To evaluate the given expressions, we will address each one step by step:
To subtract an integer from a fraction, we first express the integer as a fraction with the same denominator as the first term.
\[\frac{18}{49} - 8 = \frac{18}{49} - \frac{8 \times 49}{49}\]
Since \(8 \times 49 = 392\), we have:
\[\frac{18}{49} - \frac{392}{49} = \frac{18 - 392}{49} = -\frac{374}{49}\]
This is a straightforward addition and subtraction problem. We compute the terms from left to right:
\[8 + 2 = 10\]
\[10 + 13 = 23\]
\[23 - 1 = 22\]
For mixed numbers, we separate the integer parts and the fractional parts to simplify the addition:
Integer part: \(16 + 25 = 41\)
Fractional part: \(\frac{2}{3} + \frac{3}{4}\)
To add the fractions, find a common denominator, which is 12:
\[\frac{2}{3} + \frac{3}{4} = \frac{2 \times 4}{3 \times 4} + \frac{3 \times 3}{4 \times 3} = \frac{8}{12} + \frac{9}{12} = \frac{17}{12}\]
Since \(\frac{17}{12} = 1 \frac{5}{12}\), we add this to the sum of the integers:
\[41 + 1 \frac{5}{12} = 42 \frac{5}{12}\]
Alternatively, written as an improper fraction: \(\frac{42 \times 12 + 5}{12} = \frac{504 + 5}{12} = \frac{509}{12}\).
Arithmetic skills are fundamental in many daily tasks, such as managing a budget or adjusting cooking recipes. For example, when balancing a checkbook, you might subtract expenses from your initial balance, similar to \(\frac{18}{49} - 8\). When combining ingredients for a large batch of a recipe, you often add mixed units or weights, much like summing fractions and integers as seen in \(16 \frac{2}{3} + 25 \frac{3}{4}\). Mastering these basic calculations ensures accuracy in handling finances, construction measurements, or even scientific measurements.