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

**Step I:**

**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\(\frac{1}{4}\)

= \(\frac{(7 × 4) + 1}{4}\)

= \(\frac{28 + 1}{4}\)

= \(\frac{29}{4}\)

**● ****Fraction**

Representations of Fractions on a Number Line

Conversion of Mixed Fractions into Improper Fractions

Conversion of Improper Fractions into Mixed Fractions

Interesting Fact about Equivalent Fractions

Addition and Subtraction of Like Fractions

Addition and Subtraction of Unlike Fractions

Inserting a Fraction between Two Given Fractions

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