Measurement & Time

Problem

Convert to one unit, then compare lengths

Three buildings have heights given in mixed units: the post office is 24 ft 1 in, the school is 320 in, and the fire station is 267 in. Put the buildings in order from shortest to tallest.
Measurement & data
Your answer
How to solve
Strategy Analyze the Units — The heights are in different units (feet-and-inches versus inches), so they can't be compared directly. First convert everything to one unit (inches), then list the three numbers and order them.
1STEP 1

Convert the post office to inches

Change 24 ft 1 in into inches. Each foot is 12 inches, so 24 feet is 24 times 12, then add the extra 1 inch.

24 × 12 = 288, 288 + 1 = 289
2STEP 2

List all three heights in inches

Now every height is in inches: post office 289 in, school 320 in, fire station 267 in.

267, 289, 320
3STEP 3

Order from shortest to tallest

Order the inch values 267 < 289 < 320: fire station is shortest, post office next, school tallest.

267 < 289 < 320
Answer
From shortest to tallest: fire station (267 in), post office (24 ft 1 in = 289 in), school (320 in).
All three are a few hundred inches (about 22-27 feet), reasonable building heights, and the order 267 < 289 < 320 inches is correct. Converting back, 289 in = 24 ft 1 in matches the post office.
Takeaway

Make every height use the same unit first, then it's just Grade 2 'which number is bigger' comparing!

  • Convert the post office to inches
  • List all three heights in inches
  • Order from shortest to tallest
Where next?
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