Question

solve the equation.
$7\frac{1}{9}=2\frac{2}{7}+n$
$n=\frac{304}{63}$
(type a whole number, fraction, or mixed number.)

Explanation:

Step1: Convert mixed numbers to improper fractions

First, convert \(7\frac{1}{9}\) and \(2\frac{2}{7}\) to improper fractions.
For \(7\frac{1}{9}\): \(7\frac{1}{9}=\frac{7\times9 + 1}{9}=\frac{63 + 1}{9}=\frac{64}{9}\)
For \(2\frac{2}{7}\): \(2\frac{2}{7}=\frac{2\times7 + 2}{7}=\frac{14 + 2}{7}=\frac{16}{7}\)
The equation becomes \(\frac{64}{9}=\frac{16}{7}+n\)

Step2: Solve for \(n\)

Subtract \(\frac{16}{7}\) from both sides of the equation:
\(n=\frac{64}{9}-\frac{16}{7}\)
Find a common denominator, which is \(9\times7 = 63\).
Rewrite the fractions with the common denominator:
\(\frac{64}{9}=\frac{64\times7}{9\times7}=\frac{448}{63}\)
\(\frac{16}{7}=\frac{16\times9}{7\times9}=\frac{144}{63}\)
Now subtract:
\(n=\frac{448}{63}-\frac{144}{63}=\frac{448 - 144}{63}=\frac{304}{63}\)
If we want to convert this improper fraction to a mixed number, divide 304 by 63:
\(63\times4 = 252\), \(304-252 = 52\), so \(\frac{304}{63}=4\frac{52}{63}\)

Answer:

\(n = 4\frac{52}{63}\) (or \(n=\frac{304}{63}\))