EXERCISE 3.2 Check your answers using your calculate 1. Calculate: a ) \( \frac{1}{2}+2 \frac{3}{4}-\frac{3}{8} \)

To tackle this math problem, we need to convert all fractions to have a common denominator. The least common multiple of 2, 4, and 8 is 8. So: 1. \( \frac{1}{2} = \frac{4}{8} \) 2. \( 2 \frac{3}{4} = 2 \cdot \frac{4}{4} + \frac{3}{4} = \frac{8}{4} + \frac{3}{4} = \frac{11}{4} = \frac{22}{8} \) 3. \(-\frac{3}{8} = -\frac{3}{8} \) Now, we can express everything with the common denominator: \( \frac{4}{8} + \frac{22}{8} - \frac{3}{8} = \frac{4 + 22 - 3}{8} = \frac{23}{8} \). In mixed number form, this is \( 2 \frac{7}{8} \). Now you've got a fun math problem solved! Let’s dive into its historical significance: This type of fraction manipulation has its roots in ancient mathematics, notably among the Egyptians and Babylonians, who were pioneering such calculations thousands of years ago. The use of fractions for trade and measurement was crucial in their civilizations, laying the foundational stones for today's arithmetic! If you want to see how fractions play out in our daily lives, consider cooking! Recipes often require precise measurements, and understanding fractions ensures that your dish turns out perfectly every time. Whether you’re halving a recipe or needing to double it, fractions are your trusty kitchen companions!