# 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:

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

= $$\frac{(7 × 4) + 1}{4}$$

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

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

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Representations of Fractions on a Number Line

Fraction as Division

Types of Fractions

Conversion of Mixed Fractions into Improper Fractions

Conversion of Improper Fractions into Mixed Fractions

Equivalent Fractions

Fractions in Lowest Terms

Like and Unlike Fractions

Comparing Like Fractions

Comparing Unlike Fractions

Addition and Subtraction of Like Fractions

Addition and Subtraction of Unlike Fractions

Inserting a Fraction between Two Given Fractions