Fractions in Mathematics

What are fractions?

The word fraction means a part of something that is whole i.e. its value should be less than 1.
Fractions are a type of rational numbers (which are of the form  p/q, where p and q are integers and q≠0), and have numerator less than the denominator (p < q) and both p and q are in the lowest terms.
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Some common fractions
A fraction is in the lowest terms if the only common factor between the numerator and denominator is 1.
Eg. 5/10 is not in the lowest terms since the common factors are 1 and 5; whereas 3/7 is in its lowest form.

A fraction can be treated as a division problem.

Equivalent fractions:
Two fractions are said to be equivalent if the cross products are equal. Cross product is the product of the numerator of one fraction with the denominator of another.

What are Equivalent Fractions?, Equivalent fractions in maths,
What are equivalent fractions?

Unit fractions:
Those fractions in which the numerator is one.
Eg. 1/2, 1/3, 1/4 etc.

Like and unlike fractions:
•   Like fractions are those which have the same denominators.
Eg. 1/9, 2/9, 4/9.

•   Unlike fractions are those which have different denominators.
Eg. 2/5, 2/3, 2/9.

Proper, improper and mixed fractions:
•  Fractions in which the numerator is less than the denominator are known as proper fractions.
Eg. 3/4, 5/10, 3/9 etc.

•  Fractions in which the denominator is less than the numerator are known as improper fractions.
Eg. 5/4, 9/8, 11/2 etc.

•  Fractions which are a combination of a whole number and a fraction are called mixed fractions or mixed numbers.
Eg. 11/4, 31/9 etc.
Mixed fractions are an example of improper fractions.
Improper fractions can be converted into mixed fractions and vice versa.

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Even and Odd Numbers
Co-prime or Relatively Prime Numbers
What are Perfect Numbers?