-4 17/42 +3 3/14

To add the mixed numbers \(-4 \frac{17}{42}\) and \(3 \frac{3}{14}\), follow these steps:

1. Convert the mixed numbers into improper fractions.
2. Find a common denominator.
3. Add the fractions.
4. Convert back to a mixed number if necessary.

Step 1: Convert to improper fractions

For \(-4 \frac{17}{42}\):

\(-4 = -\frac{168}{42}\) (since \(-4 \times 42 = -168\))

So, \(-4 \frac{17}{42} = -\frac{168}{42} + \frac{17}{42} = -\frac{168 - 17}{42} = -\frac{151}{42}\).

For \(3 \frac{3}{14}\):

\(3 = \frac{42}{14}\) (since \(3 \times 14 = 42\))

So, \(3 \frac{3}{14} = \frac{42}{14} + \frac{3}{14} = \frac{42 + 3}{14} = \frac{45}{14}\).

Step 2: Find a common denominator

The denominators are 42 and 14. The least common multiple (LCM) of 42 and 14 is 42.

Step 3: Convert \( \frac{45}{14} \) to have a denominator of 42

\(\frac{45}{14} = \frac{45 \times 3}{14 \times 3} = \frac{135}{42}\).

Step 4: Add the fractions

Now we can add the two fractions:

\[ -\frac{151}{42} + \frac{135}{42} = \frac{-151 + 135}{42} = \frac{-16}{42}. \]

Step 5: Simplify the fraction

\(-\frac{16}{42}\) can be simplified:

\(-\frac{16 \div 2}{42 \div 2} = -\frac{8}{21}\).

Final Result

Thus, the sum of \(-4 \frac{17}{42}\) and \(3 \frac{3}{14}\) is:

\[ -\frac{8}{21}. \]