Question

Express the following as mixed fractions
(a) \[\dfrac{20}{3}\]
(b) \[\dfrac{11}{5}\]
(c) \[\dfrac{17}{7}\]
(d) \[\dfrac{28}{5}\]
(e) \[\dfrac{19}{6}\]
(f) \[\dfrac{35}{9}\]

Answer 1

Hint: In this question, we first need to write the numerator in the given fractions as sum of multiple of denominator and remainder. Then simplify further by dividing the multiple with the denominator. Here, it can be expressed as \[a\dfrac{b}{c}=\dfrac{ac+b}{c}\]. Now, this can be expressed as a mixed fraction accordingly.

Complete step by step answer:
FRACTION:
A fraction is a number representing ratio or division of two natural numbers.
MIXED FRACTION:
It consists of two parts, an integer and a fraction
Examples of mixed fractions are given by \[2\dfrac{1}{5},5\dfrac{1}{4}\].
As we already know that conversion of mixed fraction to fraction is given by
\[\Rightarrow a\dfrac{b}{c}=\dfrac{ac+b}{c}\]
(a) Now, the given number in the question is
\[\dfrac{20}{3}\]
Now, the numerator in the above fraction can be further written as
\[\Rightarrow \dfrac{18+2}{3}\]
Let us now write the numerator as sum of multiple of denominator and remainder
\[\Rightarrow \dfrac{3\times 6+2}{3}\]
Now, we can further write it in the simplified form as
\[\Rightarrow 6+\dfrac{2}{3}\]
Now, the mixed fraction representation of the above fraction using the mentioned conversion is
\[\Rightarrow 6\dfrac{2}{3}\]
(b) Now, the given number in the question is
\[\dfrac{11}{5}\]
Now, we can express the numerator in the above fraction as
\[\Rightarrow \dfrac{10+1}{5}\]
Let us now write the numerator as sum of multiple of denominator and remainder
\[\Rightarrow \dfrac{5\times 2+1}{5}\]
Now, this can be further written in the simplified form as
\[\Rightarrow 2+\dfrac{1}{5}\]
Now, the mixed fraction representation of the above fraction using the mentioned conversion is
\[\Rightarrow 2\dfrac{1}{5}\]
(c) Now, the given number in the question is
\[\dfrac{17}{7}\]
Now, the numerator in the above fraction can be further written as
\[\Rightarrow \dfrac{14+3}{7}\]
Let us now write the numerator as sum of multiple of denominator and remainder
\[\Rightarrow \dfrac{7\times 2+3}{7}\]
Now, this can be further written in the simplified form as
\[\Rightarrow 2+\dfrac{3}{7}\]
We get the mixed fraction representation of the above fraction using the mentioned conversion is
\[\Rightarrow 2\dfrac{3}{7}\]
(d) Now, the given number in the question is
\[\dfrac{28}{5}\]
Now, the numerator in the above fraction can be further written as
\[\Rightarrow \dfrac{25+3}{5}\]
Let us now write the numerator as sum of multiple of denominator and remainder
\[\Rightarrow \dfrac{5\times 5+3}{5}\]
Now, this can be further written in the simplified form as
\[\Rightarrow 5+\dfrac{3}{5}\]
Now, the mixed fraction representation of the above fraction using the mentioned conversion is
\[\Rightarrow 5\dfrac{3}{5}\]
(e) Now, the given number in the question is
\[\dfrac{19}{6}\]
Now, the numerator in the above fraction can be further written as
\[\Rightarrow \dfrac{18+1}{6}\]
Let us now write the numerator as sum of multiple of denominator and remainder
\[\Rightarrow \dfrac{6\times 3+1}{6}\]
Now, this can be further written in the simplified form as
\[\Rightarrow 3+\dfrac{1}{6}\]
Now, the mixed fraction representation of the above fraction using the mentioned conversion is
\[\Rightarrow 3\dfrac{1}{6}\]
(f) Now, the given number in the question is
\[\dfrac{35}{9}\]
Now, the numerator in the above fraction can be further written as
\[\Rightarrow \dfrac{27+8}{9}\]
Let us now write the numerator as sum of multiple of denominator and remainder
\[\Rightarrow \dfrac{9\times 3+8}{9}\]
Now, this can be further written in the simplified form as
\[\Rightarrow 3+\dfrac{8}{9}\]
Now, the mixed fraction representation of the above fraction using the mentioned conversion is
\[\Rightarrow 3\dfrac{8}{9}\]

Note:
Instead of writing the numerator as sum of a multiple of denominator and remainder we can also solve it by directly multiplying the quotient with the fraction having remainder in the numerator and divisor in the denominator which gives the same result.
It is important to note that while expressing the numerator we need to write the term in the summation as the largest multiple possible which is near to the given numerator in the fraction.