The problem is to subtract two fractions: $\frac{12}{7} - \frac{2}{3}$. We need to find a common denominator, rewrite the fractions with the common denominator, and then perform the subtraction.

1. Problem Description

The problem is to subtract two fractions: $\frac{12}{7} - \frac{2}{3}$. We need to find a common denominator, rewrite the fractions with the common denominator, and then perform the subtraction.

2. Solution Steps

First, we need to find a common denominator for the fractions $\frac{12}{7}$ and $\frac{2}{3}$. The least common multiple of 7 and 3 is

2

1. We rewrite the fractions with the common denominator of

2

1. To rewrite $\frac{12}{7}$ with a denominator of 21, we multiply both the numerator and the denominator by 3:

$\frac{12}{7} = \frac{12 \times 3}{7 \times 3} = \frac{36}{21}$

To rewrite $\frac{2}{3}$ with a denominator of 21, we multiply both the numerator and the denominator by 7:

$\frac{2}{3} = \frac{2 \times 7}{3 \times 7} = \frac{14}{21}$

Now we can subtract the two fractions:

$\frac{36}{21} - \frac{14}{21} = \frac{36 - 14}{21} = \frac{22}{21}$

3. Final Answer

$\frac{12}{7} - \frac{2}{3} = \frac{36}{21} - \frac{14}{21} = \frac{22}{21}$