Diego changed 200 euros to Argentine Peso. The exchange rate was 1 euro - 24.8 pesos. Work out how many pesos he received.

Here are the solutions to the problems: 4. (b) Diego changed 200 euros to Argentine Peso. The exchange rate was 1 euro = 24.8 pesos. Work out how many pesos he received. Step 1: Multiply the amount in euros by the exchange rate. Pesos received = Euros × Exchange rate Pesos received = 200 × 24.8 Pesos received = 4960 Diego received 4960 pesos. 4. (c) The distance between Madrid and Buenos Aires is 10 050 km. Diego's return flight took 12 hours and 30 minutes. Calculate the average speed, in km/h, for the return flight. Step 1: Convert the time to hours. 12 hours 30 minutes = 12 + (30)/(60) hours 12 hours 30 minutes = 12 + 0.5 hours Time = 12.5 hours Step 2: Calculate the average speed using the formula Speed = Distance / Time. Speed = 10\,050 km12.5 h Speed = 804 km/h The average speed is 804 km/h. 5. Find the highest odd number that is a factor of both 60 and 90. Step 1: List the factors of 60. Factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60 Step 2: List the factors of 90. Factors of 90: 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90 Step 3: Identify the common factors. Common factors: 1, 2, 3, 5, 6, 10, 15, 30 Step 4: Identify the odd common factors and find the highest one. Odd common factors: 1, 3, 5, 15 The highest odd number that is a factor of both 60 and 90 is 15. 6. Put in one pair of brackets in each statement to make it correct. 6. (a) 16 + (8 + 4 × 2) = 1 To get 1, we need the expression to evaluate to 16 - 15. Let's try placing brackets to make the part after 16 equal to -15. This is not possible with addition. Let's re-examine the problem. It's 16 ÷ (8 + 4 × 2) = 1. Assuming the operation is division, not addition, to make the result 1. If it's 16 ÷ (8 + 4 × 2) = 1: 16 ÷ (8 + (4 × 2)) = 1 16 ÷ (8 + 8) = 1 16 ÷ 16 = 1 So, the brackets should be: 16 ÷ (8 + 4 × 2) = 1. Self-correction: The image clearly shows a plus sign, not a division sign. Let's re-evaluate with the plus sign. If the equation is 16 + (8 + 4 × 2) = 1, this is impossible to make true by just adding one pair of brackets, as 16 + (positive number) will always be greater than 16. However, if the question implies that the operation itself might be missing or incorrect, and we are meant to insert brackets to make it true, it's ambiguous. Given the context of typical math problems, it's highly probable that the operation shown is incorrect or there's a typo in the question. If we assume the operation is division, the solution above works. If we strictly stick to the plus sign, no single pair of brackets will make 16 + (something) equal to 1. Let's assume there's a typo and it should be 16 - (8 + 4 × 2) = 1 or 16 ÷ (8 + 4 × 2) = 1. Given the student's previous work, they might be expecting a division or subtraction. If it's 16 - (8 + 4 × 2) = 1: 16 - (8 + 8) = 1 16 - 16 = 0 ≠ 1. If it's 16 ÷ (8 + 4 × 2) = 1: 16 ÷ (8 + 8) = 1 16 ÷ 16 = 1. This works. Let's assume the operation is division, as it's the most common way to get 1 from 16 and another number. 16 ÷ (8 + 4 × 2) = 1 6. (b) 16 + (8 + 4 × 2) = 12 We need the expression to evaluate to 16 - 4 = 12. So, the part in brackets should result in -4. This is not possible with the given numbers and operations. Let's try to make the part in brackets equal to -4. If we assume the operation is subtraction: 16 - (8 + 4) × 2 = 12 16 - (12) × 2 = 12 16 - 24 = -8 ≠ 12. If we assume the operation is subtraction: 16 - (8 + 4 × 2) = 12 16 - (8 + 8) = 12 16 - 16 = 0 ≠ 12. Let's consider if the brackets change the order of operations to make the result 12. Original expression without brackets: 16 + 8 + 4 × 2 = 16 + 8 + 8 = 32. We need to reduce this to 12. Try (16 + 8) + 4 × 2 = 24 + 8 = 32. Try 16 + (8 + 4) × 2 = 16 + 12 × 2 = 16 + 24 = 40. Try 16 + 8 + (4 × 2) = 16 + 8 + 8 = 32. It seems there might be a typo in the question or the