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Forms of fractions

Vulgar fraction

Definition.
A vulgar fraction or common fraction or simple fraction — is a rational number written as one integer (the numerator) m divided by a non-zero integer (the denominator) n, such as mn.

Proper fraction

Definition.
A vulgar fraction is said to be a proper fraction if the absolute value of the numerator is less than the absolute value of the denominator.
7,  5 — proper fractions.
96

Improper fraction

Definition.
A vulgar fraction is said to be an improper fraction or composed fraction if the absolute value of the numerator is greater than or equal to the absolute value of the denominator.
9,  3 — improper fractions.
73

Mixed number (mixed fraction)

It is possible to present any improper fraction in the form of the sum of whole number and a proper fraction.

Definition.
A mixed number is the sum of a whole number and a proper fraction. This sum is implied without the use of any visible operator such as "+".
32 = 3 + 2 = 21 + 2 = 23
77777

Decimal

Definition.
Decimals are fractions that have: integer part (thousands, hundreds, tens, ones) and decimal point and fractional part (tenths, hundredths, thousandths – decimal position).
3.2609 = 3 + 2 + 6 + 0 + 9 = 3 + 2609
1010010001000010000

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