6) \( 22 \frac{4}{5}+a=-18 \frac{3}{7} \)

To solve for \( a \) in the equation \( 22 \frac{4}{5}+a=-18 \frac{3}{7} \), first convert the mixed numbers to improper fractions. Here, \( 22 \frac{4}{5} = \frac{114}{5} \) and \( -18 \frac{3}{7} = -\frac{129}{7} \). Now, rewrite the equation as: \[ a = -\frac{129}{7} - \frac{114}{5} \] To perform this operation, find a common denominator, which would be 35. Convert both fractions: \[ -\frac{129}{7} = -\frac{645}{35} \] \[ -\frac{114}{5} = -\frac{798}{35} \] Now combine the fractions: \[ a = -\frac{645}{35} - \frac{798}{35} = -\frac{1443}{35} \] Thus, \( a = -\frac{1443}{35} \) or approximately \( -41.23 \). --- Did you know that mixed numbers were often used as a way to make calculations easier in ancient times? They allowed for a more intuitive approach to adding and subtracting fractions without needing to deal strictly with improper fractions! Solving equations like this one is super useful in real life! Whether you're budgeting your expenses, cooking with precise measurements, or managing time, being comfortable with fractions can save you from costly mistakes or culinary disasters. So next time you're tackling a recipe or your budget, remember this handy skill!