3/5 – 1/3 give your answer as a fraction in its simplest form
The Correct Answer and Explanation is :
To solve the problem ( \frac{3}{5} – \frac{1}{3} ) and express the answer in its simplest form, we need to follow several steps involving finding a common denominator, performing the subtraction, and then simplifying the result if necessary.
Step 1: Find a Common Denominator
The denominators in our fractions are 5 and 3. To perform the subtraction, we need a common denominator, which is the least common multiple (LCM) of these two numbers. The multiples of 5 are 5, 10, 15, 20, etc., and the multiples of 3 are 3, 6, 9, 12, 15, etc. The smallest common multiple is 15. Therefore, our common denominator will be 15.
Step 2: Convert Each Fraction
Next, we convert each fraction to an equivalent fraction with the common denominator of 15:
- For ( \frac{3}{5} ):
[
\frac{3}{5} = \frac{3 \times 3}{5 \times 3} = \frac{9}{15}
] - For ( \frac{1}{3} ):
[
\frac{1}{3} = \frac{1 \times 5}{3 \times 5} = \frac{5}{15}
]
Step 3: Perform the Subtraction
Now that both fractions have the same denominator, we can subtract them:
[
\frac{9}{15} – \frac{5}{15} = \frac{9 – 5}{15} = \frac{4}{15}
]
Step 4: Simplify if Necessary
The fraction ( \frac{4}{15} ) is already in its simplest form since 4 and 15 have no common factors other than 1.
Final Answer
Thus, the result of the subtraction ( \frac{3}{5} – \frac{1}{3} ) is:
[
\boxed{\frac{4}{15}}
]
This method illustrates the importance of finding a common denominator when performing operations on fractions and demonstrates how to ensure that the final result is expressed in its simplest form.