Question

Perform the indicated operations 0.9(5/9-2/9)

Answer 1

Express 0.9 as:

`0.9=(9)/(10)`

Use distributive property:

`\begin{gathered} a(b+c)=ab+ac \\ so\colon \\ (9)/(10)((5)/(9)-(2)/(9))=(9)/(10)\cdot(5)/(9)-(9)/(10)\cdot(2)/(9) \\ \end{gathered}`

In order to multuply fractions you can use the following formula:

`(a)/(b)*(c)/(d)=(a* c)/(b* d)`

so:

`(9)/(10)\cdot(5)/(9)-(9)/(10)\cdot(2)/(9)=(9\cdot5)/(10\cdot9)-(9\cdot2)/(10\cdot9)=(45)/(90)-(18)/(90)`

Finally, use this property:

`(a)/(c)\pm(b)/(c)=(a\pm b)/(c)`

so:

`(45)/(90)-(18)/(90)=(45-18)/(90)=(27)/(90)=(3)/(10)`

Answer:

`(3)/(10)=0.3`