Question

Solve the given fractions: $\dfrac{3}{4}-\dfrac{1}{3}$

Answer 1

Hint: As we are asked to find the difference between two fractions with different denominators, we must make the denominator the same by taking the LCM of the denominators. Also, the denominators of one of the fractions are co-primes, and we know that the LCM of two coprime numbers is equal to their product.

Complete step-by-step answer:
The given expression is:
 $\dfrac{3}{4}-\dfrac{1}{3}$
So, we are asked to find the difference between two fractions with different denominators, we must make the denominator the same by taking the LCM of the denominators.
Now, we can see that the denominators of the terms are 4 and 3, which are co-primes, i.e., they don’t have any common factor other than 1, and we know that the LCM of two coprime numbers is equal to their product. So, the LCM of denominator is $3\times 4=12$ .
Now let us make the denominator of each term equal to 12 by multiplying the denominator and the numerator by suitable terms. On doing so, we get
$\dfrac{3\times 3}{4\times 3}-\dfrac{1\times 4}{3\times 4}$
$=\dfrac{9}{12}-\dfrac{4}{12}$
$=\dfrac{9-4}{12}=\dfrac{5}{12}$
Also, 5 and 12 are co-primes, so the fraction cannot be further simplified. Hence the answer to the above question is $\dfrac{5}{12}$ .

Note: The above question is purely calculation based and the only possible part where you can make a mistake is while taking the LCM or in the calculation part. So, be careful in the mentioned parts and cross check you answer once completed.