MULTIPLICATION 



and 4 rows contain 4X7X1 dime or 28 dimes. 

 Each vertical row contains 4X1 dime, and 7 

 rows contain 7X4X1 dime or 28 dimes. 



We see that the product (as the answer in 

 multiplication is called) is the same in both 



FIG. 1 



cases. The number used is called the multi- 

 plicand; the number which tells how many 

 times the multiplicand is to be used is the 

 multiplier. But we have seen above that we 

 may use either number as the multiplicand or 

 multiplier, and the products are the same; for 

 example, 6X$5=5X$6, for one equals 6X5 

 X$l, and the other 5X6X$1, or each equals 

 30X$1; 7X8c=8X7c; 9X4 ft.=4X9 ft., and so 

 on. 



A man buys 7452 bushels of apples at $3 per 

 bushel. What did they cost? 



The cost is 7452 X $3. This is an awkward 

 multiplication. Since we know that this is the 

 equivalent of 3X7452X$1, we multiply in the 

 simpler way: 



7452 



8 



22356 



The child learning multiplication should 

 build up many concrete groups that he may see 

 hange oj multiplier and multiplicand. 

 This is called commutation. He should learn 

 many multiplication facts in building and tak- 

 ing apart concrete groups; he should use vari- 

 ous units of measure to measure distances, 

 finding the whole distance as a product rathi-r 

 than a sum. For example, he finds his table 

 to be 7X3 inches long and 6X3 inches wide; 

 he finds the schoolroom to be 9X3 feet long 

 and 7X3 feet wide. Many of these facts should 

 be learned before I..- formulates the multi- 

 plication tables. The "tables" may be built 

 with inch cube blocks, cardboard squares, draw- 

 ings on squared paper, etc. The tables should 

 be learned after the facts are understood, 

 i&h much concrete work. Many methods 

 of work and play may be evolved to learn 

 Cards with multiplication facts written 



MULTIPLICATION 



large may be held up in rapid succession by 

 the teacher; individuals may answer, class may 

 answer, sides may be taken and a rival game 

 ensue. Products may appear on cards, and the 

 child may tell what numbers make them, as 

 45=9X5, 64=8X8. 



A series of products may be placed upon the 

 blackboard : 



45 = 



32 = 



72 = 

 The class fill out with correct factors, as 



45 = 9X5 

 32 = 8X4 

 72 = 9X8 



Or such a series as this may be placed on the 

 board : 



nX8 = 72 



6Xn = 30 



The. class go to the board, erase n and put in 

 the correct number. 



(1) 2xi3 = n 



(a) 13 = 10 + 3 



2X13=(2X10) + (2X3)=26 



(b) 13 

 X2 

 20 



6 



26 



(c) 13 



XJ2 



6 



20 

 ~~26 



(d) 13 



X2 



"26 



In (a) we see 13 as 10 and 3; and to have 

 2 thirteens, we must have 2 tens and 2 threes. 

 In (b) this is set down in more concise form. 

 In (c) we put 2 threes, or 6, down first, and 

 then 2 tens. In (d) we set 20 down as 2 in 

 ten's place. 



(2) 4Xl22 = n 



(a) 122 = 100 + 20 + 2 

 4X100 = 400 

 4X 20= 80 

 4X 2= 8 

 4X122 = 400 + 80 + 8 = 488 



In the last part of (3), he holds or "carries" 

 in mind the 10 of the 18, and adds 1 ten to 6 

 tens, which he gets by multiplying 3 by 2. 



