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 your questions: 5. Using the correct order of operations (BODMAS), work out the value of the expression: 24 ÷ 3 + 2 × 5 - 4. Step 1: Perform division. 24 ÷ 3 = 8 The expression becomes: 8 + 2 × 5 - 4. Step 2: Perform multiplication. 2 × 5 = 10 The expression becomes: 8 + 10 - 4. Step 3: Perform addition. 8 + 10 = 18 The expression becomes: 18 - 4. Step 4: Perform subtraction. 18 - 4 = 14 The final answer is B. 14. 6. In a mathematics test, a student was asked to express the fraction (3)/(8) as a decimal. Which of the following is correct? Step 1: Divide the numerator by the denominator. (3)/(8) = 3 ÷ 8 Step 2: Perform the division. 3 ÷ 8 = 0.375 The final answer is A. 0.375. 7. What is the final result when you calculate the square root of the mixed fraction sqrt((6 (1)/(4)))? Step 1: Convert the mixed fraction to an improper fraction. 6 (1)/(4) = ((6 × 4) + 1)/(4) = (24 + 1)/(4) = (25)/(4) Step 2: Calculate the square root of the improper fraction. sqrt((25)/(4)) = sqrt(25)sqrt(4) Step 3: Find the square roots of the numerator and the denominator. sqrt(25)sqrt(4) = (5)/(2) Step 4: Convert the improper fraction back to a mixed number. (5)/(2) = 2 (1)/(2) The final answer is A. 2 (1)/(2). 8. A farmer has n cows and m goats in his farm. If he sells 5 of his cows, which algebraic expression represents the total remaining animals? Step 1: Identify the initial number of each type of animal. Number of cows = n Number of goats = m Step 2: Determine the number of cows remaining after selling 5. Remaining cows = n - 5 Step 3: Write the expression for the total remaining animals by adding the remaining cows and the goats. Total remaining animals = (Remaining cows) + (Number of goats) Total remaining animals = (n - 5) + m Total remaining animals = n - 5 + m The final answer is B. n - 5 + m. 9. Convert the decimal number 0.45 into a fraction and then reduce it to its simplest form. Step 1: Convert the decimal to a fraction. The decimal 0.45 means 45 hundredths. 0.45 = (45)/(100) Step 2: Reduce the fraction to its simplest form by finding the greatest common divisor (GCD) of the numerator and the denominator. The GCD of 45 and 100 is 5. Step 3: Divide both the numerator and the denominator by their GCD. (45 ÷ 5)/(100 ÷ 5) = (9)/(20) The final answer is B. (9)/(20). Last free one today — make it count tomorrow, or type /upgrade for unlimited.