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.
ScanSolve AI Answer
a) To fill in the empty boxes on the number line, first determine the interval size between the given numbers. Step 1: Calculate the difference between the known values and the number of intervals between them. The known values are -0.8 and 1.0. The difference is 1.0 - (-0.8) = 1.0 + 0.8 = 1.8. There are 3 intervals between -0.8 and 1.0. The length of each interval is (1.8)/(3) = 0.6. Step 2: Fill in the empty boxes by adding or subtracting the interval length. The box to the right of -0.8 is -0.8 + 0.6 = -0.2. The box to the left of -0.8 is -0.8 - 0.6 = -1.4. The box to the left of -1.4 is -1.4 - 0.6 = -2.0. The completed number line values are: -2.0, -1.4, -0.8, -0.2, 0.4, 1.0. b) Solve the expression 3(4)/(7) × ((8)/(9) - (2)/(3)). Step 1: Convert the mixed number to an improper fraction. 3(4)/(7) = ((3 × 7) + 4)/(7) = (21 + 4)/(7) = (25)/(7) Step 2: Solve the expression inside the parentheses by finding a common denominator. (8)/(9) - (2)/(3) = (8)/(9) - (2 × 3)/(3 × 3) = (8)/(9) - (6)/(9) = (8 - 6)/(9) = (2)/(9) Step 3: Multiply the results from Step 1 and Step 2. (25)/(7) × (2)/(9) = (25 × 2)/(7 × 9) = (50)/(63) The solution is (50)/(63). Send me the next one 📸