AI generatedNumberGCSE Higher

Bounds in division

Use the opposite bound in the denominator.

  • Write the original error intervals before calculating. Keep the bounds exact.
  • Choose the combination of bounds that makes the result smallest or largest. The direction matters for subtraction and division.
  • Round only at the end. A stated upper bound need not be an attainable value.

Example 1

= 24 and = 8, each rounded to the nearest whole number. Find the lower and upper bounds of .

Lower boundSmallest quotient: smallest numerator over largest denominator. Largest quotient: reverse the choices.
Upper boundEvaluate without rounding the input bounds.
Lower bound . Upper bound .

Example 2

= 25 and = 9, each rounded to the nearest whole number. Find the lower and upper bounds of .

Lower boundSmallest quotient: smallest numerator over largest denominator. Largest quotient: reverse the choices.
Upper boundEvaluate without rounding the input bounds.
Lower bound . Upper bound .

Your turn

Question 1

= 26 and = 10, each rounded to the nearest whole number. Find the lower and upper bounds of .

Check answer
Lower boundSmallest quotient: smallest numerator over largest denominator. Largest quotient: reverse the choices.
Upper boundEvaluate without rounding the input bounds.
Lower bound . Upper bound .
Question 2

= 27 and = 11, each rounded to the nearest whole number. Find the lower and upper bounds of .

Check answer
Lower boundSmallest quotient: smallest numerator over largest denominator. Largest quotient: reverse the choices.
Upper boundEvaluate without rounding the input bounds.
Lower bound . Upper bound .
Question 3

= 28 and = 12, each rounded to the nearest whole number. Find the lower and upper bounds of .

Check answer
Lower boundSmallest quotient: smallest numerator over largest denominator. Largest quotient: reverse the choices.
Upper boundEvaluate without rounding the input bounds.
Lower bound . Upper bound .
Question 4

= 29 and = 13, each rounded to the nearest whole number. Find the lower and upper bounds of .

Check answer
Lower boundSmallest quotient: smallest numerator over largest denominator. Largest quotient: reverse the choices.
Upper boundEvaluate without rounding the input bounds.
Lower bound . Upper bound .
Question 5

= 30 and = 14, each rounded to the nearest whole number. Find the lower and upper bounds of .

Check answer
Lower boundSmallest quotient: smallest numerator over largest denominator. Largest quotient: reverse the choices.
Upper boundEvaluate without rounding the input bounds.
Lower bound . Upper bound .
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