Question

Arrange the fractions is ascending order $ \dfrac{2}{7},\dfrac{4}{5},\dfrac{3}{4} $ .
A. $ \dfrac{4}{5},\dfrac{3}{4},\dfrac{2}{7} $
B. $ \dfrac{4}{5},\dfrac{2}{7},\dfrac{3}{4} $
C. $ \dfrac{2}{7},\dfrac{3}{4},\dfrac{4}{5} $
D. $ \dfrac{3}{4},\dfrac{2}{7},\dfrac{4}{5} $

Answer 1

Hint: In order to arrange the fraction in increasing order or decreasing order, the denominator the fraction should be made equal. After that by comparing the numerator value we can arrive to the conclusion that which fraction is the biggest one or vice versa.

Complete step-by-step answer:
Complete step-by-step answer:
The comparison between the fractions can be done easily if the denominators of the fractions are made equal.
If the denominator is equal then by comparing the numerator part of the fraction, arrangement can be done in increasing or decreasing order.
The given fraction is,
 $ \dfrac{2}{7},\dfrac{4}{5},\dfrac{3}{4} $
The LCM of $ 7,5,4 $ should be taken out.
The LCM of $ 7,5,4 $ is,
  $ = 7 \times 5 \times 4 = 140 $
First fraction is $ \dfrac{2}{7} $
Multiply numerator and denominator of fraction by $ 5 \times 4 = 20 $ . The fraction becomes as
 $ \dfrac{{2 \times 20}}{{7 \times 20}} = \dfrac{{40}}{{140}} $

Second fraction is $ \dfrac{4}{5} $
Multiply numerator and denominator of fraction by $ 7 \times 4 = 28 $ . The fraction becomes as
 $ \dfrac{{4 \times 28}}{{5 \times 28}} = \dfrac{{112}}{{140}} $

Third fraction is $ \dfrac{3}{4} $
Multiply numerator and denominator of fraction by $ 7 \times 5 = 35 $ . The fraction becomes as
 $ \dfrac{{3 \times 35}}{{4 \times 35}} = \dfrac{{105}}{{140}} $
Now on comparing the modified fractions $ \dfrac{{40}}{{140}},\dfrac{{112}}{{140}},\dfrac{{105}}{{140}} $ .
The fractions in increasing or ascending order is $ \dfrac{{40}}{{140}},\dfrac{{105}}{{140}},\dfrac{{112}}{{140}} $ .
The order concerning the original fractions are $ \dfrac{2}{7},\dfrac{3}{4},\dfrac{4}{5} $ .
So, the correct answer is “Option C”.

Note: The thing that should be remembered is that the fraction can be compared only when their denominators are equal.
Another way by which it can be done is by converting the fractions into decimal form.
The decimal from of $ \dfrac{2}{7} = 0.2857 $
The decimal from of $ \dfrac{4}{5} = 0.8 $
The decimal from of $ \dfrac{3}{4} = 0.75 $
It is clear that $ \dfrac{2}{7} $ is the smallest fraction while $ \dfrac{4}{5} $ is the greatest fraction.
So the correct order is , $ \dfrac{2}{7},\dfrac{3}{4},\dfrac{4}{5} $ .