https://r2.erweima.ai/mathbot/image/17267856542815iua6uam.jpg

Let's analyze and solve the two fractional problems from the image:

### v) \(\frac{13}{4} - \frac{4}{5} + \frac{1}{6}\)

1. First, find a common denominator for the fractions.
   - The denominators are \(4\), \(5\), and \(6\).
   - The least common denominator (LCD) is 60.

2. Convert each fraction:
   - \(\frac{13}{4} = \frac{195}{60}\)
   - \(\frac{4}{5} = \frac{48}{60}\)
   - \(\frac{1}{6} = \frac{10}{60}\)

3. Perform the operations:
   - \(\frac{195}{60} - \frac{48}{60} + \frac{10}{60}\)
   - First subtract: \(\frac{195}{60} - \frac{48}{60} = \frac{147}{60}\)
   - Now add: \(\frac{147}{60} + \frac{10}{60} = \frac{157}{60}\)

4. Simplify if necessary. Since \(\frac{157}{60}\) is already in its simplest form, the final answer is:

   \[
   \boxed{\frac{157}{60}}
   \]

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### vi) \(\frac{2}{9} - \frac{1}{7} + \frac{2}{3}\)

1. Find the least common denominator (LCD) for the fractions:
   - The denominators are \(9\), \(7\), and \(3\).
   - The LCD is 63.

2. Convert each fraction:
   - \(\frac{2}{9} = \frac{14}{63}\)
   - \(\frac{1}{7} = \frac{9}{63}\)
   - \(\frac{2}{3} = \frac{42}{63}\)

3. Perform the operations:
   - \(\frac{14}{63} - \frac{9}{63} + \frac{42}{63}\)
   - First subtract: \(\frac{14}{63} - \frac{9}{63} = \frac{5}{63}\)
   - Now add: \(\frac{5}{63} + \frac{42}{63} = \frac{47}{63}\)

4. The final answer is:

   \[
   \boxed{\frac{47}{63}}
   \]

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Would you like further explanations on any of the steps? Here are five related questions to deepen your understanding:

1. How do you find the least common denominator (LCD) for multiple fractions?
2. What is the method for converting a fraction to an equivalent fraction with a new denominator?
3. How can you simplify complex fractions after performing operations?
4. What happens when you subtract a larger fraction from a smaller one in terms of negative numbers?
5. How can these operations be applied in real-world scenarios involving fractions?

**Tip:** Always check if the final fraction can be simplified by finding the greatest common divisor (GCD) of the numerator and denominator.

Solve the fractional problems v) 13/4 - 4/5 + 1/6 and vi) 2/9 - 1/7 + 2/3.

Learn how to solve the fractional problems 13/4 - 4/5 + 1/6 and 2/9 - 1/7 + 2/3 by finding the least common denominator (LCD) and performing addition and subtraction. Suitable for students in Grades 6-8.

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