Sure! Let's walk through the process of adding and simplifying the given fractions.
We are given two fractions to add:
[tex]\[
\frac{7}{150} \quad \text{and} \quad \frac{41}{50}
\][/tex]
### Step 1: Find a Common Denominator
To add these fractions, we first need to find a common denominator. The denominators here are 150 and 50. The least common multiple (LCM) of 150 and 50 is 150. Thus, 150 will be our common denominator.
### Step 2: Convert the Fractions
Next, we convert both fractions to have this common denominator.
The fraction [tex]\(\frac{7}{150}\)[/tex] already has 150 as its denominator, so it remains the same.
Now, let's convert [tex]\(\frac{41}{50}\)[/tex]. To get a denominator of 150, we need to multiply both the numerator and the denominator by 3:
[tex]\[
\frac{41}{50} \times \frac{3}{3} = \frac{41 \times 3}{50 \times 3} = \frac{123}{150}
\][/tex]
### Step 3: Add the Fractions
Now that both fractions have the same denominator, we can add them:
[tex]\[
\frac{7}{150} + \frac{123}{150} = \frac{7 + 123}{150} = \frac{130}{150}
\][/tex]
### Step 4: Simplify the Fraction
To simplify [tex]\(\frac{130}{150}\)[/tex], we need to find the greatest common divisor (GCD) of the numerator and the denominator. The GCD of 130 and 150 is 10.
We divide both the numerator and the denominator by their GCD:
[tex]\[
\frac{130 \div 10}{150 \div 10} = \frac{13}{15}
\][/tex]
Thus, the sum of [tex]\(\frac{7}{150}\)[/tex] and [tex]\(\frac{41}{50}\)[/tex] in its simplest form is:
[tex]\[
\frac{13}{15}
\][/tex]
