Question

How do you evaluate $ \dfrac{1}{4} + \dfrac{2}{3} $ ?

Answer 1

Hint: Fractions are a big part of our daily life and the mathematical world, so we must understand how to perform mathematical operations on two different fractions. In the given question, we have to add the two given fractions. The fractions having the same denominator can be added easily but when the denominators are different, then we first find the LCM of the terms in the denominator and then add the fractions. Using this approach, we can find out the correct answer.

Complete step-by-step answer:
We have to find $ \dfrac{1}{4} + \dfrac{2}{3} $ .
The LCM of 4 and 3 is equal to 12, after taking the LCM we multiply the numerator with the quotient obtained by dividing the LCM by its denominator.
As the LCM is 12 and the denominator of the fraction $ \dfrac{1}{4} $ is 4, we multiply the numerator by 3. Similarly, we multiply the numerator of $ \dfrac{2}{3} $ by 4. We get –
 $ \dfrac{1}{4} + \dfrac{2}{3} = \dfrac{{3 + 8}}{{12}} = \dfrac{{11}}{{12}} $
Hence, the correct answer is $ \dfrac{{11}}{{12}} $ .
So, the correct answer is “ $ \dfrac{{11}}{{12}} $ ”.

Note: For Taking LCM of the terms in the denominator that is 3 and 4, we write both of them as a product of their prime factors as –
 $ 3 = 3 $ as 3 is itself a prime number.
 $ 4 = 2 \times 2 $
Now, the LCM is equal to the product of each of the prime numbers the greatest number of times it has appeared in the expansion of any of the numbers.
So the LCM of 3 and 4 is $ 3 \times 2 \times 2 = 12 $ , the LCM of a set of numbers is completely divisible by all the numbers.