Учебно-методическое пособие для студентов I-II курсов заочного отделения неязыковых факультетов

Addition of Fractions

Fractions cannot be added unless the denominators are all the same. If they are, add all the numerators and place this sum over the common denominator. Add up the integers, if any.

a) change the mixed numbers, if any, to improper fractions;

b) find the L.C.D.;

c) change both fractions to fractions having the L.C.D. as the denominator;

d) subtract the numerator of the second fraction from the numerator of the first, and place this difference over the L.C.D.;

e) reduce if possible.

Multiplication of Fractions

To be multiplied, fractions need not have the same denominator.

a) change the mixed numbers, if any, to improper fractions;

b) multiply all the numerators and place this product over the product

of denominators;

c) reduce the fraction if possible.

Illustration: multiply 2/3 x 2 4/7 x 5/9; 2 4/7=18/7;

2/3 x 18/7 x 5/9 = 180/189 = 20/21.

Division of Fractions

In division as in subtraction only two terms are involved. It is very important to determine which term is the first. If the problem reads 2/3 divided by 5, then 2/3 is the first term and 5 is the second. If it reads “How many times is ½ contained in1/3?”, then 1/3 is the first and ½ is the second.

a) change the mixed numbers, if any, to improper fractions;

b) invert the second fraction and multiply;

c) reduce the fraction if possible.

Illustration: divide 2/3 by 2 1/4 ; 2 1/4 =9/4; 2/3: 9/4=2/3x4/9=8/27

Addition and Subtraction of Decimal Fractions

Addition and subtraction of decimal fractions are performed in the same manner as addition and subtraction of whole numbers.

1. When we add two or several decimal fractions, all of these numbers should have the same number of places to the right of the decimal point.

2. If we subtract one decimal fraction from another both should have the same number of places to the right of the decimal point.

3. We shall refer to places to the right of the decimal point as decimal places.

In a set of addends or in a minuend or subtrahend one or several numbers may have more decimal places than the others. In such situations we note the number having the fewest decimal places and discard the digits, which are to the right of these decimal places in the other numbers, for example, in adding

45.6723

+156.78

we discard the digits 2 and 3. But we do not simply ignore these discarded digits. They may cause a change in one of the digits we intend to use. If we have 45.6723

then according to the following rule we must rewrite it as:

45.7

+ 156.7

+123.784 - 648.917

205.742

Multiplication of Decimal Fractions

The only difference between multiplication of whole numbers and decimal fractions is that we must take into consideration that some portion of one or both factors is fractional, as indicated by the decimal points. Now, instead of multiplying decimal fractions let us multiply whole numbers 3,672 and 275. To obtain 3,672 from 3.672 we move the decimal point 3 places to the right, that is we multiply the number by 1,000 and to obtain 275 from 2.75 we move the decimal point two places to the right. That is we multiply it by 100. Thus, the product 3,672 x 275 is 1000 x 100 = 100,000 times the product 3.672 x 2.75. When the product of the whole numbers 3,672 x 275 is obtained, we must divide it by 100,000. That is, we move the decimal point 5 places to the left. The multiplication of the whole number looks as follows:

3.672

x 275

18360

1009800