To evaluate the addition problem [tex]\(5 \frac{9}{50}+2 \frac{27}{40}\)[/tex], you need to make sure each fraction has a common denominator before performing the addition. It appears we are dealing with mixed numbers, which means converting them to improper fractions first will be an instrumental step.
Let's break this down step-by-step:
1. Convert the mixed numbers into improper fractions:
- For [tex]\(5 \frac{9}{50}\)[/tex]:
[tex]\[ 5 \frac{9}{50} = \frac{5 \cdot 50 + 9}{50} = \frac{250 + 9}{50} = \frac{259}{50} \][/tex]
- For [tex]\(2 \frac{27}{40}\)[/tex]:
[tex]\[ 2 \frac{27}{40} = \frac{2 \cdot 40 + 27}{40} = \frac{80 + 27}{40} = \frac{107}{40} \][/tex]
2. Rewrite the fractions with a common denominator:
- The denominators are 50 and 40. The least common multiple (LCM) of 50 and 40 is 200.
- Rewrite each fraction with the common denominator:
[tex]\[ \frac{259}{50} = \frac{259 \cdot 4}{50 \cdot 4} = \frac{1036}{200} \][/tex]
[tex]\[ \frac{107}{40} = \frac{107 \cdot 5}{40 \cdot 5} = \frac{535}{200} \][/tex]
3. Add the fractions:
[tex]\[ \frac{1036}{200} + \frac{535}{200} = \frac{1036 + 535}{200} = \frac{1571}{200} \][/tex]
4. Simplify the fraction if possible. However, for this context, conversion to a simpler form is not immediately clear, and let's refer back to the numerical result provided earlier.
Thus, an option that shows a correct first step to take in order to evaluate the given addition problem is:
[tex]\[ 5 \frac{9 \cdot 4}{50 \cdot 4}+2 \frac{27 \cdot 5}{40 \cdot 5} \][/tex]
This step involves converting the mixed numbers to improper fractions with a common denominator, which is the correct first step in solving the problem.
