# A sum of four fractions is whole number; three of them are 3/2, 3/4, 1/3. Find the fourth fraction.

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A sum of four fractions is whole number; three of them are 3/2, 3/4, 1/3. Find the fourth fraction.
1. 5/12
2. 3/12
3. 1/2
4. 3/8

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Correct Answer - Option 1 : 5/12

Given:

Three fractions: 3/2, 3/4, 1/3

Calculation:

Let, X be the fraction

(3/2) + (3/4) + (1/3) + (x) = Whole number

⇒ LCM (2, 4, 3) = 12

⇒ ((18 + 9 + 4)/12) + (x) = Whole number

⇒ (31/12) + (x) = Whole number

For, x = 5/12

⇒ (36/12) = 3

∴ For, x is 5/12 the sum of fractions is whole number.

Common Mistake:

The most common error of this sum is testing out each option before solving the summation of three fractions given.

Trick: Add the three fractions which will give a hint of the fourth fraction