Conversion of Mixed Fractions into Improper Fractions

In conversion of mixed fractions into improper fractions, we may follow the following steps:

Step I:

Obtain the mixed fraction. Let the mixed fraction be 2²/₅

Step II:

Identify the whole number and the numerator (top) and denominator (bottom) of the proper fraction.

Step III:

Multiply the whole number by the denominator of the proper fraction and add the result to the numerator of the proper fraction.

Step IV:

Write the fraction having numerator equal to the number obtained in step III and denominator same as the denominator of the fraction in step II. Thus,

$Conversion of Mixed Fractions into Improper Fractions$

For Example:

Express each of the following mixed fractions as improper fractions:

(i) Convert 8$\frac{4}{7}$ into an improper fraction.

8$\frac{4}{7}$ means 8 whole and $\frac{4}{7}$.

$Conversion of Mixed Fractions into Improper Fractions$

$\frac{4}{7}$

Solution:

8$\frac{4}{7}$ = 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + $\frac{4}{7}$

or, 8$\frac{4}{7}$ = $\frac{7}{7}$ + $\frac{7}{7}$ + $\frac{7}{7}$ + $\frac{7}{7}$ + $\frac{7}{7}$ + $\frac{7}{7}$ + $\frac{7}{7}$ + $\frac{7}{7}$ + $\frac{4}{7}$ = $\frac{60}{7}$, [$\frac{7}{7}$ means 1)

We can also convert a mixed number into an improper fraction as follows.

First multiply the whole number by denominator. Here (8 × 7) + 4 = 60. Now, put the sum as the numerator of the required improper fraction and the denominator remains the same.

8$\frac{4}{7}$ = $\frac{(8 × 7) + 4}{7}$ = $\frac{56 + 4}{7}$ = $\frac{60}{7}$

Thus, 8$\frac{4}{7}$ = $\frac{60}{7}$

(ii) 3$\frac{2}{7}$

= $\frac{(3 × 7) + 2}{7}$

= $\frac{21 + 2}{7}$

= $\frac{23}{7}$

(iii) 4$\frac{5}{9}$

= $\frac{(4 × 9) + 5}{9}$

= $\frac{36 + 5}{9}$

= $\frac{41}{9}$

(iv) 3$\frac{2}{5}$

= $\frac{(3 × 5) + 2}{5}$

= $\frac{15 + 2}{5}$

= $\frac{17}{5}$

(v) 7$\frac{1}{4}$

= $\frac{(7 × 4) + 1}{4}$