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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Here are the solutions to the questions: 7) How far is it from F to H? Step 1: Identify the positions of F and H from the ruler. Position of F = 23.0 Position of H = 24.5 Step 2: Calculate the distance. Distance = Position of H - Position of F Distance = 24.5 - 23.0 Distance = 1.5 The distance from F to H is 1.5. 8) What is the distance between A and C? Step 1: Identify the positions of A and C. Position of A = 20.0 Position of C = 21.0 Step 2: Calculate the distance. Distance = Position of C - Position of A Distance = 21.0 - 20.0 Distance = 1.0 The distance between A and C is 1.0. 9) How far is it from A to K? Step 1: Identify the positions of A and K. Position of A = 20.0 Position of K = 27.0 Step 2: Calculate the distance. Distance = Position of K - Position of A Distance = 27.0 - 20.0 Distance = 7.0 The distance from A to K is 7.0. 10) How far is it from B to J? Step 1: Identify the positions of B and J. Position of B = 20.5 Position of J = 26.0 Step 2: Calculate the distance. Distance = Position of J - Position of B Distance = 26.0 - 20.5 Distance = 5.5 The distance from B to J is 5.5. 11) What is the distance from C to F? Step 1: Identify the positions of C and F. Position of C = 21.0 Position of F = 23.0 Step 2: Calculate the distance. Distance = Position of F - Position of C Distance = 23.0 - 21.0 Distance = 2.0 The distance from C to F is 2.0. 12) The film lasted 153 min, which is ____ min to the nearest 100 min. Step 1: Identify the number to be rounded. Number = 153 Step 2: Round to the nearest 100. Since 153 is closer to 200 than to 100 (it is exactly at the midpoint or higher, so it rounds up), it rounds to 200. The film lasted 153 min, which is 200 min to the nearest 100 min. 13) Oxton to Cowster is 197 miles, which is ____ miles to the nearest 10 miles. Step 1: Identify the number to be rounded. Number = 197 Step 2: Round to the nearest 10. Since 197 is closer to 200 than to 190, it rounds to 200. Oxton to Cowster is 197 miles, which is 200 miles to the nearest 10 miles. 14) The return trip (from Oxton to Cowster and back) is ____ miles to the nearest 10 miles. Step 1: Calculate the total distance for the return trip. One-way distance = 197 miles Return trip distance = 197 × 2 = 394 miles Step 2: Round the total distance to the nearest 10 miles. Since 394 is closer to 390 than to 400, it rounds to 390. The return trip (from Oxton to Cowster and back) is 390 miles to the nearest 10 miles. 17) Shade in the quadrilaterals. A quadrilateral is a polygon with four sides. • Shape A has 5 sides (pentagon). • Shape B has 4 sides. • Shape C has 4 sides (rhombus). • Shape D has 5 sides. • Shape E has 4 sides. The quadrilaterals are shapes B, C, and E. 18) What is the product of 6 and 21? Step 1: Understand "product" means multiplication. Product = 6 × 21 Step 2: Perform the multiplication. Product = 126 The product of 6 and 21 is 126. 19) You start with 16 eggs. Half are broken so you throw them away. Half of the broken eggs are too old so you throw them away. You are now left with ____ good eggs. Step 1: Calculate the number of broken eggs. Broken eggs = (1)/(2) × 16 = 8 eggs. These are thrown away. Step 2: Calculate the number of good eggs remaining. Good eggs = 16 - 8 = 8 eggs. The information about "half of the broken eggs are too old" refers to the eggs already thrown away and does not affect the count of good eggs. You are now left with 8 good eggs. 20) Twice nine is Step 1: Understand "twice nine" means 2 × 9. Result = 2 × 9 Step 2: Perform the multiplication. Result = 18 Twice nine is 18. 21) How many children are in the class? Step 1: Sum all the numbers in the Venn diagram. Total children = (only black shoes) + (both) + (only grey socks) + (neither) Total children = 11 + 5 + 8 + 3 Step 2: Calculate the sum. Total children = 27 There are 27 children in the class. 22) How many children are wearing grey socks? Step 1: Sum the numbers within the "Grey socks" circle. Children wearing grey socks = (only grey socks) + (both) Children wearing grey socks = 8 + 5 Step 2: Calculate the sum. Children wearing grey socks = 13 There are 13 children wearing grey socks. 23) How many are wearing black shoes? Step 1: Sum the numbers within the "Black shoes" circle. Children wearing black shoes = (only black shoes) + (both) Children wearing black shoes = 11 + 5 Step 2: Calculate the sum. Children wearing black shoes = 16 There are 16 children wearing black shoes. That's 2 down. 3 left today — send the next one.