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 2^{2}/_{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\(\frac{1}{4}\)
= \(\frac{(7 × 4) + 1}{4}\)
= \(\frac{28 + 1}{4}\)
= \(\frac{29}{4}\)
● 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
Number Page
6th Grade Page
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