2/3 – 1/4 write the answer as a fraction in simplest form
The Correct Answer and Explanation is:
To solve ( \frac{2}{3} – \frac{1}{4} ) and write the answer in its simplest form, follow these steps:
Step 1: Find a common denominator
The denominators are 3 and 4. The least common denominator (LCD) of 3 and 4 is 12. Rewrite the fractions with a denominator of 12:
[
\frac{2}{3} = \frac{8}{12} \quad \text{and} \quad \frac{1}{4} = \frac{3}{12}
]
Step 2: Subtract the fractions
Now subtract the numerators while keeping the denominator the same:
[
\frac{8}{12} – \frac{3}{12} = \frac{8 – 3}{12} = \frac{5}{12}
]
Step 3: Simplify the fraction
The fraction ( \frac{5}{12} ) is already in its simplest form because 5 and 12 have no common factors other than 1.
Final Answer:
[
\frac{2}{3} – \frac{1}{4} = \frac{5}{12}
]
Detailed Explanation:
Fractions are subtracted by finding a common denominator, which allows the denominators to match. The least common denominator (LCD) is the smallest multiple that both denominators share. For 3 and 4, the smallest multiple they both divide into is 12.
Once the fractions are rewritten with the common denominator, only the numerators are subtracted. The denominator remains the same because it represents the number of equal parts the whole is divided into.
In this problem, ( \frac{2}{3} ) is converted to ( \frac{8}{12} ), and ( \frac{1}{4} ) is converted to ( \frac{3}{12} ). Subtracting ( \frac{3}{12} ) from ( \frac{8}{12} ) gives ( \frac{5}{12} ).
The final fraction, ( \frac{5}{12} ), cannot be simplified further because 5 (a prime number) does not divide evenly into 12. Therefore, ( \frac{5}{12} ) is the simplest form of the answer.
This process reinforces essential fraction operations like finding the LCD, rewriting equivalent fractions, and simplifying results. These skills are foundational for arithmetic and advanced math concepts.