In this publication, we will consider the types of ordinary fractions: proper, improper and mixed. Also, using practical examples, we will analyze how a mixed fraction can be converted into an improper one and vice versa.
Correct and Incorrect Fractions
Proper fraction is a common fraction whose numerator is less than the denominator.
,
и
are correct, because 3<7, 6<17, 4<13.
Improper fraction A simple fraction whose numerator is greater than or equal to the denominator. Those. is a rational number that is greater than or equal to one (modulo).
,
и
are incorrect, because 9>5, 10>7, 15>6.
Note: it is not the values of the numerator and denominator that should be taken into account, but their modules.
Mixed fractions
A fraction that is written as a whole number and a proper fraction is called mixed. It should be taken as the sum of the integer and fractional parts.
= 4 +
.
Converting an improper fraction to a mixed one
Any improper fraction can be represented as a mixed fraction by dividing the numerator by the denominator. In this case, the incomplete quotient of the division will be the integer part of the mixed fraction, and the remainder will be the numerator of the fractional part. The denominator remains the same (cf. Example 1).
Converting a mixed fraction to an improper
A mixed fraction can be represented as an improper fraction. To do this, multiply the integer part by the denominator of the fractional part. We add the result obtained to the numerator of the fractional part and, thus, we get the numerator of an improper fraction. The denominator stays the same (see Example 2).
Examples
Example 1
in mixed form.
Solution
In order to cope with the task, we divide the numerator by the denominator, using the algorithm described above.
=2
.
Example 2
in the wrong form.
Solution
=
=