Let's solve the expression step by step:

Given:
\[ \frac{4}{6} + \frac{7}{10} - \frac{1}{2} \]

First, simplify \(\frac{4}{6}\):
\[ \frac{4}{6} = \frac{2}{3} \]

So the expression becomes:
\[ \frac{2}{3} + \frac{7}{10} - \frac{1}{2} \]

Next, find a common denominator for the fractions \(\frac{2}{3}\), \(\frac{7}{10}\), and \(\frac{1}{2}\). The least common multiple (LCM) of 3, 10, and 2 is 30.

Convert each fraction to have a denominator of 30:

\[ \frac{2}{3} = \frac{2 \times 10}{3 \times 10} = \frac{20}{30} \]
\[ \frac{7}{10} = \frac{7 \times 3}{10 \times 3} = \frac{21}{30} \]
\[ \frac{1}{2} = \frac{1 \times 15}{2 \times 15} = \frac{15}{30} \]

Now the expression is:
\[ \frac{20}{30} + \frac{21}{30} - \frac{15}{30} \]

Combine the fractions:
\[ \frac{20 + 21 - 15}{30} = \frac{26}{30} \]

Simplify \(\frac{26}{30}\):
\[ \frac{26}{30} = \frac{13}{15} \]

So, the final answer is:
\[ \frac{13}{15} \]

Would you like more details or have any questions about this solution?

Here are 8 related questions to expand on this topic:

1. How do you find the least common multiple (LCM) of several numbers?
2. What is the process for converting fractions to have a common denominator?
3. How do you simplify a fraction?
4. What are some strategies for adding and subtracting fractions with different denominators?
5. Can you explain why \(\frac{4}{6}\) simplifies to \(\frac{2}{3}\)?
6. How do you convert mixed numbers to improper fractions?
7. What are some applications of fraction addition and subtraction in real life?
8. How can you verify the correctness of your fraction calculations?

**Tip:** When working with fractions, always try to simplify them as much as possible before performing arithmetic operations. This makes calculations easier and reduces the risk of errors.

Learn how to solve the fraction addition and subtraction problem \(\frac{4}{6} + \frac{7}{10} - \frac{1}{2}\) step-by-step. This problem involves adding and subtracting fractions with different denominators, finding the least common multiple (LCM), and simplifying fractions. Suitable for students in Grades 6-8.

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