Question
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Answer
\( \frac{10}{11} - \frac{2}{3} = \frac{8}{33} \)
Solution
To subtract the fractions \( \frac{10}{11} \) and \( \frac{2}{3} \), follow these steps:
1. **Find a Common Denominator:**
The least common denominator (LCD) of 11 and 3 is 33.
2. **Convert Each Fraction:**
- \( \frac{10}{11} = \frac{10 \times 3}{11 \times 3} = \frac{30}{33} \)
- \( \frac{2}{3} = \frac{2 \times 11}{3 \times 11} = \frac{22}{33} \)
3. **Subtract the Fractions:**
\[
\frac{30}{33} - \frac{22}{33} = \frac{30 - 22}{33} = \frac{8}{33}
\]
**Final Answer:**
\( \frac{10}{11} - \frac{2}{3} = \frac{8}{33} \)
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Simplify this solution Extra Insights
To subtract the fractions \( \frac{10}{11} \) and \( \frac{2}{3} \), you need a common denominator. The least common multiple of 11 and 3 is 33. Convert \( \frac{10}{11} \) to have a denominator of 33 by multiplying both the numerator and denominator by 3: \[ \frac{10}{11} = \frac{30}{33} \] Now convert \( \frac{2}{3} \) to have a denominator of 33 by multiplying both the numerator and denominator by 11: \[ \frac{2}{3} = \frac{22}{33} \] Now you can subtract: \[ \frac{30}{33} - \frac{22}{33} = \frac{8}{33} \] So, \( \frac{10}{11} - \frac{2}{3} = \frac{8}{33} \).
