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: 18+15+12=45, so every line adds to 45. Top row: 18+?+16=45, so ?=45−34=11. (13 and 19 belong to the empty cells; 9 is 45−36, a slip in adding 18+16.)
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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