How to Convert Mixed Fractions to Improper Fractions

We have already learned how to convert improper fractions to mixed fractions.  In this post, we are going to learn how to convert mixed fractions to improper fractions.  In converting mixed fractions to improper fractions, the denominator stays as it is. You only have to calculate for the numerator.  To get the numerator of the improper fraction, multiply the denominator to the whole number and then add the numerator of the mixed fraction.

Let’s have three examples.

Example 1

Convert 6 \displaystyle \frac{2}{5} to improper fraction.


Denominator: 5

Numerator: 5 \times 6 + 2

Final Answer: \displaystyle \frac{32}{5}


Example 2

Convert \displaystyle 4 \frac{2}{3} to improper fraction. 


Denominator: 3

Numerator: 3 \times 4 + 2 = 14

Final Answer: \displaystyle \frac{14}{3}


Example 3

Convert 8 \frac{21}{28} to improper fraction.


We can reduce \frac{21}{28} to \frac{3}{4}, so given fraction can be converted to 8 \frac{3}{4}. Now, we can now convert the mixed fraction to improper fraction.

Denominator: 4

Numerator: 4 \times 8 + 3 = 35

Final Answer: \frac{35}{4}

From the pattern above, the fraction c \displaystyle \frac{a}{b}, where c is the whole number, a is the numerator and b is the denominator can be converted to the improper fraction

\frac{b \times c + a}{b}.

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