\(5\frac{2}{3}\) - \(7\frac{1}{2}\)
First, convert \(5\frac{2}{3}\) to an improper fraction. Use this rule: \(a\frac{b}{c}\) = \(\frac{ac+b}{c}\) / Your problem should look like: \(\frac{5x3+2}{3}\) - \(7 \frac{1}{2}\)
Second, simplify 5 × 3 to 15. / Your problem should look like: \(\frac{15+2}{3}\) - \(7 \frac{1}{2}\)
Third, simplify 15 + 2 to 17. / Your problem should look like: \(\frac{17}{3}\) - \(7\frac{1}{2}\)
Fourth, convert \(7\frac{1}{2}\) to an improper fraction. Use this rule: \(a \frac{b}{c}\) = \(\frac{ac+b}{c}\) / Your problem should look like: \(\frac{17}{3}\) - \(\frac{7x2+1}{2}\)
Fifth, simplify 7 × 2 to 14. / Your problem should look like: \(\frac{17}{3}\) - \(\frac{14+1}{2}\)
Sixth, simplify 14 + 1 to 15. / Your problem should look like: \(\frac{17}{3}\) - \(\frac{15}{2}\)
Seventh, find the least common denominator (LCD)
3: 3, 6
2: 2, 4, 6
The LCD is 6.
Eighth, make the denominators the same. / Your problem should look like: \(\frac{17x2}{3x2}\) - \(\frac{15x3}{2x3}\)
Ninth, simplify. Your denominators should now be the same. / Your problem should look like: \(\frac{34}{6}\) - \(\frac{45}{6}\)
Tenth, join the denominators. / Your problem should look like: \(\frac{34-45}{6}\)
Eleventh, simplify. / Your problem should look like: \(-\frac{11}{6}\)
Twelfth, convert to a mixed fraction. / Your problem should look like: \(-1\frac{5}{6}\)
Answer as fraction: \(-1\frac{5}{6}\)
Answer as decimal: -1.8333
