Evaluate:
$-3+\frac{11}{16}=$
(Type an integer or a simplified fraction.)
To evaluate the expression \(-3 + \frac{11}{16}\), we need to perform the addition of an integer and a fraction. The first step is to represent the integer \(-3\) as a fraction with a denominator of \(16\). Since \(-3 = \frac{-3}{1}\), we can multiply both the numerator and the denominator by \(16\) to obtain:
\[-3 = \frac{-3 \times 16}{1 \times 16} = \frac{-48}{16}.\]
Now that both terms have the same denominator, we can add them by summing their numerators while keeping the denominator constant:
\[\frac{-48}{16} + \frac{11}{16} = \frac{-48 + 11}{16}.\]
Calculating the numerator, \(-48 + 11 = -37\), we get the final fraction:
\[\frac{-37}{16}.\]
The fraction \(\frac{-37}{16}\) is already in its simplest form because \(37\) is a prime number and is not divisible by \(16\). Thus, the calculation is complete. The result of \(-3 + \frac{11}{16}\) is \(\boxed{-\frac{37}{16}}\).
Understanding how to combine integers and fractions is essential in daily life, such as when managing budgets or working with measurements. For instance, if you have a debt of 3 dollars and receive a partial payment of 11/16 of a dollar, you can track your remaining balance by calculating \(-3 + \frac{11}{16} = -\frac{37}{16}\), which tells you your exact standing. Mastery of these fractional operations provides a solid foundation for financial planning and precise measurements in various crafts.