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For which pairs of whole numbers a and b is a - b certainly a whole number?

Class 6Whole NumbersWhole Numbers
  • AFor every pair
  • BOnly when a is less than b
  • COnly when a is greater than or equal to b
  • DOnly when a and b are both even

Step-by-Step Solution

If a is at least as large as b the difference is 0 or more, which is a whole number. If a is smaller, as in 3 - 8 = -5, the answer is negative and leaves the whole numbers. Subtraction works in one direction only, which is precisely why it is not closed. Answering "for every pair" assumes subtraction behaves like addition.
Answer: C) Only when a is greater than or equal to b

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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