Page:Elementary algebra (1896).djvu/42

24 Rh CHAPTER IV.

Multiplication.

36. Multiplication in its primary sense signifies repeated addition.

Thus 3 \times 4= 3 taken 4 times =3+3+3+3.

Here the multiplier contains 4 units, and the number of times we take 3 is the same as the number of units in 4.

Again a \times b=a taken b times

=a+a+a+\ldots, the number of terms being b.

Also 3 \times 4=4 \times 3; and so long as a and b denote positive whole numbers, it is easy to show that a \times b=b \times a.

37. When the two quantities to be multiplied together are not positive whole numbers, we may define multiplication as an operation performed on one quantity which when performed on unity produces the other. For example, to multiply {4}{5} by {3}{7}, we perform on {4}{5} that operation which when performed on unity gives {4}{5}; that is, we must divide {4}{5} into 7 equal parts and take 3 of them. Now each part will be equal to {4}{5 7} and the result of taking 3 of such parts is expressed by {4 3}{5 7} Hence {4}{3} {3}{7} = {4 3}{5 7}