MULTIPLICATION. 94. Multiplication is the process of taking a number (of things) a number of times. NOTE 1.-The word number as first used in the above statement, stands for measured magnitude. The second word number does not stand for measured magnitude, but rather for pure number, representing simply the times the number (of things) is to be repeated. 95. The multiplicand is the number (of things) taken or repeated. * 96. The multiplier is the number that shows how many times the multiplicand is to be repeated. 97. The product is the number (of things) obtained by multiplying. 98. The sign, x, which is read multiplied by, indicates that the number preceding the sign is a multiplicand, and the number following it, a multiplier. NOTE. - For other uses of this sign, see Werner Arithmetic, Book II., page 274. 99. PRINCIPLES. 1. The multiplier is always an abstract number. 2. The denomination of the product is always the same as that of the multiplicand. 100. PRIMARY FACTS OF MULTIPLICATION. There are sixty-four primary facts of multiplication. See Werner Arithmetic, Book II., p. 275. "The multiplicand, however written, must always be understood to express measured quantity; it is always concrete."-Psychology of Number, McClellan & Dewey, page 76. 7. Tell which is the multiplicand, which the multiplier, and which the product, in each of the above examples. 102. Observe that in each of the above examples the multiplier is a pure number. 103. Observe that in each of the above examples the denomination of the product is the same as the denomination of the multiplicand. 104. MULTIPLICATION AND ADDITION COMPARED. Find the sum of each of the following groups of numbers and compare the result with the product in the corresponding problem in article 101. MULTIPLICATION—Simple Numbers. 105. Find the product of 563 and 7. Operation. 563 7 Explanation. Seven times 3 units of the first order are 21 units of the first order; they are equal to 1 unit of the first order and 2 units of the second order. Write the 1 unit of the first order and add the 2 units of the second order to the next partial product. 3941 Seven times 6 units of the second order are 42 units of the second order; 42 + 2 = 44; 44 units of the second order equal 4 units of the second order and 4 units of the third order. Write the 4 units of the second order and add the 4 units of the third order to the next partial product. Seven times 5 units of the third order are 35 units of the third order; 35+ 4 = 39; 39 units of the third order equal 9 units of the third order and three units of the fourth order. Write the 9 units of the third order and the 3 units of the fourth order. The product of 563 and 7 is 3941. 106. Find the product of 3426 and 57. Operation. 3426 57 23982 17130 195282 Explanation. Seven times 3426 equals 23982. Fifty times 3246 equals 171300.* Fifty times the number plus 7 times the number equals 57 times the number. Therefore adding 23982 and 171300 gives 57 times 3426. The product of 3426 and 57 is 195282. (a) Find the sum of the ten products. *Ten times five times a number equals fifty times the number. See Werner Arithmetic, Book II., p. 61. 437.022 NOTE 1.-The separatrix is used to indicate t of the decimal point in the number denoting one tenth multiplicand. NOTE 2.-The decimal point should be written in the when, in the process of multiplication, the place is reached belongs. Do not multiply all the figures and then attempt mine the place of the point. 109. Find the product of 746.2 and .25 Operation. 7'46.2 .25 37.310 149.24 186.550 Explanation. To multiply by .25 means to take 25 times dredth of the number. One hundredth of 746.2 is 7.462. Five tim equals 37.310. Twenty times 7.462 equals 37.310149.24 = 186.550. NOTE. For direction as to the use of the trix, see Werner Arithmetic, Book II., p. 133, 110. Observe that when a multiplication of decim complete, the number of decimal places in the prod equal to the number of decimal places in the multip and multiplier. |