1. **State the problem:** We have four rows of distances in various units and need to perform operations such as subtraction, ordering, unit conversion, addition, and comparisons. 2. **Important rules and formulas:** - 1 km = 1000 m - 1 m = 100 cm - To subtract or add distances, convert all to the same unit first. - Ordering distances requires consistent units. 3. **Step 1: Subtract 350 m from all distances on the top row.** Top row distances: 4.7 km, 5250 m, 7.9 km, 6.45 km Convert all to meters: $$4.7\text{ km} = 4700\text{ m},\quad 5250\text{ m} = 5250\text{ m},\quad 7.9\text{ km} = 7900\text{ m},\quad 6.45\text{ km} = 6450\text{ m}$$ Subtract 350 m: $$4700 - 350 = 4350\text{ m}$$ $$5250 - 350 = 4900\text{ m}$$ $$7900 - 350 = 7550\text{ m}$$ $$6450 - 350 = 6100\text{ m}$$ Convert back to km where appropriate: $$4350\text{ m} = 4.35\text{ km},\quad 4900\text{ m} = 4.9\text{ km},\quad 7550\text{ m} = 7.55\text{ km},\quad 6100\text{ m} = 6.1\text{ km}$$ 4. **Step 2: Order second row distances from shortest to longest.** Second row: 7 7/10 km, 45.26 km, 185 cm, 3 ¼ km Convert mixed numbers: $$7\frac{7}{10} = 7.7\text{ km},\quad 3\frac{1}{4} = 3.25\text{ km}$$ Convert 185 cm to km: $$185\text{ cm} = 1.85\text{ m} = 0.00185\text{ km}$$ Order: $$0.00185\text{ km} < 3.25\text{ km} < 7.7\text{ km} < 45.26\text{ km}$$ 5. **Step 3: Order third row distances from longest to shortest.** Third row: 5900 m, 15.315 km, 9 ½ km, 17.8 m Convert mixed number: $$9\frac{1}{2} = 9.5\text{ km}$$ Convert all to km: $$5900\text{ m} = 5.9\text{ km},\quad 17.8\text{ m} = 0.0178\text{ km}$$ Order descending: $$15.315\text{ km} > 9.5\text{ km} > 5.9\text{ km} > 0.0178\text{ km}$$ 6. **Step 4: Order fourth row distances from longest to shortest.** Fourth row: 750 cm, 9 1/4 m, 2.7 km, 450 m Convert mixed number: $$9\frac{1}{4} = 9.25\text{ m}$$ Convert all to meters: $$750\text{ cm} = 7.5\text{ m},\quad 2.7\text{ km} = 2700\text{ m},\quad 450\text{ m} = 450\text{ m}$$ Order descending: $$2700\text{ m} > 450\text{ m} > 9.25\text{ m} > 7.5\text{ m}$$ 7. **Step 5: Convert all second row distances to meters.** $$7.7\text{ km} = 7700\text{ m},\quad 45.26\text{ km} = 45260\text{ m},\quad 185\text{ cm} = 1.85\text{ m},\quad 3.25\text{ km} = 3250\text{ m}$$ 8. **Step 6: Add 500 m to the longest distance on the bottom row.** Longest bottom row distance is 2.7 km = 2700 m Add 500 m: $$2700 + 500 = 3200\text{ m} = 3.2\text{ km}$$ 9. **Step 7: Find distance less than 2 meters on the Target Board.** From all distances, only 185 cm = 1.85 m is less than 2 m. 10. **Step 8: Distances between 5 ½ km and 6 ½ km.** Convert bounds: $$5\frac{1}{2} = 5.5\text{ km},\quad 6\frac{1}{2} = 6.5\text{ km}$$ Check distances: - Top row after subtraction: 4.35, 4.9, 7.55, 6.1 km Only 6.1 km is between 5.5 and 6.5 km. 11. **Step 9: Difference between longest and shortest distances on top row.** Original top row in meters: $$4700, 5250, 7900, 6450$$ Longest: 7900 m, shortest: 4700 m Difference: $$7900 - 4700 = 3200\text{ m} = 3.2\text{ km}$$ 12. **Step 10: If target distance is 10 km, what to add to each distance on first row?** Distances on first row: $$4.7, 5.25, 7.9, 6.45\text{ km}$$ Calculate difference to 10 km: $$10 - 4.7 = 5.3\text{ km}$$ $$10 - 5.25 = 4.75\text{ km}$$ $$10 - 7.9 = 2.1\text{ km}$$ $$10 - 6.45 = 3.55\text{ km}$$ **Final answers:** 1. Top row after subtracting 350 m: 4.35 km, 4.9 km, 7.55 km, 6.1 km 2. Second row ordered shortest to longest: 185 cm, 3 ¼ km, 7 7/10 km, 45.26 km 3. Third row ordered longest to shortest: 15.315 km, 9 ½ km, 5.9 km, 17.8 m 4. Fourth row ordered longest to shortest: 2.7 km, 450 m, 9 1/4 m, 750 cm 5. Second row in meters: 7700 m, 45260 m, 1.85 m, 3250 m 6. Longest bottom row + 500 m: 3.2 km 7. Distance less than 2 m: 185 cm (1.85 m) 8. Distances between 5 ½ km and 6 ½ km: 6.1 km 9. Difference longest-shortest top row: 3.2 km 10. Add to each first row distance to reach 10 km: 5.3 km, 4.75 km, 2.1 km, 3.55 km