\( 1 \leftarrow \quad \frac { x } { 7 } - \frac { 8 } { 21 } = \frac { 1 } { 7 } \)

To solve the equation \( \frac{x}{7} - \frac{8}{21} = \frac{1}{7} \), first, let's express \( \frac{8}{21} \) in terms of a denominator of 7. Since \( \frac{8}{21} = \frac{8 \div 3}{21 \div 3} = \frac{8}{21} \) can be converted, we find a common denominator which is 21. So, multiply \( \frac{1}{7} \) by \( \frac{3}{3} \) to get \( \frac{3}{21} \). Now, we rewrite the equation as: \[ \frac{x}{7} - \frac{8}{21} = \frac{3}{21} \] Next, add \( \frac{8}{21} \) to both sides: \[ \frac{x}{7} = \frac{3}{21} + \frac{8}{21} = \frac{11}{21} \] Now, multiply both sides by 7 to isolate x: \[ x = 7 \cdot \frac{11}{21} \] Simplifying this gives: \[ x = \frac{77}{21} \] And after reducing, we find \( x = \frac{11}{3} \). Hence, the value of \( x \) is \( \frac{11}{3} \). Now, let's take a moment to appreciate the historical backdrop of fractions! The concept of fractions dates back to ancient civilizations, including Egyptians and Babylonians, who used them in commerce and trade. The Egyptians, for instance, predominantly utilized unit fractions, writing each as a sum of fractions with one in the numerator—like \( \frac{1}{3} \), \( \frac{1}{5} \), etc. Who knew math could be so historical and fascinating? And speaking of fun with fractions, here's a tip: always find a common denominator before performing operations with fractions! One common mistake is forgetting this step when adding or subtracting, which can lead to mix-ups in your calculations. So, grab a pizza (oooh, delicious fractions) and remember, each slice must fit perfectly for the math to add up!