Solve problems involving length
Theory
To solve a length problem, change every measurement to the same unit, then add for a total or subtract for a difference or what is left.
Lengths can only be added or subtracted when they share the same unit. First pick a common unit and convert.
Multiply to change to a smaller unit and divide to change to a larger one, using \(10\) between mm and cm, \(100\) between cm and m, and \(1000\) between m and km.
Then add to find a total distance, or subtract to find a difference or how much is left.
Match the operation to what the question asks.
| Question asks for… | Do this |
|---|---|
| Total distance | add |
| Difference / how much longer | subtract |
| How much is left | subtract |
How to solve a length problem
- Choose a common unit and convert every measurement to it.
- Decide whether to add (a total) or subtract (a difference or what is left).
- Work out the answer and give it in the unit asked for.
All in metres, so add: \(1200 + 850 = 2050\), then \(2050 + 2300 = 4350\).
He rides 4350 m.
\(1.8 \times 1000 = 1800\), then \(1800 - 950 = 850\).
The track is 850 m longer.
\(2.4 \times 100 = 240\), then \(240 - 185 = 55\).
The first rope is 55 cm longer.
\(250 \div 100 = 2.5\), then \(12 - 4.5 = 7.5\) and \(7.5 - 2.5 = 5\).
There is 5 m left.
Common pitfalls
Frequently asked questions
Why convert to the same unit first?
Lengths can only be added or subtracted when they share a unit. Adding \(2.4\) m to \(185\) cm directly would give the wrong answer.
Which unit should you choose?
Usually the unit the answer is asked for, or the smaller unit so the numbers are whole. Convert every measurement to that one unit.
Do you add or subtract?
Add to find a total distance. Subtract to find a difference, how much longer, or how much is left.
How do you find how much is left after cutting pieces?
Convert every piece to one unit, then subtract each cut piece from the starting length in turn.