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 for the remaining questions. c) Sunita buys 5 kg of rice at Rs 90 per kg and 2 kg of sugar at Rs 70 per kg. i) Write a mathematical expression and simplify it to find the total cost of these two items. Step 1: Calculate the cost of rice. Cost of rice = 5 kg × Rs 90/kg = Rs 450 Step 2: Calculate the cost of sugar (assuming Rs 70 per kg). Cost of sugar = 2 kg × Rs 70/kg = Rs 140 Step 3: Write the mathematical expression for the total cost and simplify. Total cost = (5 × 90) + (2 × 70) Total cost = 450 + 140 = 590 The total cost is Rs 590. Rs 590 ii) If she gives a 1000 rupees note to the shopkeeper, how much does the shopkeeper return to her? Step 1: Subtract the total cost from the amount paid. Change = 1000 - 590 = 410 The shopkeeper returned Rs 410. Rs 410 d) On a day, there were 27 students present in class six. 16 of them are girls and the rest were boys. If only 3 boys were absent on that day, represent the information by a mathematical expression and find the number of boys in class six. Step 1: Find the total number of boys present. Total boys present = 27 - 16 = 11 Step 2: Add the absent boys to find the total number of boys in class six. Total boys in class = (27 - 16) + 3 Total boys in class = 11 + 3 = 14 The number of boys in class six is 14. 14 9. a) Let's make any four your own mixed expressions using all (+, -, ×, ÷) in each expression. Simplify them and get answers. Expression 1: 10 + 5 × 2 - 8 ÷ 4 Step 1: Perform multiplication and division from left to right. 10 + 10 - 2 Step 2: Perform addition and subtraction from left to right. 20 - 2 = 18 18 Expression 2: (20 - 5) ÷ 3 + 7 × 2 Step 1: Perform operations inside parentheses. 15 ÷ 3 + 7 × 2 Step 2: Perform division and multiplication from left to right. 5 + 14 Step 3: Perform addition. 19 19 Expression 3: 15 × 2 - (10 + 4) ÷ 2 Step 1: Perform operations inside parentheses. 15 × 2 - 14 ÷ 2 Step 2: Perform multiplication and division from left to right. 30 - 7 Step 3: Perform subtraction. 23 23 Expression 4: 100 ÷ 10 + 5 - 2 × 3 Step 1: Perform division and multiplication from left to right. 10 + 5 - 6 Step 2: Perform addition and subtraction from left to right. 15 - 6 = 9 9 9. b) Let's rewrite these simplifications and find the mistakes. Then, show the simplification in the correct way. Box 1: Given: 35 - 10 + 5 = 35 - 15 = 20 Mistake: Addition was performed before subtraction. Operations of the same precedence (addition and subtraction) should be done from left to right. Correct simplification: 35 - 10 + 5 = 25 + 5 = 30 30 Box 2: Given: 27 - 6 - 4 = 27 - 2 = 25 Mistake: The second subtraction (6-4) was performed before the first subtraction (27-6). Subtraction operations should be done from left to right. Correct simplification: 27 - 6 - 4 = 21 - 4 = 17 17 Box 3: Given: 9 + 3 × 2 = 12 × 2 = 24 Mistake: Addition was performed before multiplication. Multiplication has higher precedence than addition. Correct simplification: 9 + 3 × 2 = 9 + 6 = 15 15 Box 4: Given: 18 - 5 × 3 = 13 × 3 = 39 Mistake: Subtraction was performed before multiplication. Multiplication has higher precedence than subtraction. Correct simplification: 18 - 5 × 3 = 18 - 15 = 3 3 Box 5: (Based on the visible part, assuming the expression is 40 ÷ 5 + 3) Given: 40 ÷ 5 + 3 = 8 + 3 = 11 This simplification is correct. Division was performed before addition, following the order of operations. 11 3 done, 2 left today. You're making progress.