A line is 135 m 52 cm long. How long will it be if it is extended by 12 m 32 cm?
Understand the Problem
The question is asking to calculate the new length of a line that is currently 135 meters and 52 centimeters long after it is extended by 12 meters and 32 centimeters. It requires adding the two lengths together to find the total.
Answer
The new length of the line is $147 \text{ m } 84 \text{ cm}$.
Answer for screen readers
The new length of the line is (147 \text{ m } 84 \text{ cm}).
Steps to Solve
- Convert both lengths to the same unit
Convert the lengths from meters and centimeters to centimeters to simplify addition.
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The initial length is (135) meters and (52) centimeters: [ 135 \text{ m} = 135 \times 100 = 13500 \text{ cm} ] [ \text{Total initial length} = 13500 \text{ cm} + 52 \text{ cm} = 13552 \text{ cm} ]
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The extended length is (12) meters and (32) centimeters: [ 12 \text{ m} = 12 \times 100 = 1200 \text{ cm} ] [ \text{Total extended length} = 1200 \text{ cm} + 32 \text{ cm} = 1232 \text{ cm} ]
- Add the two lengths together
Now, add the total lengths in centimeters: [ \text{Total length after extension} = 13552 \text{ cm} + 1232 \text{ cm} ] [ = 14784 \text{ cm} ]
- Convert the total length back to meters and centimeters
To convert (14784) centimeters back to meters and centimeters:
- Find the number of meters: [ 14784 \div 100 = 147 \text{ m} \quad (\text{whole number}) ]
- Find the remaining centimeters: [ 14784 \mod 100 = 84 \text{ cm} ]
Thus, the total length after the extension is (147) meters and (84) centimeters.
The new length of the line is (147 \text{ m } 84 \text{ cm}).
More Information
The calculation showcases how to work with measurements in different units. Knowing how to convert between meters and centimeters is a fundamental skill in practical mathematics and everyday applications.
Tips
- Forgetting to convert both lengths to the same unit before adding, which can lead to incorrect totals.
- Miscalculating the conversion from centimeters back to meters and centimeters.
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