Add or subtract as indicated. Write answers in lowest terms as needed. 7/12 - 1/3

Verified step by step guidance

1. Convert the fractions to have a common denominator. The least common denominator (LCD) of 12 and 3 is 12.
2. Rewrite \( \frac{1}{3} \) with the denominator of 12. Multiply both the numerator and the denominator by 4 to get \( \frac{4}{12} \).
3. Now, subtract the fractions: \( \frac{7}{12} - \frac{4}{12} \).
4. Since the denominators are the same, subtract the numerators: \( 7 - 4 \).
5. Write the result as a fraction over the common denominator: \( \frac{3}{12} \). Simplify the fraction to its lowest terms.

Key Concepts

Finding a Common Denominator

To add or subtract fractions, it is essential to have a common denominator. The common denominator is a multiple of the denominators of the fractions involved. In this case, the denominators are 12 and 3. The least common multiple (LCM) of these numbers is 12, which allows us to rewrite the fractions with the same denominator for easier calculation.

Subtracting Fractions

Subtracting fractions involves taking the numerators of the fractions and performing the subtraction while keeping the common denominator. For example, in the expression 7/12 - 1/3, we first convert 1/3 to 4/12, allowing us to subtract 4 from 7. The result is then expressed over the common denominator, which is 12.

Simplifying Fractions

After performing operations on fractions, it is important to simplify the result to its lowest terms. This involves dividing both the numerator and the denominator by their greatest common divisor (GCD). For instance, if the result of the subtraction yields a fraction like 3/12, it can be simplified to 1/4 by dividing both the numerator and denominator by 3.