In a “magic square”, the sum of the numbers in each row, in each column and along the diagonals is the same. Is this a magic square?( Along the first row 4/11 + 9/11 + 2/11 = 15/11)
Solution:
As stated in the question, in a magic square, the sum of the numbers in each row, in each column and of the diagonals is the same. We can add the fractions in all rows, columns and diagonals to see if sum is the same or not.
Sum of the first row = (4/11) + (9/11) + (2/11) = (15/11)
Sum of the second row = (3/11) + (5/11) + (7/11) = (15/11)
Sum of the third row = (8/11) + (1/11) + (6/11) = (15/11)
Sum of the first column = (4/11) + (3/11) + (8/11) = (15/11)
Sum of the second column = (9/11) + (5/11) + (1/11) = (15/11)
Sum of the third column = (2/11) + (7/11) + (6/11) = (15/11)
Sum of the first diagonal = (4/11) + (5/11) + (6/11) = (15/11)
Sum of the second diagonal = (2/11) + (5/11) + (8/11) = (15/11)
Since, the sum of fractions in each row, column, and along the diagonal is the same, therefore, the given square is a magic square.
☛ Check: NCERT Solutions for Class 7 Maths Chapter 2
Video Solution:
In a “magic square”, the sum of the numbers in each row, in each column and of the diagonals is the same. Is this a magic square?( Along the first row 4/11 + 9/11 + 2/11 = 15/11)
NCERT Solutions Class 7 Maths Chapter 2 Exercise 2.1 Question 3
Summary:
In a “magic square”, the sum of the numbers in each row, in each column and of the diagonals is the same. Since, the sum of fractions in each row, column, and along the diagonal is the same, therefore, the given square is a magic square
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