operation. If the operation was subtraction, for example: 16 - (8 + 4) = 12 16 - 12 = 4 ≠ 12. If it was 16 - (8 - 4) × 2 = 12 16 - (4) × 2 = 12 16 - 8 = 8 ≠ 12. Let's assume the question intends for the brackets to be placed such that the expression evaluates to 12. If the operation is 16 - (8 + 4) ÷ 2 = 12: 16 - 12 ÷ 2 = 12 16 - 6 = 10 ≠ 12. Given the exact wording "Put in one pair of brackets in each statement to make it correct", and the presence of a plus sign, it's highly likely there's a typo in the question itself, as 16 + (positive number) cannot equal 12. However, if we consider the possibility of a division sign instead of a plus sign, similar to part (a): If it's 16 ÷ (8 - 4) × 2 = 12: 16 ÷ 4 × 2 = 12 4 × 2 = 8 ≠ 12. Let's assume the question is 16 - (8 - 4 × 2) = 12. 16 - (8 - 8) = 12 16 - 0 = 16 ≠ 12. Let's try to make the expression 16 + (something) equal to 12. This means the "something" must be -4. This is not possible with 8, 4, 2 and multiplication/addition. There must be a typo in the question. If we assume the operation is subtraction, for example: 16 - (8 - 4) × 2 = 12 16 - (4) × 2 = 12 16 - 8 = 8 ≠ 12. Let's consider if the question meant 16 - (8 + 4) + 2 = 12. 16 - 12 + 2 = 4 + 2 = 6 ≠ 12. Given the constraints, and the high probability of a typo in the question, I cannot provide a solution that strictly adheres to "one pair of brackets" and the given operations to reach 12. If we assume the question meant 16 - (8 - 4) × 2 = 12, it doesn't work. If we assume the question meant 16 - (8 + 4) ÷ 2 = 12, it doesn't work. Let's assume the question meant to be 16 - (8 - 4) × 2 = 12 but the numbers are slightly different. If the question was 16 - (8 - 2) × 2 = 12: 16 - (6) × 2 = 12 16 - 12 = 4 ≠ 12. I will state that this question appears to have a typo, as it's not possible to achieve 12 with the given numbers and operations using only one pair of brackets and the addition sign. However, if we consider a common type of problem where the operation might be different, for example, if it was 16 - (8 - 4 × 2) = 12: 16 - (8 - 8) = 12 16 - 0 = 16 ≠ 12. Let's try to make the expression 16 + (something) equal to 12. This means the "something" must be -4. This is not possible with 8, 4, 2 and multiplication/addition. I will provide the most plausible interpretation if a typo is assumed. If the question was 16 - (8 - 4) × 2 = 12, it would be 16 - (4) × 2 = 16 - 8 = 8. If the question was 16 - (8 + 4) + 2 = 12, it would be 16 - 12 + 2 = 6. Given the ambiguity, I will state that the problem as written with a '+' sign cannot be solved by adding one pair of brackets. If there was a typo and it was 16 - (8 + 4) = 12, then 16 - 12 = 4 ≠ 12. If it was 16 - (8 - 4) = 12, then 16 - 4 = 12. This would work if the operations were different. Assuming the operations are fixed, and only brackets can be added: 16 + (8 + 4 × 2) = 16 + (8 + 8) = 16 + 16 = 32 ≠ 12. 16 + (8 + 4) × 2 = 16 + 12 × 2 = 16 + 24 = 40 ≠ 12. 16 + 8 + (4 × 2) = 16 + 8 + 8 = 32 ≠ 12. It is not possible to make this statement correct with the given operations and numbers by adding one pair of brackets. There is likely a typo in the question. 7. (a) Write the number 0.0605 in standard form. Step 1: Move the decimal point to get a number between 1 and 10. To get 6.05, the decimal point needs to move 2 places to the right. Step 2: Determine the power of 10. Since the decimal point moved 2 places to the right, the exponent will be -2. 0.0605 = 6.05 × 10^-2 The number in standard form is 6.05 × 10^-2. 7. (b) Calculate (1.63 × 10^12) × (2.47 × 10^-4). Give your answer in standard form. Step 1: Multiply the numerical parts. 1.63 × 2.47 = 4.0201 Step 2: Multiply the powers of 10 by adding their exponents. 10^12 × 10^-4 = 10^12 + (-4) = 10^12 - 4 = 10^8 Step 3: Combine the results. 4.0201 × 10^8 The numerical part 4.0201 is already between 1 and 10, so no further adjustment is needed. The answer in standard form is 4.0201 × 10^8. What's next?