Question 1.

Write the reciprocals of the following numbers:

Question 2.

Carry out the following Divisions:

**Intext Questions and Activities**

Question 1.

Ramanujan’s Magic square. (Textbook pg. no. 28)

- Add the four numbers in the rows, the columns and along the diagonals of this square.
- What is the sum?
- Is it the same every time?
- What is the peculiarity?
- Look at the numbers in the first row, 22 – 12 – 1887. Find out why this date is special.

Obtain and read a biography of the great Indian mathematician Srinivasa Ramanujan.

Solution:

Sum of the numbers in each row:

i. 22 + 12 + 18 + 87 = 139

ii. 88 + 17 + 9 + 25 = 139

iii. 10 + 24 + 89 + 16 = 139

iv. 19 + 86 + 23 + 11 = 139

Sum of the numbers along the diagonals:

i. 22 + 17 + 89 + 11 = 139

ii. 87 + 9 + 24 + 19 = 139

Sum of the numbers in each column:

i. 22 + 88 + 10 + 19 = 139

ii. 12 + 17 + 24 + 86 = 139

iii. 18 + 9 + 89 + 23 = 139

iv. 87 + 25 + 16 + 11 = 139

∴ We observe that the sum of the numbers in each of the rows, the columns and along each diagonal remains the same every time. The numbers in the first row 22 – 12 – 1887 is the birth date of Srinivasa Ramanujan.