Subjects
Grades
Types of Fractions
Concept sheet | Mathematics
Secondary
1-2
Percentages
The percentage, denoted by |\%,| is a way of symbolizing a fraction with a denominator of 100.
||\dfrac{80}{100} = 80\ \%||
Mixed Numbers
A mixed number is a number that contains a whole number part and a fractional part.
Note that mixed numbers are rational numbers.
Below are 5 pizzas, each cut into 3 slices. At a party, 4 full pizzas were eaten as well as 2 out of the 3 slices of the last pizza.
The mixed number that represents the situation is the following: |4\dfrac{2}{3}|
Improper Fractions
A fraction is said to be improper when the value of the numerator is greater than the denominator.
In other words, an improper fraction can always be expressed as a mixed number.
Equivalent Fractions
Equivalent fractions are fractions that represent the same value.
This value can be expressed in decimal notation or simply in a drawing.
||\frac{1}{2}=\frac{5}{10}=\frac{40}{80}||
To learn more about the methods of reducing fractions, consult the following concept sheet: Equivalent Fractions and Symplifying Fractions.
Irreducible Fractions
An irreducible fraction, also called a simplified fraction or a fraction in lowest terms, is a fraction whose numerator and denominator do not share a common factor.
We can also say that the numerator and the denominator are co-prime (mutually prime).
|\dfrac{1}{2},| |\dfrac{2}{5},| and |\dfrac{33}{35}| are all irreducible fractions.
Both in arithmetic and algebra, answers which include fractions must be reduced as much as possible.
To learn more about the methods of reducing fractions, visit the following concept sheet: Equivalent Fractions and Simplifying Fractions.
Reducible Fractions
A reducible fraction is a fraction whose numerator and denominator can be divided by the same number.
When reducing a fraction, always make sure to work with whole numbers.
||\frac{6}{8}^{\div 2}_{\div 2} = \frac{3}{4}||
Decimal Fractions
A decimal fraction is a fraction whose denominator is a power of 10 (i.e. 1, 10, 100, 1000, ...).
This type of fraction also refers to the decimal notation of numbers.
||\dfrac{3}{10}\ ,\ \dfrac{27}{100}\ ,\ \dfrac{669}{1\ 000}||
Similar Fractions
Similar fractions are fractions that have the same denominator.
It is important to understand the difference between similar fractions and equivalent fractions.
||\frac{3}{7} \ , \ \frac{4}{7} \ , \ \frac{1}{7}||
Periodic Fractions
A periodic fraction is a fraction where dividing the numerator by the denominator gives a periodic number (repeating number).
To identify this type of fraction, we need to perform the division, and then analyze the decimal part of the resulting number.
The fraction |\dfrac{3}{11}| is periodic, because
||3\div11= 0.27272727= 0{.}\overline{27}||
Unit Fractions
A unit fraction is a fraction where the numerator is 1 and the denominator is a positive integer.
No matter the value we want to represent, only one portion of the whole is considered.
||\frac{1}{2} \ , \ \frac{1}{3} \ , \ \frac{1}{7}||
Whole Fractions
A whole fraction is a fraction representing a single whole (the number 1).
By this definition, all whole fractions are equivalent.
||\frac{4}{4}=\frac{11}{11}=\frac{30}{30}=1||