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A line segment is of length 5 cm 7 mm. Another line segment of length 9 cm 6 mm is joined to it in the same direction. The length of the combined line segment is:
14 cm 3 mm
14 cm 6 mm
15 cm 7 mm
15 cm 3 mm
15 cm 3 mm
Add the centimeters and millimeters separately: (5+9) cm + (7+6) mm = 14 cm 13 mm. Since 10 mm = 1 cm, carry the 1 from 13 to the centimeters to get 15 cm 3 mm.
Length 1 = 5 cm 7 mm, Length 2 = 9 cm 6 mm
Total Length=(L1,cm+L2,cm) cm +(L1,mm+L2,mm) mm
Add the centimeters and millimeters separately: (5+9) cm + (7+6) mm = 14 cm 13 mm. Since 10 mm = 1 cm, carry the 1 from 13 to the centimeters to get 15 cm 3 mm.
Many students fail to convert the excess millimeters (13 mm) into centimeters and millimeters (1 cm 3 mm) and incorrectly add them to the centimeters, leading to errors like 14 cm 13 mm or simply adding wrongly.
Add the components
Add the centimeters together and the millimeters together: 5 cm +9 cm=14 cm and 7 mm +6 mm=13 mm.
(5+9) cm +(7+6) mm=14 cm 13 mm
Convert mm to cm
Since 1 cm=10 mm, convert 13 mm into centimeters: 13 mm=1 cm 3 mm.
13 mm=1 cm +3 mm
Calculate total length
Add the converted centimeter value to the previous centimeter sum: 14 cm +1 cm +3 mm=15 cm 3 mm.
14 cm +1 cm 3 mm=15 cm 3 mm
D is correct because adding 5 cm 7 mm and 9 cm 6 mm results in 14 cm 13 mm, which simplifies to 15 cm 3 mm.
This unit conversion logic (base 10 for length) is identical to currency calculations (e.g., paise to rupees) or time calculations (seconds to minutes) where you must account for the carry-over value.
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