Chapter 12 Discovering Systematic Procedures
6 Casting out of 9’s. For multiplications involving larger numbers, pupils should be encouraged to apply a special check based on their earlier discovery of the test for divisibility of numbers by 9 Since this test is clearly explained in exercise 20, Part VII of Book II of Mathematics, the explanation given here is restricted to indicating how it would be applied to the multiplication 1,356 by 743, above. Cast out the 9’s from the sum of the digits in each number, thus:
Multiply the remainders obtained from the two numbers to be multiplied and again cast out the 9’s: 6 × 5 = 30
30 — 27 = 3
This remainder is seen to equal the remainder 3 found by casting out 9’s from the answer. When this equality is obtained the multiplication is probably correct.
Discovering The Procedure For Division 1
Published on Nov 18, 2009