Question

Which fraction is smaller?
 $ (i) $ $ \dfrac{3}{8} $ or $ \dfrac{4}{5} $
 $ (ii) $ $ \dfrac{8}{{15}} $ or $ \dfrac{4}{7} $
 $ (iii) $ $ \dfrac{7}{{26}} $ or $ \dfrac{{10}}{{39}} $

Answer 1

Hint: First we have to define what the terms we need to solve the problem are.
By the given set of question, we have to first find the smallest integers (numerator or denominator) among the given set of fractions, we use the basic operation which is division and using that we will divide all given set of fractions among them and to find the smallest fraction as well as.

Complete step by step answer:
Let as first take $ (i) $ $ \dfrac{3}{8} $ or $ \dfrac{4}{5} $
And assume $ \dfrac{3}{8} $ is equation \[\left( 1 \right)\] and $ \dfrac{4}{5} $ as the equation \[\left( 2 \right)\]
Now we will divide the equations from \[1\] by \[2\] we get $ \Rightarrow \dfrac{{\dfrac{3}{8}}}{{\dfrac{4}{5}}} $
Now turn the division part into the multiplication part (division is inverse of multiplication)
Which is $ \dfrac{3}{8} \times \dfrac{5}{4} $ (multiply three times of five and also multiply eight times of four)
 $ \Rightarrow \dfrac{{3 \times 5}}{{8 \times 4}} = \dfrac{{15}}{{32}} $ as we clearly see the denominator is greater than the numerator.
Hence among equation one and two, equation one is smallest fraction that is $ \dfrac{3}{8} $
Or we are also able to find the smallest fraction by just division so that it occurs the decimal values and comparing we get the same result as above.
Now take the second term which is $ (ii) $ $ \dfrac{8}{{15}} $ or $ \dfrac{4}{7} $
And assume $ \dfrac{8}{{15}} $ is equation \[\left( 3 \right)\] and $ \dfrac{4}{7} $ is the equation \[\left( 4 \right)\]
Now we will divide the equations from \[3\] by \[4\] we get $ \Rightarrow \dfrac{{\dfrac{8}{{15}}}}{{\dfrac{4}{7}}} $
Now turn the division part into the multiplication part (division is inverse of multiplication)
Which is $ \dfrac{8}{{15}} \times \dfrac{7}{4} $ (multiply eight times of seven and also multiply fifteen times of four)
 $ \dfrac{8}{{15}} \times \dfrac{7}{4} = \dfrac{{56}}{{60}} $ as we clearly see the denominator is greater than the numerator.
Hence among equation three and four, equation three is smallest fraction that is $ \dfrac{8}{{15}} $
Similarly for the final value $ (iii) $ $ \dfrac{7}{{26}} $ or $ \dfrac{{10}}{{39}} $ taken as equation five and six respectively
Now we will divide the equations from 5 by 6 we get $ \Rightarrow \dfrac{{\dfrac{7}{{26}}}}{{\dfrac{{10}}{{39}}}} $
Now turn the division part into the multiplication part (division is inverse of multiplication)
Which is $ \Rightarrow \dfrac{{\dfrac{7}{{26}}}}{{\dfrac{{10}}{{39}}}} = \dfrac{7}{{26}} \times \dfrac{{39}}{{10}} = \dfrac{{273}}{{260}} $ we clearly see the numerator is greater than denominator.
Hence among equation five and six, equation six is smallest fraction that is $ \dfrac{{10}}{{39}} $

Note: We can also simply able to find the smallest fraction by division which is
 $ (i) $ $ \dfrac{3}{8} $ or $ \dfrac{4}{5} $ = $ 0.375 $ or $ 0.8 $ respectively and hence $ \dfrac{3}{8} $ is smallest.
 $ (ii) $ $ \dfrac{8}{{15}} $ or $ \dfrac{4}{7} $ = $ 0.533 $ or $ 0.57 $ respectively and hence $ \dfrac{8}{{15}} $ is smallest.
 $ (iii) $ $ \dfrac{7}{{26}} $ or $ \dfrac{{10}}{{39}} $ = $ 0.269 $ or $ 0.256 $ respectively and hence $ \dfrac{{10}}{{39}} $ is smallest.