Question

Solve the following:
$\dfrac{5}{6}-\dfrac{1}{3}$

Answer 1

Hint: Make the denominator of both the fractions same and then subtract the numerators and hence find the result of the given subtraction. Verify your answer by checking that the result in addition by $\dfrac{1}{3}$ yields $\dfrac{5}{6}$.

Complete step-by-step answer:
Before solving the question, we need to understand the process of subtraction of two fractions.
When subtracting two fractions, we perform four simple steps.
Step 1: Find the LCM of the denominators of the two fractions
Step 2: Make the denominators of both the fractions equal to the LCM.
Step 3: Subtract the numerators over the common denominator,
Step 4: Express the result in lowest terms.
We will follow the above steps for the above question.
We have the denominators 3 and 6.
Step 1: Finding the LCM of 3 and 6
 

Hence the LCM of 3 and 6 is $3\times 2=6$
Step 2: We make the denominators of both the fractions as 6.
The fraction $\dfrac{5}{6}$ has already the denominator as 6
The fraction $\dfrac{1}{3}=\dfrac{1\times 2}{3\times 2}=\dfrac{2}{6}$
Hence the denominators of both the fractions is 6
Step 3: Subtract the numerators over the common denominator
We have the numerators are 5 and 2
Hence, we have $\dfrac{5}{6}-\dfrac{1}{3}=\dfrac{5}{6}-\dfrac{2}{6}=\dfrac{5-2}{6}=\dfrac{3}{6}$
Step 4: Expressing the given fraction in lowest terms
We have
$\dfrac{3}{6}=\dfrac{\dfrac{3}{3}}{\dfrac{6}{3}}=\dfrac{1}{2}$
Hence, we have
$\dfrac{5}{6}-\dfrac{1}{3}=\dfrac{1}{2}$, which is the required answer.

Note: Verification:
We have $\dfrac{1}{2}+\dfrac{1}{3}=\dfrac{3+2}{6}=\dfrac{5}{6}$
Hence, our answer is verified to be correct.