Length stories use the same thinking as other word problems, with units like inches or meters. Keep the unit with your answer.
Why it works
A length is like a distance on a number line. Putting things end to end adds their lengths. Cutting a piece off takes length away. Comparing two lengths finds the difference.
Worked example: End to end
Two boards are 34 inches and 28 inches long. They are placed end to end. How long are they together?
- End to end means the lengths join: add.
- $34 + 28 = 62$.
Answer: 62 inches
Worked example: Cut off
A rope is 80 centimeters long. Sam cuts off 35 centimeters. How long is the rope now?
- Cutting off makes it shorter: subtract.
- $80 - 35 = 45$.
Answer: 45 centimeters
Worked example: The start is missing
Pat cut 18 inches off a ribbon. Now 47 inches are left. How long was the ribbon at first?
- The first ribbon is the whole. The 18 cut off and the 47 left are its parts.
- $47 + 18 = 65$.
- Check: $65 - 18 = 47$.
Answer: 65 inches
Key idea
Draw the lengths as jumps on a number line or as a tape. Add when lengths join; subtract when length is cut off or compared. Use one unit.
Common mistake
Mixing units. 1 foot and 6 inches is not “7” of anything. Change to one unit first: 1 foot is 12 inches, so 1 foot and 6 inches is 18 inches.
Grown-up tip: Use a measuring tape for real problems: How much ribbon do we need for two bows?