By MacLane S.

Writing generally in English with in simple terms occasional tours into arithmetic, Saunders (b. 1909) recounts the intertwining of his lifestyles and paintings as an American researcher, instructor, and political recommend for technological know-how in the course of lots of the twentieth century. He was once learning at Göttingen with the likes of Hilbert, Weyl, and Bernays because the Nazis begun dismantling the culture of arithmetic there. He went directly to give a contribution to numerous parts of summary and common arithmetic. merely names are index.

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**Example text**

6 + 1 = 7. Thus 32 X 24 = 768 We can write it as follows 32 24 ¯¯¯¯ 668 1 ¯¯¯¯ 768. , 1 is placed under the previous digit 3 X 2 = 6 and added. After sufficient practice, you feel no necessity of writing in this way and simply operate or perform mentally. 5 28 X 35. Step (i) : 8 X 5 = 40. 0 is retained as the first digit of the answer and 4 is carried over. Step (ii) : 2 X 5 = 10; 8 X 3 = 24; 10 + 24 = 34; add the carried over 4 to 34. Now the result is 34 + 4 = 38. Now 8 is retained as the second digit of the answer and 3 is carried over.

15x3 v) 3 X 0 = 0 Hence the product is 15x3 + 38x2 + 59x + 42 Find the products using urdhva tiryagbhyam process. 1) 25 X 16 2) 32 X 48 3) 56 X 56 4) 137 X 214 5) 321 X 213 6) 452 X 348 7) (2x + 3y) (4x + 5y) 9) (6x2 + 5x + 2 ) (3x2 + 4x +7) 8) (5a2 + 1) (3a2 + 4) 10) (4x2 + 3) (5x + 6) Urdhva – tiryak in converse for division process: As per the statement it an used as a simple argumentation for division process particularly in algebra. Consider the division of (x3 + 5x2 + 3x + 7) by (x – 2) process by converse of urdhva – tiryak : i) x3 divided by x gives x2 .

Hence second term of Q is 7x. x3 + 5x2 + 3x + 7 ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ x–2 gives Q = x2 + 7x + - - - - - - - - iii)We now have – 2 X 7x = -14x. But the 3rd term in the dividend is 3x for which ‘17x more’ is required since 17x – 14x =3x. Now multiplication of x by 17 gives 17x. , 17 multiplied by –2 gives 17X–2 = -34 but the relevant term in dividend is 7. So 7 + 34 = 41 ‘more’ is required. As there no more terms left in dividend, 41 remains as the remainder. x3 + 5x2 + 3x + 7 ________________ x–2 gives Q= x2 + 7x +17 and R = 41.