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Express the following as improper fractions : (a) \(7{\dfrac{3}{4}}\) (b) \(5{\dfrac{6}{7}}\) (c) \(2{\dfrac{5}{6}}\) (d) \(10{\dfrac{3}{5}}\) (e) \(9{\dfrac{3}{7}}\) (f) \(8{\dfrac{4}{9}}\)

Solution:

We use the concepts of fractions, improper fractions, and mixed fractions to express the given fractions as improper fractions. To convert a mixed fraction into an improper fraction, 

To convert a mixed fraction into an improper fraction, we need to multiply the denominator with the whole number and then add the numerator. The resulting term will be written as a numerator of an improper fraction. The denominator remains the same as that of a mixed fraction. Let us apply this concept to solve all the different cases of the given problem.
\(7{\dfrac{3}{4}}\) = (7 × 4 + 3)/4 = 31/4
\(5{\dfrac{6}{7}}\) = (5 × 7 + 6)/7 = 41/7
\(2{\dfrac{5}{6}}\) = (2 × 6 + 5)/6 = 17/6
\(10{\dfrac{3}{5}}\) = (10 × 5 + 3)/5 = 53/5
\(9{\dfrac{3}{7}}\) = (9 × 7 + 3)/7 = 66/7
\(8{\dfrac{4}{9}}\) = (8 × 9 + 4)/9 = 76/9

NCERT Solutions for Class 6 Maths Chapter 7 Exercise 7.2 Question 3

Express the following as improper fractions : (a) \(7{\dfrac{3}{4}}\) (b) \(5{\dfrac{6}{7}}\) (c) \(2{\dfrac{5}{6}}\) (d) \(10{\dfrac{3}{5}}\) (e) \(9{\dfrac{3}{7}}\) (f) \(8{\dfrac{4}{9}}\)

Summary:

Using the concepts of fractions, improper fractions, and mixed fractions, the given fractions have been expressed as improper fractions  (a) 31/4, (b) 41/7, (c) 17/6, (d) 53/5, (e) 66/7 and, (f) 76/9.

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