Fraction, definitions, types, and examples.

whenever the word fraction is mentioned, it simply means part of something or part of a whole. for instance, if a quantity is divided into four equal parts, then we can say that each part is one-fourth of the quantity. which is often written as \frac{1}{4}
A fraction like \frac{2}{7} of mangoes simply means you divide the mangoes into seven equal parts and take two of those seventh
When you have numbers like \frac{1}{8} and \frac{1}{7} they are called vulgar fractions or common fractions. mathematically we write fractions as  \frac{A}{B}. The top number is called the numerator and the down number is called the denominator.

Types of Fractions

There are only three types of fractions, this includes common fractions, decimal fractions, and percentages.
Common fraction: when we say fraction, we often refer to a common fraction. examples are  \frac{1}{2}, \frac{4}{7}.
Numbers in a form of 0.78, 0.15 are called decimals fractions. It is often called decimals. We write them with a decimal point.
Now, numbers that are written in this form 78%, 25% are called percentages. We write them with percentages or the symbol %.

Types of common fraction

There are five types of common fractions, which includes:
. Proper fractions: this is a type of fraction whose numerator is less than the denominator. Examples  \frac{15}{17}, \frac{3}{7}, \frac{9}{21}
. Improper fraction: this is a type of fraction whose numerator is bigger than the denominator. Examples \frac{8}{3},  \frac{18}{17}, \frac{156}{26}
. Like fractions: when two or more fractions often have the same denominators then they are called Like fractions. Examples \frac{3}{8},  \frac{5}{8},  \frac{1}{8}
. Unlike fractions: when two or more fractions have different denominators, then they are called, unlike fractions. Examples \frac{1}{7} and  \frac{6}{8},  \frac{3}{9} and \frac{7}{15}.
. Mixed numbers: These fractions often contain a whole number part and a fraction part. some people at times called them mixed fractions. Examples 2\frac{7}{29},  1\frac{9}{15}

Equivalent fraction

when two or more fractions look different but have the same value then it is called equivalent fractions. If you have a fraction like \frac{3}{4}. To find the equivalent fractions of this fraction, multiply both the numerator and denominator by the same number. For instance

\frac{3\times2}{4\times2} = \frac{6}{8}\\

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\frac{3\times3}{4\times3} = \frac{9}{12}

this, therefore, means that \frac{3}{4}, \frac{6}{8}, and \frac{9}{12} are equivalent fractions
 Examples: Find out which of the following pairs of fractions are equivalent

a. \frac{4}{5} and \frac{16}{20}

b. \frac{3}{5} and \frac{33}{55}

c. \frac{6}{7} and \frac{24}{28}

solutions

a. \frac{4}{5} = \frac{4\times4}{5\times4} = \frac{16}{20}

Hence \frac{4}{5} and \frac{16}{20} are equivalent fractions

b. \frac{3}{5} = \frac{3\times11}{5\times11}= \frac{33}{55}

Hence \frac{3}{5} and \frac{33}{55} are equivalent fractions.

c. \frac{6}{7} = \frac{6\times4}{7\times4} = \frac{24}{28}

Hence \frac{6}{7} and \frac{24}{28} are equivalent fractions

On addition of fractions with solved examples, click here