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In this magic square every row, column and diagonal has the same sum. Which number replaces the ? in the top row?

Class 6Whole NumbersWhole Numbers
  • A13
  • B11
  • C19
  • D9

Step-by-Step Solution

The diagonal is complete: , so every line adds to 45. Top row: , so . (13 and 19 belong to the empty cells; 9 is , a slip in adding )
Answer: B) 11

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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