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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2 and Exercise 4.3. Exercise 4.2: Multiplication and division flow diagrams 1. a) Draw the two spidergrams. Then fill in each output number. Spidergram 1 (Rule: × 4) Input: 3 3 × 4 = 12 Output: 12 Input: 5 5 × 4 = 20 Output: 20 Input: 7 7 × 4 = 28 Output: 28 Input: 9 9 × 4 = 36 Output: 36 Spidergram 2 (Rule: ÷ 4) Input: 12 12 ÷ 4 = 3 Output: 3 Input: 20 20 ÷ 4 = 5 Output: 5 Input: 28 28 ÷ 4 = 7 Output: 7 Input: 36 36 ÷ 4 = 9 Output: 9 1. b) What do you notice in these diagrams? The outputs of the first spidergram are the inputs of the second spidergram, and the inputs of the first spidergram are the outputs of the second spidergram. The rules (× 4 and ÷ 4) are inverse operations. 2. a) Draw tables to show the inputs and outputs in question 1. Table for Spidergram 1 (Rule: × 4) | Input number | 3 | 5 | 7 | 9 | | :----------- | :-: | :-: | :-: | :-: | | Output number | 12 | 20 | 28 | 36 | Table for Spidergram 2 (Rule: ÷ 4) | Input number | 12 | 20 | 28 | 36 | | :----------- | :-: | :-: | :-: | :-: | | Output number | 3 | 5 | 7 | 9 | Exercise 4.3: Complete these pairs of number sentences. Use multiplication to check your answers to the divisions. 1. 18 ÷ 6 = 3 3 × 6 = 18 2. 28 ÷ 7 = 4 4 × 7 = 28 3. 15 ÷ 3 = 5 5 × 3 = 15 4. 36 ÷ 12 = 3 3 × 12 = 36 What's next?