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MathidiaMathematics Academy
Number fluency, bounds and accuracy
Lesson 2 of 75
Easy practice

Bounds in calculations

Objective. Select lower and upper bounds through sums, differences, products and quotients.

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

Learn: the key idea

This topic is about combining upper and lower bounds correctly when measurements are used in calculations. For addition, add the two upper bounds for the maximum and the two lower bounds for the minimum. For subtraction, the maximum of A − B uses the upper bound of A minus the lower bound of B, and the minimum uses the lower bound of A minus the upper bound of B. The same crossing pattern applies to division: the maximum of A ÷ B uses upper A over lower B. Always identify which combination of bounds gives the extreme result before calculating.

Worked example

A rectangle has length 8.4 cm and width 3.2 cm, each measured to 1 decimal place. Find the upper bound for the area.

Diagram of a rectangle
  1. 1Length bounds: 8.35 ≤ l < 8.45.
  2. 2Width bounds: 3.15 ≤ w < 3.25.
  3. 3Maximum area uses the upper bounds of both: 8.45 × 3.25.
  4. 48.45 × 3.25 = 27.4625 cm².

Answer: 27.4625 cm²

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Common mistake. A common error is subtracting the lower bound of A from the lower bound of B when finding the maximum of A − B. Always use upper A minus lower B for the maximum difference.

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