Calculate 10/21 + 4/21 - 11/21. Give your answer as a fraction in its simplest form.
Understand the Problem
The question is asking to perform a calculation involving fractions. Specifically, it requires adding and subtracting fractions with a common denominator and then simplifying the result to its simplest form.
Answer
The final answer is $\frac{1}{7}$.
Answer for screen readers
The final answer is $\frac{1}{7}$.
Steps to Solve
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Identify the common denominator All the fractions have a common denominator of 21. This makes addition and subtraction straightforward.
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Combine the fractions Add the first two fractions and then subtract the third: $$ \frac{10}{21} + \frac{4}{21} - \frac{11}{21} $$
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Perform the addition Combine the numerators: $$ \frac{10 + 4 - 11}{21} = \frac{3}{21} $$
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Simplify the fraction Reduce the fraction to its simplest form by dividing both the numerator and denominator by their greatest common divisor, which is 3: $$ \frac{3 \div 3}{21 \div 3} = \frac{1}{7} $$
The final answer is $\frac{1}{7}$.
More Information
This answer represents a simplified form of the result after adding and subtracting the given fractions. The process required common denominators and basic fraction simplification.
Tips
- Forgetting common denominators: Make sure to check that all fractions share the same denominator before combining them.
- Incorrect arithmetic: Double-check the arithmetic when combining and simplifying fractions.
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