3 answers
To simplify the fraction \( \frac{24}{55} \), we need to find the greatest common divisor (GCD) of the numerator (24) and the denominator (55).
The factors of 24 are: 1, 2, 3, 4, 6, 8, 12, 24.
The factors of 55 are: 1, 5, 11, 55.
The only common factor is 1, which means that \( 24 \) and \( 55 \) have no common divisors other than 1. Therefore, \( \frac{24}{55} \) is already in its simplest form.
So, \( \frac{24}{55} \) simplified is still \( \frac{24}{55} \).
Let’s solve the equation step by step:
Given the equation:
\[ \frac{8}{11} \left( x + \frac{4}{5} \right) = \frac{24}{55} \]
Step 1: Eliminate the fraction on the left side.
Multiply both sides by \( 11 \) to get rid of the \( \frac{8}{11} \):
\[ 8 \left( x + \frac{4}{5} \right) = 11 \cdot \frac{24}{55} \]
Step 2: Simplify the right side:
Calculating \( 11 \cdot \frac{24}{55} \):
\[ \frac{11 \cdot 24}{55} = \frac{24}{5} \]
So the equation now is:
\[ 8 \left( x + \frac{4}{5} \right) = \frac{24}{5} \]
Step 3: Divide both sides by 8:
\[ x + \frac{4}{5} = \frac{24}{5} \div 8 = \frac{24}{5} \cdot \frac{1}{8} = \frac{24}{40} = \frac{3}{5} \]
Step 4: Subtract \( \frac{4}{5} \) from both sides:
\[ x = \frac{3}{5} - \frac{4}{5} = \frac{3 - 4}{5} = \frac{-1}{5} \]
So, \( x = -\frac{1}{5} \).
You are correct! The solution is \( x = -\frac{1}{5} \).
