Questions: 9/7 - 7/12 + 1/6 = (Type an integer or a simplified fraction.)

Solution Steps

To solve the given problem of adding and subtracting unlike fractions, we need to follow these steps:

1. Find the least common denominator (LCD) of the fractions.
2. Convert each fraction to an equivalent fraction with the LCD as the denominator.
3. Perform the addition and subtraction of the numerators.
4. Simplify the resulting fraction if possible.

We start with the expression: \[ \frac{9}{7} - \frac{7}{12} + \frac{1}{6} \]

The denominators are \(7\), \(12\), and \(6\). The least common denominator (LCD) is calculated as: \[ \text{LCD} = \text{lcm}(7, 12, 6) = 84 \]

Next, we convert each fraction to have the common denominator of \(84\): \[ \frac{9}{7} = \frac{9 \times 12}{7 \times 12} = \frac{108}{84} \] \[ \frac{7}{12} = \frac{7 \times 7}{12 \times 7} = \frac{49}{84} \] \[ \frac{1}{6} = \frac{1 \times 14}{6 \times 14} = \frac{14}{84} \]

Now we can substitute the converted fractions back into the expression: \[ \frac{108}{84} - \frac{49}{84} + \frac{14}{84} \] Combining the numerators: \[ \frac{108 - 49 + 14}{84} = \frac{73}{84} \]

The resulting fraction is already in its simplest form, as \(73\) is a prime number and does not share any common factors with \(84\).

Final Answer