To subtract, we may proceed in either of two ways.
To add or subtract decimals, we must reduce them to the same denomination, i.e.
She can add and subtract with great rapidity up to the sum of one hundred; and she knows the multiplication tables as far as the FIVES.
Similarly we cannot subtract 8 from 15, if 15 means 1 ten + 5 ones; we must either write 15-815-8=(10+5)-8= (I o - 8)+5 = 2+5 = 7, or else resolve the 15 into an inexpressible number of ones, and then subtract 8 of them, leaving 7.
To add or subtract fractional numbers, we must reduce them to a common denominator; and similarly, to multiply or divide surds, we must express them as power-numbers with the same index.