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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3: 1. Round off these lengths to the nearest 10 m and 100 m. a) 34566 m Step 1: To the nearest 10 m, look at the units digit (6). Since 6 5, round up the tens digit. 34566 m ≈ 34570 m Step 2: To the nearest 100 m, look at the tens digit (6). Since 6 5, round up the hundreds digit. 34566 m ≈ 34600 m b) 135 m Step 1: To the nearest 10 m, look at the units digit (5). Since 5 5, round up the tens digit. 135 m ≈ 140 m Step 2: To the nearest 100 m, look at the tens digit (3). Since 3 < 5, round down. 135 m ≈ 100 m c) 2408 m Step 1: To the nearest 10 m, look at the units digit (8). Since 8 5, round up the tens digit. 2408 m ≈ 2410 m Step 2: To the nearest 100 m, look at the tens digit (0). Since 0 < 5, round down. 2408 m ≈ 2400 m 2. Round off these lengths to the nearest 1000 m. a) 3500 m Step 1: To the nearest 1000 m, look at the hundreds digit (5). Since 5 5, round up the thousands digit. 3500 m ≈ 4000 m b) 34567 m Step 1: To the nearest 1000 m, look at the hundreds digit (5). Since 5 5, round up the thousands digit. 34567 m ≈ 35000 m c) 1423 m Step 1: To the nearest 1000 m, look at the hundreds digit (4). Since 4 < 5, round down. 1423 m ≈ 1000 m 3. Do these calculations. a) 32456 m + 12123 m Step 1: Add the two lengths. 32456 m + 12123 m = 44579 m b) 9 km - 7367 m Step 1: Convert 9 km to metres (1 km = 1000 m). 9 km = 9 × 1000 m = 9000 m Step 2: Subtract the lengths. 9000 m - 7367 m = 1633 m c) 34 (1)/(2) cm + 12 cm + 500 mm Step 1: Convert all lengths to centimetres (1 cm = 10 mm). 34 (1)/(2) cm = 34.5 cm 500 mm = (500)/(10) cm = 50 cm Step 2: Add the lengths. 34.5 cm + 12 cm + 50 cm = 96.5 cm d) (1)/(8) m + (2)/(8) m Step 1: Add the fractions with the same denominator. (1)/(8) m + (2)/(8) m = (1+2)/(8) m = (3)/(8) m 4. Do these calculations. a) 340 m × 12 Step 1: Multiply the values. 340 m × 12 = 4080 m b) 224 km × 15 Step 1: Multiply the values. 224 km × 15 = 3360 km c) 440 m ÷ 20 Step 1: Divide the values. 440 m ÷ 20 = 22 m d) 345 cm ÷ 5 Step 1: Divide the values. 345 cm ÷ 5 = 69 cm 5. How many quarters of a metre are there in 4 (3)/(4) m? Step 1: Convert the mixed number to an improper fraction. 4 (3)/(4) m = ((4 × 4) + 3)/(4) m = (16+3)/(4) m = (19)/(4) m Step 2: A quarter of a metre is (1)/(4) m. To find how many quarters are in (19)/(4) m, divide (19)/(4) by (1)/(4). (19)/(4) ÷ (1)/(4) = (19)/(4) × (4)/(1) = 19 There are 19 quarters of a metre. 6. The odometers recorded the following distances from the odometers of her aunts and uncles. 12374 km; 25135 km; 60901 km; 78345 km; 11961 km Order the distances the cars have travelled from the shortest to the longest distance. Step 1: Compare the given distances. 11961 km, 12374 km, 25135 km, 60901 km, 78345 km Estimate and then calculate the total distance that all the cars have travelled. Step 1: Estimate the total distance by rounding each distance to the nearest thousand kilometres. 12374 km ≈ 12000 km 25135 km ≈ 25000 km 60901 km ≈ 61000 km 78345 km ≈ 78000 km 11961 km ≈ 12000 km Estimated total: 12000 + 25000 + 61000 + 78000 + 12000 = 188000 km Step 2: Calculate the exact total distance by adding all the given distances. 12374 km + 25135 km + 60901 km + 78345 km + 11961 km = 188716 km What's next?