# 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,

For Example:

1. 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 $$\frac{4}{7}$$.

$$\frac{4}{7}$$

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$$\frac{1}{4}$$

= $$\frac{(7 × 4) + 1}{4}$$

= $$\frac{28 + 1}{4}$$

= $$\frac{29}{4}$$

Conversion of a Mixed Fraction into an Improper Fraction:

2. Let us convert 5$$\frac{4}{5}$$ into an improper fraction.

Step I: Multiply the whole number 5 by the denominator 5.  [5 × 5 = 25]

Step II: Add the numerator to it.   [25 + 4 = 29]

Step III: This gives the numerator of the improper fraction.  [$$\frac{29}{7}$$]

Denominator will remain the same. So. 5$$\frac{4}{5}$$ = $$\frac{29}{7}$$

Worksheet on Conversion of Mixed Fractions into Improper Fractions:

1. Convert the following into Improper Fractions:

(i) 4$$\frac{1}{3}$$

(ii) 2$$\frac{1}{2}$$

(iii) 4$$\frac{2}{3}$$

(iv) 7$$\frac{4}{9}$$

(v) 4$$\frac{5}{7}$$

1. (i) $$\frac{13}{3}$$

(ii) $$\frac{5}{2}$$

(iii) $$\frac{14}{3}$$

(iv) $$\frac{67}{9}$$

(v) $$\frac{33}{7}$$

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