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A teacher asks the class to share 0 sweets equally among 8 children, and then to share 8 sweets equally among 0 children. Which sharing makes sense?

Class 6Whole NumbersWhole Numbers
  • AOnly the second, and each child gets 8 sweets
  • BBoth sharings make sense
  • CNeither sharing makes sense
  • DOnly the first, and each child gets 0 sweets

Step-by-Step Solution

Sharing 0 sweets among 8 children is fine: 0 ÷ 8 = 0, so each child gets nothing. Sharing 8 sweets among 0 children is meaningless, because there is nobody to share with. That is exactly why division by 0 is not defined, and why giving 8 ÷ 0 any value at all is wrong.
Answer: D) Only the first, and each child gets 0 sweets

Key idea: Closure: when an operation 'stays inside' the whole numbers

Adding two whole numbers always gives a whole number — addition is **closed** on whole numbers. Multiplying two whole numbers always gives a whole number — multiplication is **closed** too. But subtraction is **not** closed: 5 − 7 = −2, which is not a whole number. Division is also not closed: 7 ÷ 2 = 3.5, not a whole number. Closure is the property that lets us trust an operation never to take us 'outside' the world of whole numbers.

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