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Grade 6 · Mathematics

Converting units with ratios

Use equivalent quantities to convert length, mass, time and rates.

Before you begin

  • Decimal multiplication and division
  • Unit rates

Use a conversion factor equal to one

One kilometre and 1,000 metres are the same length, so their ratio equals one. Multiplying a measurement by this ratio changes its unit without changing the physical quantity. Arrange the factor so the old unit cancels. Write the units through each step; they help you decide whether to multiply or divide and expose conversion factors used in the wrong direction.

Convert a rate one unit at a time

A rate has two units, so converting it may require changing both the numerator and denominator. For metres per minute to metres per second, one minute contains 60 seconds, so divide by 60. The number must decrease because the distance travelled in one second is less than in one minute. Always use a stated conversion for unfamiliar or non-metric units.

See the reasoning

Worked example

Convert 2.4 km to metres, then convert 150 cm to metres.

Show the worked solution
  1. Use 1 km = 1,000 m: 2.4 × 1,000 = 2,400 m.
  2. Use 100 cm = 1 m: 150 ÷ 100 = 1.5 m.
  3. Check direction: the numerical value increases for smaller units and decreases for larger units.

2,400 m; 1.5 m.

Try it yourself

Convert 90 metres per minute to metres per second.

Common mistakes

  • Time units do not all convert in powers of ten.
  • An area conversion uses the square of a length conversion factor.
Recall without your notes

What can you explain now?

A runner travels at 6 km/h. Convert this to metres per minute.

Compare with the explanation

100 m/min.

6 km/h = 6,000 m/h. Divide by 60 minutes per hour to get 100 m/min.

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Bring the ideas together

Ratios, rates and percentages

Try the unit review

Original StudyForA content. AI-assisted checks completed; subject-teacher review is still pending. These lessons are not endorsed by an exam board.

Common Core mathematics standards ↗