 2.1. Introduction
General simplifications involve the operations of addition, subtraction, multiplication, division, finding out square roots, cube roots, etc., with different figures including common fractions and decimal fractions. In workshop calculations, we find that several problems can be solved utilizing general simplifications. It is observed that many students while dealing with these problems make the process tedious and complicated, subsequently they cannot secure correct answers, given their wrong way of interpretations. This results loss of interest in the subject matter. Hence certain easy methods and tricks are necessary to evaluate the problems so that the subject matter is very interesting. Let us study such easy methods one after another, being dealt with in this chapter.
2.2. Fractions
Fraction means part of a number. Fractions are classified into two categories ie, common fractions and decimal fractions. Examples of common fractions are â…—; 5/4Â etc. This figure above the line is known as the numerator. etc. whereas the figure, below the line, is the denominator. Common fractions are further classified into three classes. (1) Proper fraction, example: 7/8 (2) Improper fraction, example: 15/4 and (3) Mixed fraction which is the combination of full number part plus proper fraction; example: 3 by 4/7. In proper fractions, the numerator is smaller than the denominator. In improper fractions, the numerator is greater than the denominator. Improper fractions may be converted into a mixed fractions and vice versa. For example 16/5 = 3 into 1/5Â 4 into 2 /3 14/3 = etc.Â
2.3. Decimal Fractions
Common fractions may be converted into decimal fractions, ie. the denominator is in a common fraction reduced to 1 so that the fraction that appears is known as a decimal fraction. “Deci” means the 10th part. Hence 10th part of any figure is termed a “decimal”. From this sense, the term “decimal fraction” came into effect. The number of digits after the decimal point is known as the decimal part.
Consider a decimal fraction 0.356 in which the value of 3 in the decimal place is 3/10; the value of 5 in the decimal place is 5/100; the value of 6 in the decimal place is 6/1000
2.4. Lowest Common Multiple (L.C.M.)
While dealing with additions and subtractions there is a need to find as suitable number through which all the denominators are easily divisible without fractions. Hence the L.C.M. of certain numbers is the smallest number, which can be divided by each of the numbers without leaving any remainder.
2.5. Multiplication of Decimals
Decimal numbers are multiplied like ordinary numbers. In the product, a decimal is placed as many digits to the left as is the total of digits to the right decimal in the multiplications.
2.6. Division of Decimals
While dividing a decimal fraction with another decimal fraction, we have to see decimal points are shifted to an equal number of digits, both in numerator and denominator, so that we obtain a common fraction that can be simplified easily.
2.7. Conversions of Fractions From One Form to AnotherÂ
Common fractions may be converted into decimal fractions. In such a way decimal fractions may be converted into common fractions.Â
2.8. Multiplication and Division of Decimal with Numbers like 10, 100, 1000, etc.
When a number is multiplied by another number, its value is increased. Similarly, decimal fractions also. Hence in decimal fractions, the decimal point will be shifted to the right-hand side.
When a number is divided by another number, its value reduces. A similar case applied to decimal fractions also. In such a case, the decimal point shifted to the back side ie., to the left-hand side.