Add or subtract as indicated. Write answers in lowest terms as needed. 7/12-1/9

Verified step by step guidance

1. First, identify the fractions involved: \( \frac{7}{12} \) and \( \frac{1}{9} \).
2. To subtract these fractions, they must have a common denominator. Find the least common multiple (LCM) of the denominators 12 and 9.
3. The LCM of 12 and 9 is 36. Convert each fraction to an equivalent fraction with a denominator of 36.
4. Multiply the numerator and denominator of \( \frac{7}{12} \) by 3 to get \( \frac{21}{36} \).
5. Multiply the numerator and denominator of \( \frac{1}{9} \) by 4 to get \( \frac{4}{36} \). Now subtract the fractions: \( \frac{21}{36} - \frac{4}{36} \).

Key Concepts

Finding a Common Denominator

To add or subtract fractions, it is essential to find a common denominator. The common denominator is a multiple of the denominators of the fractions involved, allowing them to be expressed with the same base. For example, in the fractions 7/12 and 1/9, the least common multiple of 12 and 9 is 36, which will be used to rewrite both fractions before performing the operation.

Performing Fraction Operations

Once the fractions have the same denominator, you can perform the addition or subtraction by combining the numerators while keeping the common denominator. For instance, after converting 7/12 and 1/9 to equivalent fractions with a common denominator, you would subtract the numerators and place the result over the common denominator to get the final answer.

Simplifying Fractions

After performing the operation, it is important to simplify the resulting fraction to its lowest terms. This involves dividing both the numerator and the denominator by their greatest common divisor (GCD). For example, if the result of the operation is 5/36, it is already in simplest form, but if it were 10/36, you would simplify it to 5/18.