Exercise: 2-B
Q1: Study the following patterns. In each case write the next three steps :
i. 111 ÷ 3 = 37
222 ÷ 6 = 37
333 ÷ 9 = 37
444 ÷ 12 = 37
Next steps:
555 ÷ 15 = 37
666 ÷ 18 = 37
777 ÷ 21 = 37
ii. 999999 × 1 = 0999999
999999 × 2 = 1999998
999999 × 3 = 2999997
999999 × 4 = 3999996
Next steps:
999999 × 5 = 4999995
999999 × 6 = 5999994
999999 × 7 = 6999993
iii. 12345679 × 9 = 111111111
12345679 × 18 = 222222222
12345679 × 27 = 333333333
12345679 × 36 = 444444444
Next steps:
12345679 × 45 = 555555555
12345679 × 54 = 666666666
12345679 × 63 = 777777777
Q2: Observe the following pattern and answer the questions that follow:
1 + 2 + 3 + 4 + 5 = 15
2 + 3 + 4 + 5 + 6 = 20
3 + 4 + 5 + 6 + 7 = 25
i. By which number should we multiply the middle number to get the sum?
The middle number is multiplied by 5 to give the sum.
ii. Write the row of the pattern which gives the sum as 75:
We need the sum to be 75. Let’s check:
13 + 14 + 15 + 16 + 17 = 75
iii. Can there be any row of the pattern which gives the sum as 92?
No, it is not possible for the sum to be 92, as the sum increases by 5 in each subsequent row and no row will add up to 92.
Q3: Complete each of the following magic squares by supplying the missing numbers:
i.
┌────┬────┬────┐ │ │ 9 │ 2 │ ├────┼────┼────┤ │ │ 5 │ │ ├────┼────┼────┤ │ 8 │ │ │ └────┴────┴────┘
Solution:
In this magic square, we need to ensure that the sum of each row, column, and diagonal is the same. The sum for this magic square is 15.
The missing numbers are 4, 3, 7, 1 and 6.
The completed magic square is:
┌────┬────┬────┐ │ 4 │ 9 │ 2 │ ├────┼────┼────┤ │ 3 │ 5 │ 7 │ ├────┼────┼────┤ │ 8 │ 1 │ 6 │ └────┴────┴────┘
ii.
┌────┬────┬────┐ │ 16 │ 2 │ │ ├────┼────┼────┤ │ │ 10 │ │ ├────┼────┼────┤ │ │ │ 4 │ └────┴────┴────┘
Solution:
The sum of the numbers in this magic square is 30.
The missing numbers are 12, 4, 14, 8 and 18.
The completed magic square is:
┌────┬────┬────┐ │ 16 │ 2 │ 12 │ ├────┼────┼────┤ │ 6 │ 10 │ 14 │ ├────┼────┼────┤ │ 8 │ 18 │ 4 │ └────┴────┴────┘
iii.
┌────┬────┬────┬────┐ │ 2 │ 15 │ 16 │ │ ├────┼────┼────┼────┤ │ 9 │ 12 │ │ │ ├────┼────┼────┼────┤ │ │ │ 7 │ 10 │ ├────┼────┼────┼────┤ │ 14 │ │ │ 17 │ └────┴────┴────┴────┘
Solution:
The sum of the numbers in this magic square is 38.
The missing numbers are 5, 11, 6, 13, 8, 3 and 4.
The completed magic square is:
┌────┬────┬────┬────┐ │ 2 │ 15 │ 16 │ 5 │ ├────┼────┼────┼────┤ │ 9 │ 12 │ 11 │ 6 │ ├────┼────┼────┼────┤ │ 13 │ 8 │ 7 │ 10 │ ├────┼────┼────┼────┤ │ 14 │ 3 │ 4 │ 17 │ └────┴────┴────┴────┘
iv.
┌────┬────┬────┬────┐ │ │ 18 │ 17 │ 4 │ ├────┼────┼────┼────┤ │ │ │ 14 │ 11 │ ├────┼────┼────┼────┤ │ │ 9 │ 10 │ │ ├────┼────┼────┼────┤ │ 19 │ │ │ 16 │ └────┴────┴────┴────┘
Solution:
The sum of the numbers in this magic square is 46.
The missing numbers are 11, 13, 10, and 14.
The completed magic square is:
┌────┬────┬────┬────┐ │ 7 │ 18 │ 17 │ 4 │ ├────┼────┼────┼────┤ │ 8 │ 13 │ 14 │ 11 │ ├────┼────┼────┼────┤ │ 12 │ 9 │ 10 │ 15 │ ├────┼────┼────┼────┤ │ 19 │ 6 │ 5 │ 16 │ └────┴────┴────┴────┘
