What is 12/22 + 1/11? Give your answer in its lowest terms.
Understand the Problem
The question asks us to add two fractions, 12/22 and 1/11, and then simplify the result to its lowest terms.
Answer
$\frac{7}{11}$
Answer for screen readers
$\frac{7}{11}$
Steps to Solve
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Find a common denominator To add fractions, we need a common denominator. The least common multiple of 22 and 11 is 22. We can convert $\frac{1}{11}$ to a fraction with a denominator of 22 by multiplying both the numerator and denominator by 2: $$\frac{1}{11} = \frac{1 \times 2}{11 \times 2} = \frac{2}{22}$$
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Add the fractions Now that both fractions have the same denominator, we can add them: $$\frac{12}{22} + \frac{2}{22} = \frac{12 + 2}{22} = \frac{14}{22}$$
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Simplify the fraction To simplify the fraction $\frac{14}{22}$, we find the greatest common divisor (GCD) of 14 and 22. The GCD of 14 and 22 is 2. We divide both the numerator and denominator by 2: $$\frac{14}{22} = \frac{14 \div 2}{22 \div 2} = \frac{7}{11}$$
$\frac{7}{11}$
More Information
The final simplified fraction is $\frac{7}{11}$, which cannot be simplified further because 7 and 11 are both prime numbers, and they don't share any common factors other than 1.
Tips
A common mistake is forgetting to find a common denominator before adding the fractions. Another mistake is not simplifying the fraction to its lowest terms after adding.
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