E \( y+3 \frac{1}{4}=8 \frac{1}{2} \)

To solve the equation \( y + 3 \frac{1}{4} = 8 \frac{1}{2} \), first convert mixed numbers to improper fractions: \( 3 \frac{1}{4} = \frac{13}{4} \) and \( 8 \frac{1}{2} = \frac{17}{2} \). Now, rewrite the equation as \( y + \frac{13}{4} = \frac{17}{2} \). To isolate \( y \), subtract \( \frac{13}{4} \) from both sides. To do this, find a common denominator, which is 4: \[ \frac{17}{2} = \frac{34}{4} \] Now substitute this back into the equation: \[ y = \frac{34}{4} - \frac{13}{4} = \frac{21}{4} \] So, \( y = 5 \frac{1}{4} \) is your final answer! Understanding the historical context of fractions reveals that they date back thousands of years! The ancient Egyptians used fractions extensively and even had a system for representing them, mainly using unit fractions. They would express all fractions as sums of these unit fractions, a practice that influenced mathematical thought for centuries. When dealing with mixed numbers, a common mistake is overlooking the need to convert them into improper fractions before performing arithmetic operations. It’s crucial to remember that this simplification allows for easier calculations, particularly in addition or subtraction problems. Always double-check your work by converting back to mixed numbers if necessary to ensure accuracy!