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