Question

16\frac{2}{3}
-7\frac{4}{9}

Explanation:

Step1: Convert mixed numbers to improper fractions

First, convert \(16\frac{2}{3}\) 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 for \(16\frac{2}{3}\), we have \(a = 16\), \(b = 2\), \(c = 3\). Then \(\frac{16\times3 + 2}{3}=\frac{48 + 2}{3}=\frac{50}{3}\).

Next, convert \(7\frac{4}{9}\) to an improper fraction. Here, \(a = 7\), \(b = 4\), \(c = 9\). So \(\frac{7\times9 + 4}{9}=\frac{63 + 4}{9}=\frac{67}{9}\).

Step2: Find a common denominator

The denominators are 3 and 9. The least common denominator of 3 and 9 is 9. So we need to convert \(\frac{50}{3}\) to a fraction with denominator 9. We multiply the numerator and denominator by 3: \(\frac{50\times3}{3\times3}=\frac{150}{9}\).

Step3: Subtract the fractions

Now we subtract \(\frac{67}{9}\) from \(\frac{150}{9}\). When subtracting fractions with the same denominator, we subtract the numerators and keep the denominator: \(\frac{150 - 67}{9}=\frac{83}{9}\).

Step4: Convert back to a mixed number (optional, but common for mixed number subtraction)

To convert \(\frac{83}{9}\) to a mixed number, we divide 83 by 9. 9 times 9 is 81, so the quotient is 9 and the remainder is \(83 - 81 = 2\). So \(\frac{83}{9}=9\frac{2}{9}\).

Answer:

\(9\frac{2}{9}\)