3: The sum of one -fifth of a number and \( 3 \frac{7}{10} \) is 7

To solve the equation, we start by expressing the problem as an equation. Let the unknown number be \( x \). The equation can be set up as follows: \[ \frac{1}{5}x + 3.7 = 7 \] Now, we can isolate \( x \). First, subtract \( 3.7 \) from both sides: \[ \frac{1}{5}x = 7 - 3.7 \] \[ \frac{1}{5}x = 3.3 \] Next, multiply both sides by \( 5 \) to solve for \( x \): \[ x = 3.3 \times 5 = 16.5 \] So, the number is \( 16.5 \). To validate, we can substitute it back into the original equation: \[ \frac{1}{5} \cdot 16.5 + 3.7 = 3.3 + 3.7 = 7 \] Thus, everything checks out perfectly! Now for some extra fun facts! Did you know that the fraction \( \frac{1}{5} \) represents a 20% portion? Fractional thinking has deep historical roots; ancient civilizations like the Egyptians used fractions for trade and construction, leading to significant mathematical advancements! If you're working with fractions regularly, practice makes perfect! One common mistake is forgetting to convert mixed numbers into improper fractions. Keep your calculations tidy and check your work—fractions can be sneaky little devils!