The Psychology of Number And Its Applications to Methods of Teaching Arithmetic;

Cover The Psychology of Number And Its Applications to Methods of Teaching Arithmetic;
The Psychology of Number And Its Applications to Methods of Teaching Arithmetic;
J a James Alexander Mclellan
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The numbers in italics, taken in order, are the product, 274181.
|3 6 5[ 487 |3 6 5[ 487 |3 6 5| 487 13651 487 [365| 487 Proofs of Multiplication. — (1) By repeating the operation with the factors interchanged. (2) The prod- uct divided by either factor should give the other factor.
(3) By casting the nines out of the multiplier and the multiplicand, then multiplying these remainders together and casting the nines out of their product ; the remainder thus obtained should equal the remainder fro
...m casting the nines out of the product of multiplier and multi- plicand. For example, test the following by casting out the nines: dbyGoogk 216 THE PSrCHOLOGY OF NUMBER.
987761 X 56789 = 56,093,959,429.
7 . . out of product of 2 and 8.
Out of multiplicand ..2X8.. out of multiplier.
7 . . out of product.
This proof is not a perfectly sure test of accuracy. It does not point out an error of 9, or of a multiple of 9, in the product. Thus, if has been written for 9 or 9 for 0, or if a partial product has been set down in the wrong place, or if one or more noughts have been inserted or omitted in any of the products, or if two figures have been inter- changed, or if one figure set down is as much too great as another is too small, casting out the nines will fail to detect the error, for the remainder from dividing by 9 will not be affected.


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