Mathematics for the General Course in Engineering, Volume I covers the syllabus in mathematics for the G.1 year of the general course in engineering. Provided in this text are 31 unworked examples, which form a comprehensive revision course that students are recommended to work through toward the end of the G.l year. Answers to the text examples are provided at the end. The subjects covered in this book are arithmetic; indices, logarithms, and the use of tables; length, area, and volume; algebra; geometry; and trigonometry. This volume provides students taking mathematics for the G.1 year in engineering a sound basis for the work of the G.2 year.
This chapter discusses proper fractions or fractions. By multiplying both the numerator and the denominator of a fraction by the same number, the new fraction would come out exactly equal to the old. However, by dividing both the numerator and the denominator of a fraction by the same number, the new fraction would come out exactly equal to the old. It is easy to add fractions whose denominators are equal. However, if one takes 10 pounds weight of pure water at 62°Fâthe air pressure is also specified as 30 inches of mercuryâthe volume that it occupies would be called a standard gallon. If a standard gallon is divided into four equal parts, each part would be called a quart. However, if a quart is divided into two equal parts, each part would be called a pint. This is the British system for measuring capacity. Whenever measured values are used in a calculation, the final answer must always be inaccurate as it is based on measured values that are themselves inaccurate.
FRACTIONS
Suppose we take the number 1 and break it into smaller pieces. These smaller pieces are called PROPER FRACTIONS or simply FRACTIONS.
When 1 is divided into 2 equal parts each part is called a HALF and is written
.
DIAGRAM 1
Further fractions are illustrated below.
DIAGRAM 2
Names of the Fundamental Fractions
The above list can be extended indefinitely and we shall call these fractions the FUNDAMENTAL fractions. Any other fraction can be expressed in terms of them.
When we meet a fraction such as
the number at the top has a special name. It is called the NUMERATOR. The number at the bottom also has a special name. It is called the DENOMINATOR.
An important principle
If we take a fraction and MULTIPLY both the numerator and the denominator by the same number then the new fraction is exactly equal to the old.
If we take a fraction and DIVIDE both the numerator and the denominator by the s...
