Aptitude - Decimal Fraction - Discussion

These type of problems can be solved by Cross Multiplication principle.

I will try to explain with the present problem scenario

Consider (1/3) and (2/5)

STEP 1: Multiply numerator of 1st with denominator of 2nd
Multiply denominator of 1st with numerator of 2nd

STEP 2: The result is (1*5) and (3*2)
i.e.., 5 and 6
Now Check which number is greater of the two.
In this case 6>5
STEP 3: Check which fraction's numerator is part of the product
that results in greater number(6)

In this case 6 has numerator of 2nd fraction (2/5)
So we can say that (2/5) >(1/3)

SO ON WITH THE NEXT FRACTIONS ALSO

Arrange numerators in ascending order and then write their corresponding denominators like this:

1/3, 2/5, 3/7, 4/5, 5/6, 6/7.

Now, if you carefully observe, numerator increases by +1 and denominator increases by +2.

In such case, when numerators and denominators increase by some value and for each fraction of that value is same, then greater the numerator, greater will the fraction and smaller the numerator, smaller will be the fraction.

Hence, here arranging in descending order,

6/7> 5/6> 4/5> 3/7> 2/5> 1/3.

Another simple method:

Lets option A that is:
1/3 , 2/5 , 3/7 , 4/5 , 5/6 ,6/7

Take the LCM of all the denominators which is
3,5,7,5,6,7

LCM is 210
make the denominator 210. The fraction which is
70/210 , 84/210 , 90/210 ,168/210 , 175/210 ,180/210

now we can easily compare the values because all the denominator is same.
So the decending order is:

180/210 , 175/210 ,168/210 ,90/210 ,84/210 , 70/210.

i.e.

6/7 , 5/6 , 4/5 , 3/7 , 2/5 , 1/3.

This is the answer, it is very short to solve, hope now you will got it.

Check this technique:

In starting it may be consume some time but after practice we will solve in second.

6/7, 5/6, 4/5, 3/7, , 2/5, 1/7.

Check difference between numerator and denominator and then divide numerator with difference.

6-7 = 1.
6/1 = 6.

5-6 = 1.
5/1 = 5.

Don't confuse with numerator greater or smaller.

4-5 = 1.
4/1 = 4.

3-7 = 4.
3/4 = 0.7.

2-5 = 3.
2/3 = 0.6.

1-7 = 6.
1/6 = 0.1.

Simply Multiply all value with 100 so that you will get the answers regarding 100
like 1/3*100, 2/5*100, 3/7*100, 4/5*100, 5/6*100, 6/7*100

Now taking the answers of all the values in decimal we will get the values as
33.33, 40, 42.84, 80, 83.35, 85.68

Now arranging the value in descending order we get as
85.68, 83.35, 80, 42.84, 40, 33.33

6/7, 5/6, 4/5, 3/7, 2/5, 1/3 right answer.

If the given fractions,the numerators are increasing by a definite value and the denominator is also increasing by a definite value but the value of denominator is greater than numerator, then the fraction having smaller numerator will be smallest fraction and the fraction having larger numerator will be largest fraction..

1/3 = 5/15.
2/5 = 6/15.

So option 1,2 & 3 will be wrong because of 5/15<6/15(not in descending order).

And for 4th one:

6/7=36/42.
5/6=35/42(so 6/7>5/6).

5/6=25/30.
4/5=24/30(so 5/6>4/5).

4/5=28/35.
3/7=15/35(so 4/5>3/7).

3/7=15/35.
2/5=14/35(so 3/7>2/5).

2/5=6/15.
1/3=5/15(so 2/5>1/3).

Another shortcut to solve this que is to multiply numerator by 100 and simply dividing it with denominator like this:

100/3=33.3.
200/5=40.
300/7=42.8.
400/5=80.
500/6=83.3.
600/7=85.6.

Then we have the answer.

85.6>83.3>80>42.8>40>33.3.

Answer is 6/7 > 5/6 >4/5 > 3/7 > 2/5 > 1/3.

Easy trick for solving this type of question 1st take difference of numerator and denominator and arrange them according to there acceding and descending order and respective fraction is answer of question if deference is common between 2 fraction then select greater base between them is higher value fraction.

@All.

Here, we can use

Smaller the numerator, the smaller the fraction, and vice versa.

Alternative methods for lesser variables:

1. If the denominator is less than 10, then directly divide and arrange
2. Cross multiplication can lead to check for LHS and RHS of options in required order.