In conversion of improper fractions into mixed fractions, we follow the following steps:
Step I:
Obtain the improper fraction.
Step II:
Divide the numerator by the denominator and obtain the quotient and remainder.
Step III:
Write the mixed fraction as: Quotient\(\frac{Remainder}{Denominator}\).
Let us convert \(\frac{7}{5}\) into a mixed number.
As you know if a fraction has same number as numerator and denominator, it makes a whole. Here in \(\frac{7}{5}\) we can take out \(\frac{5}{5}\) to make a whole and the remaining fraction we have is \(\frac{2}{5}\). So, \(\frac{7}{5}\) can be written in mixed numbers as 1\(\frac{2}{5}\).
\(\frac{5}{5}\) = 1 + \(\frac{2}{5}\)
\(\frac{7}{5}\) = \(\frac{5}{5}\) + \(\frac{2}{5}\) = 1 + \(\frac{2}{5 }\) = 1\(\frac{2}{5}\)
Actually, \(\frac{7}{5}\) means 7 ÷ 5. When we divide 7 by 5 we get 1 as quotient and 2 as remainder. To convert an improper fraction into a mixed number we place the quotient 1 as the whole number, the remainder 2 as the numerator and the divisor 5 as the denominator of the proper fraction. 
For Example:
Express each of the following improper fractions as mixed fractions:
(i) \(\frac{17}{4}\)
We have,
Therefore, Quotient = 4, Remainder = 1, Denominator = 4.
Hence, \(\frac{17}{4}\) = 4\(\frac{1}{4}\)
(ii) \(\frac{13}{5}\)
We have,
Therefore, Quotient = 2, Remainder = 3, Denominator = 5.
Hence, \(\frac{13}{5}\) = 2\(\frac{3}{5}\)
(iii) \(\frac{28}{5}\)
We have,
Therefore, Quotient = 5, Remainder = 3, Denominator = 5
Hence, \(\frac{28}{5}\) = 5\(\frac{3}{5}\).
(iv) \(\frac{28}{9}\)
We have,
Therefore, Quotient = 3, Remainder = 1, Denominator = 9
Hence, \(\frac{28}{9}\) = 3\(\frac{1}{9}\).
(v) \(\frac{226}{15}\)
We have,
Therefore, Quotient = 15, Remainder = 1, Denominator = 15
Hence, \(\frac{226}{15}\) = 15\(\frac{1}{15}\).
● Fraction
Representations of Fractions on a Number Line
Conversion of Mixed Fractions into Improper Fractions
Conversion of Improper Fractions into Mixed Fractions
Interesting Fact about Equivalent Fractions
Addition and Subtraction of Like Fractions
Addition and Subtraction of Unlike Fractions
Inserting a Fraction between Two Given Fractions
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