If we diminish one of the parts, as d, by a number x, we diminish the whole number just as much, or
a - x = b + c + (d - x).
27. EXERCISES.
What is a + 2b - c, where a = 12, b = 18, c = 7?—Answer, 41.
| What is | aa - bb |
| ——— | |
| a - b |
where a = 6 and b = 2?—Ans. 8.
What is the difference between (a + b)(c + d) and a + bc + d, for the following values of a, b, c, and d?
| a | b | c | d | Ans. |
| 1 | 2 | 3 | 4 | 10 |
| 2 | 12 | 7 | 1 | 25 |
| 1 | 1 | 1 | 1 | 1 |
SECTION II.
ADDITION AND SUBTRACTION.
28. There is no process in arithmetic which does not consist entirely in the increase or diminution of numbers. There is then nothing which might not be done with collections of pebbles. Probably, at first, either these or the fingers were used. Our word calculation is derived from the Latin word calculus, which means a pebble. Shorter ways of counting have been invented, by which many calculations, which would require long and tedious reckoning if pebbles were used, are made at once with very little trouble. The four great methods are, Addition, Subtraction, Multiplication, and Division; of which, the last two are only ways of doing several of the first and second at once.