Angol Matematika

-Fractions                                                                                                        

Sometimes the quotient of two whole numbers may not be a whole number. For instance, 2:3 and 3:2 do not come out as whole numbers. In this case we will call the quotients fractional numbers or by short, fractions.

The denominator shows the number of equal parts into which the whole has been divided, whilst the numerator tells how many of these equal parts are taken.

-Common fraction

A common fraction is one in which the dividend, called the fraction’s numerator, is written over the divisor, called the faction’s denominator, with a slanting or a horizontal line between them to indicate the intended division.

-Proper fraction, improper fraction

A proper fraction has a value less than 1, because, by definition, it has a numerator smaller than its denominator.

An improper fraction has a value greater than 1 because, by definition, it has a numerator larger than its denominator.

-Mixed numbers

A mixed number consists of a whole number and a fraction written together with the understanding that they are to be added to each other.

Simple fraction, complex fraction A simple fraction is one in which both numerator and denominator are whole numbers.

A complex fraction is one
-in which either the numerator or the denominator is a fraction or a mixed number,
-or in which both the numerator and the denominator are fractions or mixed numbers

-Fundamental rule of fractions

When the numerator and the denominator of a fraction are both multiplied or divided by the same number, the value of the fraction remains unchanged.

Two fractions are equivalent if they have the same value.

-Reduction of fractions

To change a fraction to its lowest terms, divide its numerator and its denominator by the largest whole number which will divide both exactly.

The particular form of a fraction which has the smallest possible whole numbers for its numerator and denominator is called the fraction in its lowest term.

-Comparing the size of fractions

When the values of two or more fractions are to be compared, we express each of the fractions with the same denominator.

-Addition and subtraction of fractions

Two fractions which have the same denominator can be added together by adding their numerators.

When two fractions have different denominators, they cannot be added together directly.

First we express the fractions with the same denominators, then we add the numerators and put the sum over the common denominators.

-Multiplication of fractions

To multiply fractions we multiply their numerators and then we multiply their denominators.

If any factors are common to a numerator and a denominator, they should be cancelled before multiplication.

Mixed numbers must be converted into improper fractions before multiplication.

-Division of fractions

To divide by a fraction, invert it and multiply.

Dividing fractions is the same as multiplying by the reciprocal. (A fraction multiplied by its reciprocal equals to 1.)

-Operations with fractions

The sequence of operations is the same as that used when we deal with whole numbers.

1. work out the contents of any brackets

2. multiply and/or divide

3. add and/or subtract

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