thing as 52. This is the difference of 64 and 12, and is read sixty-four minus twelve (minus is the Latin for less).
III. 9 × 8 means that 8 is to be taken 9 times, and is the same thing as 72. This is the product of 9 and 8, and is read nine into eight.
IV. 108/6 means that 108 is to be divided by 6, or that you must find out how many sixes there are in 108; and is the same thing as 18. This is the quotient of 108 and 6; and is read a hundred and eight by six.
V. When two numbers, or collections of numbers, with the foregoing signs, are the same, the sign = is put between them. Thus, that 7 and 5 make 12, is written in this way, 7 + 5 = 12. This is called an equation, and is read, seven plus five equals twelve. It is plain that we may construct as many equations as we please. Thus:
| 12 | ||
|---|---|---|
| 7 + 9 - 3 = 12 + 1; | — | - 1 + 3 × 2 = 11, |
| 2 |
and so on.
- It often becomes necessary to speak of something which is true not of any one number only, but of all numbers. For example, take 10 and 7; their sum2 is 17, their difference is 3. If this sum and difference be added together, we get 20, which is twice the greater of the two numbers first chosen. If from 17 we take 3, we get 14, which is twice the less of the two numbers. The same thing will be found to hold good of any two numbers, which gives this general proposition,—If the sum and difference of two numbers be added together, the result is twice the greater of the two; if the difference be taken from the sum, the result is twice the lesser of the two. If, then, we take any numbers, and call them the first number and the second number, and let the first number be the greater; we have