Write the rule for fractions with a denominator of 2 to change them to whole numbers and provide a reason. Also, find the rule for the number of sunflowers planted in each row based on the provided pa

You're on a roll — here are the solutions to the next questions. Question 3 3.5 Write the rule that should be applied to a list of inputs that are fractions with a denominator of 2 to change them to whole numbers. Provide a reason for your answer. Step 1: Determine the operation needed to eliminate the denominator. To change a fraction with a denominator of 2 into a whole number, you need to multiply it by 2. Step 2: Provide a reason. Multiplying a fraction by its denominator cancels out the denominator, resulting in the numerator as a whole number. For example, (x)/(2) × 2 = x. The rule is to multiply by 2. The reason is that multiplying a fraction by its denominator will cancel out the denominator, leaving the numerator as a whole number. Question 4 4.1 Complete the table below to show the relationship between the rows and the number of sunflowers planted in each row. First, let's identify the pattern in the number of sunflowers: Row 1: 4 sunflowers Row 2: 7 sunflowers Row 3: 10 sunflowers Row 4: 13 sunflowers Step 1: Find the common difference between consecutive terms. 7 - 4 = 3 10 - 7 = 3 13 - 10 = 3 The number of sunflowers increases by 3 for each subsequent row. This is an arithmetic sequence. Step 2: Determine the rule for the n-th row. The general formula for an arithmetic sequence is a_n = a_1 + (n-1)d, where a_n is the number of sunflowers in row n, a_1 is the number of sunflowers in the first row, and d is the common difference. Here, a_1 = 4 and d = 3. So, a_n = 4 + (n-1)3 a_n = 4 + 3n - 3 a_n = 3n + 1 Step 3: Calculate the number of sunflowers for Row 7. For n=7: a_7 = 3(7) + 1 = 21 + 1 = 22. The completed table is: | Row Number | 1 | 2 | 3 | 4 | 7 | n | |---|---|---|---|---|---|---| | Number of Sunflowers | 4 | 7 | 10 | 13 | 22 | 3n+1 | 4.2 Which row will have 106 sunflowers? Show your calculations. Step 1: Use the rule a_n = 3n + 1 and set a_n = 106. 3n + 1 = 106 Step 2: Solve for n. 3n = 106 - 1 3n = 105 n = (105)/(3) n = 35 The 35th row will have 106 sunflowers. What's next? 📸