Evaluate the following expression for $x = 6.35$ and $y = -0.8$.
$x \div y$
The goal is to calculate the quotient of two real numbers, \(x = 6.35\) and \(y = -0.8\). The expression to evaluate is \(x \div y\). Since one number is positive and the other is negative, the resulting quotient must be a negative value. We are asked to provide the result as a decimal.
To evaluate the expression \(6.35 \div -0.8\), we can write it as a fraction:
\[\frac{6.35}{-0.8}\]
To simplify the division, we can multiply both the numerator and the denominator by \(100\) to eliminate the decimals:
\[\frac{6.35 \times 100}{-0.8 \times 100} = \frac{635}{-80}\]
Now, we divide \(635\) by \(80\). Since we know the result must be negative, we can perform the division \(635 \div 80\) and assign a negative sign to the result. Dividing \(635\) by \(80\) gives \(7.9375\). Applying the negative sign, we get \(-7.9375\).
The quotient of \(6.35\) and \(-0.8\) is \(-7.9375\). This completes the evaluation of the expression \(x \div y\). The final result is \(\boxed{-7.9375}\).
In personal finance, if you have a total debt of \(\$6.35\) and you want to pay it off using a system that debits \(\$0.80\) per transaction (represented as \(-0.8\)), calculating the number of transactions needed is a real-life application of this division. Here, \(6.35 \div -0.8 \approx -7.94\), which would tell you the effective change or the number of units involved in such a financial adjustment. Dividing by negative values is common in scenarios involving debt, temperature drops, or net change calculations.