Question

Evaluate \[\left( {5 \div 2.25} \right) \div \left( {9 \div 2.25} \right)\]
A. \[\dfrac{5}{9}\]
B. \[\dfrac{{100}}{9}\]
C. \[\dfrac{9}{5}\]
D. $1$

Answer 1

Hint: We write the division of two numbers in terms of fraction where the numerator is the dividend and denominator is the divisor. Write two separate fractions and then again use the between two fractions to write the terms in fraction form.
* If ‘a’ is divided by ‘b’ then we can write \[a \div b = \dfrac{a}{b}\]
* If the terms of a fraction are fractions then we can write the main fraction as \[\dfrac{{\dfrac{a}{b}}}{{\dfrac{c}{d}}} = \dfrac{a}{b} \times \dfrac{d}{c}\]

Complete step-by-step solution:
We have to evaluate\[\left( {5 \div 2.25} \right) \div \left( {9 \div 2.25} \right)\]............… (1)
We can write the division inside two brackets in terms of fractions.
Then \[\left( {5 \div 2.25} \right) = \dfrac{5}{{2.25}}\] and \[\left( {9 \div 2.25} \right) = \dfrac{9}{{2.25}}\]
Substitute these values of fractions in equation (1)
\[ \Rightarrow \left( {5 \div 2.25} \right) \div \left( {9 \div 2.25} \right) = \dfrac{5}{{2.25}} \div \dfrac{9}{{2.25}}\]
Now the fraction on the left of the division sign acts as the new dividend and the fraction on the right of the division sign acts as the new divisor. Then convert the RHS of the equation in terms of fraction.
\[ \Rightarrow \left( {5 \div 2.25} \right) \div \left( {9 \div 2.25} \right) = \dfrac{{\dfrac{5}{{2.25}}}}{{\dfrac{9}{{2.25}}}}\]
Write the fraction in right hand side of the equation in simpler form
\[ \Rightarrow \left( {5 \div 2.25} \right) \div \left( {9 \div 2.25} \right) = \dfrac{5}{{2.25}} \times \dfrac{{2.2.5}}{9}\]
Cancel same factors from numerator and denominator in right hand side of the equation
\[ \Rightarrow \left( {5 \div 2.25} \right) \div \left( {9 \div 2.25} \right) = \dfrac{5}{9}\]
\[\therefore \]The value of \[\left( {5 \div 2.25} \right) \div \left( {9 \div 2.25} \right)\] is \[\dfrac{5}{9}\]

\[\therefore \]Option A is the correct option

Note: Students many times make the mistake of converting the fraction having fractions as numerator and denominator wrong. Keep in mind the denominator of the fraction existing in any part of a fraction goes to the opposite part of the main fraction i.e. the denominator of a fraction existing in numerator of main fraction will be written in denominator of main fraction, similarly the denominator of a fraction existing in denominator of main fraction will be written in numerator of main fraction.