It would be difficult to overestimate the extent to which mathematics enters into the conditions of everyday life. In its elementary stages, as the science of number, it teaches us the relations of magnitude, and enables us to build up a system of calculation and measurement which, applied to the relations observed to exist in nature, gives results of far-reaching importance.
The properties of number are investigated in arithmetic, and methods examined by which those engaged in practical science are able to work out their results to any degree of approximation.
With the help of algebra, we arrive at a system of logarithms by which many of these results may be reached with the minimum of labor.
The measurement of lines and angles, by methods investigated in geometry and trigonometry, enables us to calculate areas, and work out various problems met with in surveying, and is of the first importance in astronomy.
Arithmetic, which deals with the properties of numbers, forms the basis of all mathematical calculation. (For the primary treatment of numbers, see under [The Child World].)
COMMON FRACTIONS
A Fraction is one or more of the equal parts into which a unit has been divided. A Common Fraction is expressed by two numbers; the one written above the line is called the Numerator, the one below, the Denominator: both, called the Terms, denote the value of the fraction.
Thus, in the fraction 3⁄4, the denominator 4, denotes that a unit or whole thing has been divided into four equal parts; and the numerator 3, shows that three of those parts are taken or expressed in the fraction.
A Proper Fraction is one whose numerator is less than its denominator; as 1⁄2, 3⁄4, 7⁄8, etc. Its value is always less than 1.