[tex] -\frac{5}{6} [/tex] ÷ [tex] \frac{9}{10} [/tex]
First, apply the rule (easiest way if you have learned it): [tex]a[/tex] ÷ [tex] \frac{b}{c} = a[/tex] × [tex] \frac{c}{b} [/tex]
[tex]- \frac{5}{6} [/tex] × [tex] \frac{10}{9} [/tex]
Second, apply the last rule: [tex] \frac{a}{b} [/tex] × [tex] \frac{c}{d} = \frac{ac}{bd} [/tex]
[tex]- \frac{5*10}{6*9} [/tex]
Third, multiply 5 × 10 to get 50.
[tex]- \frac{50}{6*9} [/tex]
Fourth, multiply 6 × 9 to get 54.
[tex] -\frac{50}{54} [/tex]
Fifth, find the GCF of 50 and 54.
The GCF should be 2.
Sixth, divide the numerator by the GCF.
[tex]50 [/tex] ÷ [tex]2 = 25[/tex]
Seventh, divide the denominator by the GCF.
[tex]54[/tex] ÷ [tex]2 = 27[/tex]
Eighth, now put 25 and 27 together to get the simplified fraction.
[tex]- \frac{25}{27} [/tex]
Answer as fraction: [tex] -\frac{25}{27} [/tex]
Answer as decimal: 0.9259
