Question
Add the following fractions: Express your answer as a fraction in simplified form.
7/20 + 3/5
7/20 + 3/5
Answers
GPT-4o mini
To add the fractions \( \frac{7}{20} \) and \( \frac{3}{5} \), we first need a common denominator. The denominators are 20 and 5. The least common multiple (LCM) of 20 and 5 is 20.
Now, we can rewrite \( \frac{3}{5} \) with a denominator of 20:
\[
\frac{3}{5} = \frac{3 \times 4}{5 \times 4} = \frac{12}{20}
\]
Now, we can add \( \frac{7}{20} \) and \( \frac{12}{20} \):
\[
\frac{7}{20} + \frac{12}{20} = \frac{7 + 12}{20} = \frac{19}{20}
\]
The fraction \( \frac{19}{20} \) is already in simplified form because 19 is a prime number and does not divide 20.
Thus, the final answer is:
\[
\frac{19}{20}
\]
Now, we can rewrite \( \frac{3}{5} \) with a denominator of 20:
\[
\frac{3}{5} = \frac{3 \times 4}{5 \times 4} = \frac{12}{20}
\]
Now, we can add \( \frac{7}{20} \) and \( \frac{12}{20} \):
\[
\frac{7}{20} + \frac{12}{20} = \frac{7 + 12}{20} = \frac{19}{20}
\]
The fraction \( \frac{19}{20} \) is already in simplified form because 19 is a prime number and does not divide 20.
Thus, the final answer is:
\[
\frac{19}{20}
\]