Conversion of Improper Fractions into Mixed Fractions
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:
1. 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\(\frac{1}{15}\).
Conversion of an Improper Fraction Into a Mixed Fraction:
2. Let us convert 22/5 into an mixed fraction.
Divide the numerator 22 by the denominator 5.
The quotient 4 gives the whole number. The remainder 2 is the numerator of the fractions.
The denominator of the fraction remains the same. So, \(\frac{22}{5}\) = 4\(\frac{2}{5}\)
3. Convert \(\frac{41}{3}\) into mixed fraction.
Divide the numerator 41 by the denominator 3.
The quotient 13 gives the whole number. The remainder 2 is the numerator of the fractions.
The denominator of the fraction remains the same.
So, \(\frac{41}{3}\) = 13\(\frac{2}{3}\)
Worksheet on Conversion of Improper Fractions into Mixed Fractions:
1. Convert the following into Improper Fractions:
(i) \(\frac{11}{9}\)
(ii) \(\frac{24}{5}\)
(iii) \(\frac{26}{8}\)
(iv) \(\frac{59}{9}\)
(v) \(\frac{64}{7}\)
Answer:
1. (i) 1\(\frac{2}{9}\)
(ii) 4\(\frac{4}{5}\)
(iii) 3\(\frac{2}{8}\)
(iv) 6\(\frac{5}{9}\)
(v) 9\(\frac{1}{7}\)
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Conversion of Improper Fractions into Mixed Fractions
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