Question

7\frac{1}{9} = 2\frac{4}{5} + m

Explanation:

Step1: Rearrange the equation to solve for \( m \)

We have the equation \( 7\frac{1}{9}=2\frac{4}{5}+m \). To solve for \( m \), we subtract \( 2\frac{4}{5} \) from both sides of the equation. So, \( m = 7\frac{1}{9}-2\frac{4}{5} \).

Step2: Convert mixed numbers to improper fractions

First, convert \( 7\frac{1}{9} \) to an improper fraction. The formula for converting a mixed number \( a\frac{b}{c} \) to an improper fraction is \( \frac{a\times c + b}{c} \). So, \( 7\frac{1}{9}=\frac{7\times9 + 1}{9}=\frac{63 + 1}{9}=\frac{64}{9} \).

Next, convert \( 2\frac{4}{5} \) to an improper fraction. Using the same formula, \( 2\frac{4}{5}=\frac{2\times5 + 4}{5}=\frac{10 + 4}{5}=\frac{14}{5} \).

Step3: Find a common denominator and subtract

The common denominator of 9 and 5 is \( 9\times5 = 45 \).

Convert \( \frac{64}{9} \) to a fraction with denominator 45: \( \frac{64}{9}=\frac{64\times5}{9\times5}=\frac{320}{45} \).

Convert \( \frac{14}{5} \) to a fraction with denominator 45: \( \frac{14}{5}=\frac{14\times9}{5\times9}=\frac{126}{45} \).

Now, subtract the two fractions: \( m=\frac{320}{45}-\frac{126}{45}=\frac{320 - 126}{45}=\frac{194}{45} \).

Step4: Convert back to a mixed number (optional)

To convert \( \frac{194}{45} \) to a mixed number, divide 194 by 45. \( 45\times4 = 180 \), and \( 194 - 180 = 14 \). So, \( \frac{194}{45}=4\frac{14}{45} \).

Answer:

\( m = 4\frac{14}{45} \) (or \( m=\frac{194}{45} \))