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MathidiaMathematics Academy
Proportion and rates of change
Lesson 38 of 75
Standard practice

Density and pressure

Objective. Rearrange and use compound-measure formulae.

  1. 1. Learn
  2. 2. Worked example
  3. 3. Practice
  4. 4. Feedback
  5. 5. Continue

Learn: the key idea

Density and pressure develops a connected mathematical idea rather than an isolated trick. Model multiplicative relationships algebraically and graphically. Begin by representing the quantities or relationships, choose a rule that fits, justify each transformation, and finish by checking units, signs, scale and whether the answer is reasonable.

Worked example

Share £70 in the ratio 2:3. Give the larger share.

£70.00
Money illustration for £70
  1. 1Identify the known information, the unknown and any conditions.
  2. 2Choose a diagram, table, graph or algebraic representation that exposes the structure.
  3. 3Apply the relevant rule one justified step at a time, keeping exact values where useful.
  4. 4Check by substitution, inverse reasoning or estimation. The result is £42.

Answer: £42

Concept mastery

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Practice

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Common mistake. A common error in density and pressure is to copy a procedure without checking its conditions. Label the structure first and justify every sign, operation and unit.

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