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 problems. 1. Find the values of the following expressions: a) 28 - 7 + 8 Step 1: Perform subtraction. 28 - 7 = 21 Step 2: Perform addition. 21 + 8 = 29 The value is 29. b) 39 - 2 × 6 + 11 Step 1: Perform multiplication. 2 × 6 = 12 Step 2: Perform subtraction. 39 - 12 = 27 Step 3: Perform addition. 27 + 11 = 38 The value is 38. c) 40 - 10 + 10 + 10 Step 1: Perform operations from left to right. 40 - 10 = 30 Step 2: Continue operations from left to right. 30 + 10 = 40 Step 3: Continue operations from left to right. 40 + 10 = 50 The value is 50. d) 48 - 10 × 2 + 16 ÷ 2 Step 1: Perform multiplication and division. 10 × 2 = 20 16 ÷ 2 = 8 Step 2: Substitute values and perform subtraction. 48 - 20 + 8 28 + 8 = 36 The value is 36. e) 6 × 3 - 4 × 8 × 5 Step 1: Perform multiplications. 6 × 3 = 18 4 × 8 × 5 = 32 × 5 = 160 Step 2: Perform subtraction. 18 - 160 = -142 The value is -142. 2. Write a story/situation for each of the following expressions and find their values. a) 89 + 21 - 10 Story: "Roshni had 89 stickers. She received 21 more stickers for her birthday. Later, she gave 10 stickers to her younger brother. How many stickers does Roshni have now?" Step 1: Perform addition. 89 + 21 = 110 Step 2: Perform subtraction. 110 - 10 = 100 The value is 100. b) 5 × 12 - 6 Story: "A baker made 5 trays of muffins, with 12 muffins on each tray. He sold 6 muffins. How many muffins are left?" Step 1: Perform multiplication. 5 × 12 = 60 Step 2: Perform subtraction. 60 - 6 = 54 The value is 54. c) 4 × 9 + 2 × 6 Story: "A farmer planted 4 rows of apple trees, with 9 trees in each row, and 2 rows of pear trees, with 6 trees in each row. How many fruit trees did the farmer plant in total?" Step 1: Perform multiplications. 4 × 9 = 36 2 × 6 = 12 Step 2: Perform addition. 36 + 12 = 48 The value is 48. 3. For each of the following situations, write the expression describing the situation, identify its terms and find the value of the expression. a) Queen Alia gave 100 gold coins to Princess Elsa and 100 gold coins to Princess Anna last year. Princess Elsa used the coins to start a business and doubled her coins. Princess Anna bought jewellery and has only half of the coins left. Write an expression describing how many gold coins Princess Elsa and Princess Anna together have. Expression: (100 × 2) + (100 ÷ 2) Terms: The terms are (100 × 2) and (100 ÷ 2). Step 1: Calculate Elsa's coins. 100 × 2 = 200 Step 2: Calculate Anna's coins. 100 ÷ 2 = 50 Step 3: Calculate the total coins. 200 + 50 = 250 The value of the expression is 250 gold coins. b) A metro train ticket between two stations costs ₹50 for an adult and ₹20 for a child. What is the total cost: i) for four adults and three children? Expression: (4 × 50) + (3 × 20) Terms: The terms are (4 × 50) and (3 × 20). Step 1: Calculate the cost for adults. 4 × 50 = 200 Step 2: Calculate the cost for children. 3 × 20 = 60 Step 3: Calculate the total cost. 200 + 60 = 260 The value of the expression is ₹260. ii) for two groups having three adults and two children each? Expression: 2 × ((3 × 50) + (2 × 20)) Terms: If expanded, the terms are (2 × 3 × 50) and (2 × 2 × 20). Step 1: Calculate the cost for adults in one group. 3 × 50 = 150 Step 2: Calculate the cost for children in one group. 2 × 20 = 40 Step 3: Calculate the total cost for one group. 150 + 40 = 190 Step 4: Calculate the total cost for two groups. 2 × 190 = 380 The value of the expression is ₹380. That's 2 down. 3 left today — send the next one.