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 solutions to the numeric patterns worksheet. 1. Complete the flow diagrams below. a) Step 1: Calculate the output for input 35. 35 × 3 = 105 105 + 10 = 115 Step 2: Calculate the input for output 130 by working backward. 130 - 10 = 120 120 ÷ 3 = 40 The completed flow diagram is: Input 31 × 3 93 + 10 103 Input 35 × 3 105 + 10 115 Input 40 × 3 120 + 10 130 b) Step 1: Calculate the output for input 5. 5 × 10 = 50 50 + 6 = 56 Step 2: Calculate the input for output 116 by working backward. 116 - 6 = 110 110 ÷ 10 = 11 The completed flow diagram is: Input 5 × 10 50 + 6 56 Input 11 × 10 110 + 6 116 2. Complete the table below. Rule: +35 | Input | 2 | 4 | 23 | 32 | 120 | 204 | | :---- | :- | :- | :-- | :-- | :--- | :--- | | Output | 37 | 39 | 58 | 67 | 155 | 239 | 3. Identify the rule for the table below. Step 1: Examine the relationship between Input and Output for each pair. For Input 1, Output 9: 1 × 9 = 9 For Input 3, Output 27: 3 × 9 = 27 For Input 5, Output 45: 5 × 9 = 45 For Input 9, Output 81: 9 × 9 = 81 For Input 20, Output 180: 20 × 9 = 180 The rule is to multiply the input by 9. Rule: × 9 4. Fill in the missing numbers and identify the rule for the sequences below. a) Sequence: 8 000, 4 000, 2 000, ___, ___, ___ Step 1: Identify the pattern by finding the relationship between consecutive terms. 4000 ÷ 8000 = 0.5 2000 ÷ 4000 = 0.5 The rule is to divide by 2. Step 2: Apply the rule to find the missing numbers. 2000 ÷ 2 = 1000 1000 ÷ 2 = 500 500 ÷ 2 = 250 The sequence is: 8 000, 4 000, 2 000, 1000, 500, 250 Rule: ÷ 2 b) Sequence: 5, 10, 20, ___, ___, ___ Step 1: Identify the pattern. 10 ÷ 5 = 2 20 ÷ 10 = 2 The rule is to multiply by 2. Step 2: Apply the rule to find the missing numbers. 20 × 2 = 40 40 × 2 = 80 80 × 2 = 160 The sequence is: 5, 10, 20, 40, 80, 160 Rule: × 2 c) Sequence: 140, 180, 220, ___, ___, ___ Step 1: Identify the pattern. 180 - 140 = 40 220 - 180 = 40 The rule is to add 40. Step 2: Apply the rule to find the missing numbers. 220 + 40 = 260 260 + 40 = 300 300 + 40 = 340 The sequence is: 140, 180, 220, 260, 300, 340 Rule: + 40 What's next? Send 'em! 📸