We find that fractions follow certain laws corresponding exactly with those of integral **multipliers**, and we are therefore able to deal with the fractional numbers as if they were integers.

The principle is that 162.4 27 =100.4 2 7+ 60.4 2 7+ 2.4 2 7 = 1.42700+6.4270+2.427; but, instead of 427 writing down the separate products, we 6 427 (in effect) write 42700, 4270 and 427 in 2 4?7 separate rows, with the **multipliers** 1, 6, 2 69 174 in the margin, and then multiply each number in each column by the corresponding multiplier in the margin, making allowance for any figures to be " carried."