Mixed fractions
A fraction written as a whole number and a proper fraction is called a mixed fraction.
For example,
- mixed fractions.
A mixed fraction can be represented as an improper fraction, since an integer can always be represented as an improper fraction with any denominator, for example,
;
;
;
Then
5
1/3
= 5 +
1/3
=
15/3
+
1/3
=
16/3
;
1
11/17
= 1 +
11/17
=
17/17
+
11/17
=
28/17
.
Thus, we obtain a formula for representing mixed fractions as an improper fraction
.
Examples of representing mixed fractions as improper fractions.
1) .
2) 7
1/12
=
7*12+1/12
=
85/12
.
3) 4
11/25
=
4*25+11/25
=
111/25
.
The main property of a fraction. Reduction of fractions
The main property of a common fraction is that if the numerator and denominator of a fraction are multiplied or divided by the same natural number, the result is a fraction equal to the given fraction. This property is the basis for the reduction of fractions.
If the numerator and denominator of a fraction are divisible by the same natural number not equal to 1, then reducing the fraction means dividing both the numerator and denominator of the fraction by this number. If such a number does not exist, the fraction is called irreducible. When performing arithmetic operations with fractions, we often get reducible fractions, they must be reduced. If the answer is an improper fraction, it must be presented as a mixed fraction, select the whole part.
Examples of reducible fractions.
4)
- a reducible fraction, since both the numerator 15 and the denominator 25 of the fraction
are divisible by 5.
Therefore,
.
5)
- a reducible fraction, since both the numerator and the denominator of the fraction
are divisible by 4.
Therefore,
.
6)
- a reducible fraction, since both the numerator and the denominator of the fraction
are divisible by 7.
Therefore,
.
Example of an irreducible fraction.
7)
- an irreducible fraction, since the numerator 14 and the denominator 27 of this fraction
have no common divisors
.
Examples of representing an improper fraction as a mixed fraction.
8)
- improper fraction, we will represent it as a mixed one. To do this, we divide 5 by 2, we get 2 and 1 as a remainder, that is,
.
9)
- improper fraction, we will represent it as a mixed one. To do this, we divide 23 by 5, we get 4 and 3 as a remainder, that is
.
