 = 5 + 3 = 8 • For input 2: (2 × 5) + 3 = 10 + 3 = 13 • For input 3: (3 × 5) + 3 = 15 + 3 = 18 • For input 4: (4 × 5) + 3 = 20 + 3 = 23 • For input 5: (5 × 5) + 3 = 25 + 3 = 28 The completed table is: Input number: 1, 2, 3, 4, 5 Output number: 8, 13, 18, 23, 28 7. Fill in the missing numbers in the spidergram: The rule is: Add 2, then multiply by 3. So, (n + 2) × 3. Step 1: Apply the rule for each input number. • For input 1: (1 + 2) × 3 = 3 × 3 = 9 • For input 2: (2 + 2) × 3 = 4 × 3 = 12 • For input 3: (3 + 2) × 3 = 5 × 3 = 15 • For input 5: (5 + 2) × 3 = 7 × 3 = 21 • For input 10: (10 + 2) × 3 = 12 × 3 = 36 The missing numbers are 9, 12, 15, 21, 36. What's next? Send 'em! 📸