Fraction: A numerical quantity that is not a whole number (e.g. \(\frac{1}{2}\), 0.5), a proportion of something. A fraction simply tells us how many parts of a whole we have.
• The numerator says how many parts we have.
• The numerator says how many parts we have.
• The denominator says how many equal parts the whole is divided into.
The number of colored boxes in the table are 5 and total number of boxes of equal size, are 16,
therefore the fractional form of colored boxes is 5 out of 16 i.e. \(\frac{5}{16}\)
Types of fractions: there are three types of fractions:
(1) Proper fractions (2) Improper fractions (3) Mixed fractions
1) Proper fraction: A fraction having numerator smaller than the denominator is called proper fraction (Denominator>Numerator)
Example: \(\frac{2}{7}\), \(\frac{8}{11}\), \(\frac{3}{7}\), \(\frac{5}{8}\), \(\frac{13}{17}\) etc.
therefore the fractional form of colored boxes is 5 out of 16 i.e. \(\frac{5}{16}\)
Another example: suppose Adam had 7 candies and he ate 3 of them then the fractional form of candies that he ate is: \(\frac{3}{7}\) i.e. he ate 3 candies out of 7.
Types of fractions: there are three types of fractions:
(1) Proper fractions (2) Improper fractions (3) Mixed fractions
1) Proper fraction: A fraction having numerator smaller than the denominator is called proper fraction (Denominator>Numerator)
Example: \(\frac{2}{7}\), \(\frac{8}{11}\), \(\frac{3}{7}\), \(\frac{5}{8}\), \(\frac{13}{17}\) etc.
2) Improper fraction: A fraction having numerator greater than the denominator, is called improper fraction (Numerator>Denominator)
Example: \(\frac{7}{2}\), \(\frac{11}{8}\), \(\frac{7}{3}\), \(\frac{8}{5}\), \(\frac{19}{13}\) etc.
Example: \(\frac{7}{2}\), \(\frac{11}{8}\), \(\frac{7}{3}\), \(\frac{8}{5}\), \(\frac{19}{13}\) etc.
3) Mixed fraction: A combination of a proper fraction and a whole number is called a mixed fraction.
Example: \(2\frac{2}{7}\),\(5\frac{8}{11}\), \(4\frac{3}{7}\), \(7\frac{5}{8}\), \(11\frac{13}{19}\) etc.
Conversion of Fractions:
1) Mixed Fraction into Improper Fraction: A mixed fraction may always be converted into an improper fraction.
--The Study Zone
Example: \(2\frac{2}{7}\),\(5\frac{8}{11}\), \(4\frac{3}{7}\), \(7\frac{5}{8}\), \(11\frac{13}{19}\) etc.
Conversion of Fractions:
1) Mixed Fraction into Improper Fraction: A mixed fraction may always be converted into an improper fraction.
Rule to convert: Follow the 3-step rule given below:
Step 1: Multiply the Whole number part by the denominator
Step 2: then add to the numerator to the product found in Step 1
Step 3: This new sum will be your numerator over the denominator.
\(W\frac{N}{D}\) = \(\frac{W\times{D}+N}{D}\)
2) Improper Fraction into Mixed Fraction: An improper fraction can always be converted into a mixed fraction.
2) Improper Fraction into Mixed Fraction: An improper fraction can always be converted into a mixed fraction.
Rule to convert:
Step 1: Divide the numerator by the denominator to get the quotient and remainder.
Step 2: Then the quotient is the Whole number part and the remainder will be the Numerator over the denominator.
Example: \(\frac{37}{7}\) can be converted into mixed fraction as follows:
