Adding and subtracting lengths

In your book, Maths Mela (Chapter 5, Far and Near), Saji's smartphone shows that he walked 3 km 450 m in the morning and 4 km 650 m in the evening. How far did he walk in all? One way is to add like units: 3 km + 4 km = 7 km, and 450 m + 650 m = 1,100 m, which is 1 km 100 m. So 7 km + 1 km 100 m = 8 km 100 m. Another way is to change everything into metres: 3,450 m + 4,650 m = 8,100 m = 8 km 100 m. Both ways give the same answer.

Subtraction works the same way. Electricians need 63 m of cable to change the cables in a house, and they use 16 m 75 cm in the first room. How much is left? Change both to centimetres: 63 m = 6,300 cm and 16 m 75 cm = 1,675 cm. 6,300 − 1,675 = 4,625 cm, which is 46 m 25 cm. Or subtract like units: take 1 m from the 63 m as 100 cm, so 62 m 100 cm − 16 m 75 cm = 46 m 25 cm.

The distance from Bhopal to Sanchi is 48 km 700 m. The Bhadbhada Ghat waterfall is on the way, 17 km 900 m from Bhopal. How far is Sanchi from the waterfall? 700 m − 900 m cannot be done, so 1 km of the 48 km becomes 1,000 m: 47 km 1,700 m − 17 km 900 m = 30 km 800 m.

To find the difference between two lengths, first write them in the same unit. 6 km and 5,678 m: 6 km = 6,000 m, so 6 km is bigger, and the difference is 6,000 − 5,678 = 322 m.