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Solve measurement word problems

Measurement word problems require interpreting quantities, units, and relationships in contexts involving length, mass, capacity, time, area, and volume; selecting appropriate operations or measurement formulas; and converting between related metric or customary units. Reasoning includes representing multi-step relationships with equations or diagrams, calculating with whole numbers, fractions, and decimals, labeling results correctly, and checking whether answers are reasonable. Generalized dimensional analysis, irrational measurements, and formal error analysis are beyond this scope.

Detailed Explanation: Solve measurement word problems

When solving a measurement word problem:

  1. Identify what you know and what you need to find.
  2. Make all measurements use the same unit.
  3. Choose an operation or formula.
  4. Solve and label the answer with units.
  5. Check that the answer is reasonable.

Example:
A ribbon is (3 m 40 cm)(3\text{ m }40\text{ cm}) long. It is cut into pieces that are (60 cm)(60\text{ cm}) long. How many full pieces can be cut, and how much ribbon is left?

Step 1: Use the same unit.
The piece length is in centimeters, so convert the whole ribbon to centimeters:

3 m=300 cm3\text{ m}=300\text{ cm} 300 cm+40 cm=340 cm300\text{ cm}+40\text{ cm}=340\text{ cm}

The ribbon is (340 cm)(340\text{ cm}) long.

Step 2: Divide to find the number of pieces.

340÷60=5 remainder 40340\div 60=5\text{ remainder }40

The quotient, 55, tells us there are 5 full pieces. The remainder, (40)(40), tells us how much ribbon is left.

Step 3: State the answer with units.

5 full pieces, with 40 cm left over\boxed{5\text{ full pieces, with }40\text{ cm left over}}

Check: Five pieces use (5×60=300 cm)(5\times60=300\text{ cm}). Since (340−300=40 cm)(340-300=40\text{ cm}), the answer is reasonable.

Learn by doing: Solve measurement word problems

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    Perimeter of a Parallelogram - Picture Intro

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