Which single example is enough to prove that whole numbers are NOT closed under division?

Class 6Whole NumbersWhole Numbers

A8 ÷ 5 = 1.6
B9 ÷ 3 = 3
C0 ÷ 5 = 0
D6 ÷ 1 = 6

Step-by-Step Solution

To disprove closure you need one case where both numbers are whole numbers but the answer is not. Here 8 and 5 are whole numbers, yet 8 ÷ 5 = 1.6, a decimal. The other three all give whole-number answers, so they support closure instead of breaking it.

Answer: A) 8 ÷ 5 = 1.6

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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