What is 8/12-4/8 = reduced to its lowest terms

The Correct Answer and Explanation is :

To solve the expression ( \frac{8}{12} – \frac{4}{8} ) and reduce it to its lowest terms, we’ll follow these steps:

Step 1: Simplify each fraction

Simplifying ( \frac{8}{12} ):
To simplify ( \frac{8}{12} ), we find the greatest common divisor (GCD) of the numerator and denominator. The GCD of 8 and 12 is 4.

[
\frac{8 \div 4}{12 \div 4} = \frac{2}{3}
]

Simplifying ( \frac{4}{8} ):
For ( \frac{4}{8} ), the GCD is also 4.

[
\frac{4 \div 4}{8 \div 4} = \frac{1}{2}
]

Step 2: Rewrite the expression

Now, substituting the simplified fractions back into the expression, we have:

[
\frac{2}{3} – \frac{1}{2}
]

Step 3: Find a common denominator

The denominators 3 and 2 have a least common denominator (LCD) of 6. We need to convert both fractions:

[
\frac{2}{3} = \frac{2 \times 2}{3 \times 2} = \frac{4}{6}
]

[
\frac{1}{2} = \frac{1 \times 3}{2 \times 3} = \frac{3}{6}
]

Step 4: Perform the subtraction

Now, we can subtract the two fractions:

[
\frac{4}{6} – \frac{3}{6} = \frac{4 – 3}{6} = \frac{1}{6}
]

Final Result

Thus, the expression ( \frac{8}{12} – \frac{4}{8} ) reduces to ( \frac{1}{6} ).

Explanation

In this problem, we started with two fractions, which we first simplified to their lowest terms before performing the subtraction. Simplifying fractions involves dividing both the numerator and denominator by their greatest common divisor. This makes calculations easier and ensures clarity. The next step was to find a common denominator for the two fractions to perform the subtraction, which is essential because fractions can only be subtracted directly when they share a common denominator. After adjusting both fractions to the common denominator of 6, we could subtract them effectively, arriving at the final answer of ( \frac{1}{6} ). Reducing fractions to their simplest form and finding a common denominator are fundamental skills in arithmetic, ensuring accurate results.