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- Work out each answer from two natural numbers and name the smallest set that holds it.
- Find what is wrong with Hannah's argument about closure under subtraction.
- Decide if the integers greater than 10 are closed under addition, and check Ryan's subtraction claim.
- Test whether the natural numbers ending in 6 are closed under the operations.
- Simplify powers of an irrational number and say if each is rational or irrational.
- Give an example of each combination of irrational numbers, or explain why none exists.
- Show that the reciprocal of an irrational number is irrational, then use it to decide a follow-up question.
- Decide if the negative rational numbers are closed under each operation.
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Closure: the lesson ›More Chapter 1 worksheets: Real numbers, expressions and properties
- 1.1Elements and membership
- 1.2Writing sets: roster, rule and the empty set
- 1.3Commutative, associative and distributive properties
- 1.4Identity and inverse elements
- 1.5Closure
- 1.6Interpreting the parts of an expression
- 1.7Units, quantities and a sensible level of accuracy
- 1.8Estimating a huge quantity from small facts