3. An expression is shown. \[ -4 \frac{1}{2}+6 \frac{3}{4} \] hat is the value of the expressio

To solve the expression \( -4 \frac{1}{2}+6 \frac{3}{4} \), first convert the mixed numbers to improper fractions. The value \( -4 \frac{1}{2} \) becomes \( -\frac{9}{2} \) and \( 6 \frac{3}{4} \) becomes \( \frac{27}{4} \). Finding a common denominator of 4, you convert \( -\frac{9}{2} \) to \( -\frac{18}{4} \). Then, combine the fractions: \[ -\frac{18}{4} + \frac{27}{4} = \frac{9}{4} \] So, the value of the expression is \( \frac{9}{4} \) or \( 2 \frac{1}{4} \). Are you curious about how fractions have evolved? Historically, fractions date back to ancient civilizations like the Egyptians, who used unit fractions. They were primarily focused on practical applications such as trade and construction, laying the groundwork for modern fraction use! If you want to master working with mixed numbers and improper fractions, a common mistake is forgetting to find a common denominator or miscalculating when converting. Practice breaking down these steps and double-checking your work to avoid hanging on the math rollercoaster too long!