MULTIPLICATION.. MULTIPLICATION is a short method of Addition, and it teaches us to find what a number will amount to, when it is repeated a certain number of times. RULE. The number to be multiplied is called the Multiplicand: and the number multiplied is called the Multiplier. The number found is called the Product. *The above Table must be first learnt in such a manner that the pupil may be able to answer, in an instant, any possible question that can be formed from it; and if he has attended to what was said in Addition, p, 8, the greater part of the difficulty will be already overcome. As soon I. When the Multiplier does not exced 12. RULE. Multiply every figure in the multiplicand from right to left, consider how many tens there are in each product, the remaining units set down under the figure multiplied, and carry the tens as so many ones to the next product. The last product is to be wholly set down. Thus in the first example, I say 8 times 7 are 56, in which there are five tens and six over, I put down the six, and say 8 times 4 are 32, and NOTE. As soon as the pupil has learnt the table in columns, let him learn it as it stands below. To enable the Teacher to exercise his pupil in all the combinations, I shall add the three following series, which will be found very useful in examining boys and girls in classes. Thus he combines all the 12 numbers with the figures in rows, as 8 times 3; 8 times 2, and so on: he may then do the same in columns, as 5 times 3; 5 times 9; 5 times 5, &c. Series 1. 3, 2, 5, 7, 4, 8, 6, 12, 9, 11, 10 5, 12 2, 7, 9, 12, 6, 8, 4,10 adding the 5 from the last product, I have 37; I put down the 7, and carry the 3 for the three tens: I then say 8 times 8 are 64, and 3 are 67, and carry 6: 8 times 0 is 0, but put down the 6 brought from the last product: 8 times 2 are 16, put down the 6, and then 8 times 4 are 32, and the 1 brought forward are 33, which, as being the last product, must be set down. This character X, which is called St. Andrew's cross; is used to denote Multiplication, and when it stands between two numbers, it signifies that those numbers are to be multiplied into one another: thus 9X6 54, is read, nine multiplied by six is equal to fifty-four. Again 12× 11182, that is 12 multiplied by 11 is equal to 132. II. To multiply by 10, add an 0 to the multiplicand: thus 567 x 10 is 5670; and 567 × 100 is 56700; and. 6489 × 10000 = 64890000. Therefore, to multiply a given number of one denomination, by a number whose significant figures do not exceed 12, having a cypher or cyphers joined to it: RULE. Write down the cypher or cyphers for the first part of the product towards the right hand, and then multiply every figure in the multiplicand by the significant figures of the multiplier, as in the preceding case. Thus NOTES. * If the pupil be not sufficiently ready in multiplying, after he has worked the following twenty sums, the preceptor may, by changing the multipliers only, increase the number of examples to any extent. When 13 is the multiplier, the sum may be done in a single line, by multiplying each figure in the multiplicand by 12, and to each product add the number to be carried, if any, and also the figure which is multiplied. Here, in the first example, I say 12 times 2 are 24, and 2 are 26; 6. and carry two: 12 times 4 are 48 and 2 are 50, and 4 are 54; 4 and. carry 5 12 times 6 are 72, and 5 are 77, and 6 are 83, &c. 3469456 × 50 = 173472800, and 98765432 × 8000= Ex. 1. 6754328 X 70 Ex. 2. 987654329 X Ex. 4. 800 56780943 X 120 Ex. 6. 9237654 X 1100 Ex. 8. 7490434 X 600 RULE. The multiplicand must be multiplied by each figure of the multiplier separately, beginning with the righthand figure, and the first figure of every product must stand exactly under the figure multiplied by. Add these products together for the whole product. * NOTE. To multiply by any nutnber between 13 and 19. RULE. Multiply the units figure of the multiplicand, by the right-hand digit of the multiplier; set down the unit's figure of the product, and remember what is to be carried., Multiply the second figure of the multiplicand; to the product, add what was to be carried, and also the first figure of the multiplicand. Then set down the unit's figure, and retain in your mind the number to be carried, as before. Multiply the third figure of the multiplicand; add the number to be carried, and also the second figure of the multiplicand, and so on: thus 74365487596 17 1264218289132 Here I say 7 times 6 are 42; I put down the 2 and carry 4, and say 7times 9 are 63, and 4 are 67, then add the 6, which makes 73; put down the 3, and say 7 times 5 are 35, and 7 are 42, to which add the 9, which make 51, put down 1 and carry 5, and so on, till the last figure, when I say 7 times 7 are 49, and 3 to be carried are 52, take in the 4, which make 56, put down 6, and add 7 to the 5, and set down 12. |