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?
$\frac{4}{11}$$\frac{9}{11}$$\frac{2}{11}$
$\frac{3}{11}$$\frac{5}{11}$$\frac{7}{11}$
$\frac{8}{11}$$\frac{1}{11}$$\frac{6}{11}$
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AcademicMathematicsNCERTClass 7

To do:

We have to find whether the given square is a magic square.

Solution:

A magic square is an array of numbers where the sum of rows, columns, and diagonal elements are equal.

On adding the numbers in each row we get,

Sum of the first row $=\frac{4}{11}+\frac{9}{11}+\frac{2}{11}$

$=\frac{4+9+2}{11}$

$=\frac{15}{11}$

Sum of the second row $=\frac{3}{11}+\frac{5}{11}+\frac{7}{11}$

$=\frac{3+5+7}{11}$

$=\frac{15}{11}$

Sum of the third row $=\frac{8}{11}+\frac{1}{11}+\frac{6}{11}$

$=\frac{8+1+6}{11}$

$=\frac{15}{11}$

On adding the numbers in each column we get,

Sum of the first column $=\frac{4}{11}+\frac{3}{11}+\frac{8}{11}$

$=\frac{4+3+8}{11}$

$=\frac{15}{11}$

Sum of the second column $=\frac{9}{11}+\frac{5}{11}+\frac{1}{11}$

$=\frac{9+5+1}{11}$

$=\frac{15}{11}$

Sum of the third column $=\frac{2}{11}+\frac{7}{11}+\frac{6}{11}$

$=\frac{2+7+6}{11}$

$=\frac{15}{11}$

On adding the numbers of the diagonals we get,

Sum of the first diagonal $=\frac{4}{11}+\frac{5}{11}+\frac{6}{11}$

$=\frac{4+5+6}{11}$

$=\frac{15}{11}$

Sum of the second diagonal $=\frac{8}{11}+\frac{5}{11}+\frac{2}{11}$

$=\frac{8+5+2}{11}$

$=\frac{15}{11}$

Here, the sum of the numbers in each row, in each column, and along the diagonals is the same.

Hence, the given square is a magic square.

raja
Updated on 10-Oct-2022 13:32:37

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