Check whether the following square are magic squares or not. 15 2 10 4 9 14 8 16 3

Given magic square is 15 2 10 4 9 14 8 16 3 A magic square is an n × n square with a whole number written inside each cell, so that the sum of the numbers in every row, in every column and in each of the main diagonals is equal. In the first row sum of whole numbers is = 15 + 2 + 10 = 27 In the second row sum of whole numbers is = 4 + 9 + 14 = 27 In the third row sum of whole numbers is = 8 + 16 + 3 = 27 In the first column sum of whole numbers is = 15 + 4 + 8 = 27 In the second column sum of whole numbers is = 2 + 9 + 16 = 27 In the third column sum of whole numbers is = 10 + 14 + 3 = 27 Sum of diagonals is = 15 + 9 + 3 = 27 Sum of diagonals is = 8 + 9 + 10 = 27 Sum of all rows , columns and diagonal are equal . Thus, the given square is a magic square.

Check whether the following square are magic squares or not. 56 37 60 55 51 47 42 65 46

Given magic square is 56 37 60 55 51 47 42 65 46 A magic square is an n × n square with a whole number written inside each cell, so that the sum of the numbers in every row, in every column and in each of the main diagonals is equal. In the first row sum of whole numbers is = 56 + 37 + 60 = 153 In the second row sum of whole numbers is = 55 + 51 + 47 = 153 In the third row sum of whole numbers is = 42 + 65 + 46 = 153 In the first column sum of whole numbers is = 56 + 55 + 42 = 153 In the second column sum of whole numbers is 37 + 51 + 65 = 153 In the third column sum of whole numbers is = 60 + 47 + 46 = 153 Sum of diagonals is = 46 + 51 + 56 = 153 Sum of diagonals is = 42 + 51 + 60 = 153 Sum of all rows , columns and diagonal are equal . Thus, the given square is a magic square.

Check whether the following square are magic squares or not. 25 18 23 20 22 24 21 26 19

Given magic square is 25 18 23 20 22 24 21 26 19 A magic square is an n × n square with a whole number written inside each cell, so that the sum of the numbers in every row, in every column and in each of the main diagonals is equal. In the first row sum of whole numbers is = 25 + 18 + 23 = 66 In the second row sum of whole numbers is = 20 + 22 + 24 = 66 In the third row sum of whole numbers is = 21 + 26 + 19 = 66 In the first column sum of whole numbers is = 25 + 20 + 21 = 66 In the second column sum of whole numbers is = 18 + 22 + 26 = 66 In the third column sum of whole numbers is = 23 + 14 + 19 = 66 Sum of diagonals is = 19 + 22 + 25 = 66 Sum of diagonals is = 21 + 22 + 23 = 66 Sum of all rows , columns and diagonal are equal . Thus, the given square is a magic square.

Complete the magic box given below 12 5 8 6 7 1 13 4 9 3 10

Given magic square is 12 5 8 6 7 1 13 4 9 3 10 A magic square is an n × n square with a whole number written inside each cell, so that the sum of the numbers in every row, in every column and in each of the main diagonals is equal. In the second column sum of whole numbers is = 12 + 7 + 13 + 10 = 42 It means that sum of all columns, rows and diagonals should be 42 The number comes in fourth column is = 42 - ( 8 + 1 + 9 ) = 42 - 18 = 24 The number comes in first row is = 42 - ( 12 + 5 + 8 ) = 17 The number comes in second row is = 42 - ( 6 + 7 + 1 ) = 28 The number comes in third row is = 42 - ( 13 + 4 + 9 ) = 16 The number comes in fourth row is = 42 - ( 3 + 10 + 24 ) = 5 Thus, the whole number comes in empty box is 17 12 5 8 6 7 28 1 16 13 4 9 3 10 5 24

Complete the magic box given below 24 8 15 22 12 14 21 11 13 20 27 17 19 26 28 18 9 16

Given magic square is 24 8 15 22 12 14 21 11 13 20 27 17 19 26 28 18 9 16 A magic square is an n × n square with a whole number written inside each cell, so that the sum of the numbers in every row, in every column and in each of the main diagonals is equal. In the diagonal sum of whole numbers is = 24 + 12 + 20 + 28 + 16 = 100 It means that sum of all columns, rows and diagonals should be 100 The number comes in first row is = 100 - ( 24 + 8 + 15 + 22 ) = 31 The number comes in First column = 100 - ( 24 + 11 + 17 + 18 ) = 30 The number comes in second column = 100 - ( 31 + 12 + 13 + 19 ) = 25 The number comes in third column = 100 - ( 8 + 14 + 20 + 26 ) = 32 The number comes in second row 100 - ( 30 + 12 + 14 + 21 ) = 23 The number comes in third row 100 - 11 + 13 + 20 + 27 = 29 The number comes in fourth row 100 - 17 + 19 + 26 + 28 = 10 Thus, the whole number comes in empty box is 24 31 8 15 22 30 12 14 21 23 11 13 20 27 29 17 19 26 28 10 18 25 32 9 16

E M B I B E

New Global Mathematics - 6>Chapter 3 - Operations on Whole Numbers>EXERCISE 3.1

Dr Pooranmal and Ashfaq A Khan Solutions for Chapter: Operations on Whole Numbers, Exercise 1: EXERCISE 3.1

Author:Dr Pooranmal & Ashfaq A Khan

Dr Pooranmal Mathematics Solutions for Exercise - Dr Pooranmal and Ashfaq A Khan Solutions for Chapter: Operations on Whole Numbers, Exercise 1: EXERCISE 3.1

Attempt the free practice questions on Chapter 3: Operations on Whole Numbers, Exercise 1: EXERCISE 3.1 with hints and solutions to strengthen your understanding. New Global Mathematics - 6 solutions are prepared by Experienced Embibe Experts.