Question

1/3 - 1/2 (7 - 2/15) + 3/10

Answer 1

You are asked to perform:

`(1)/(3)-(1)/(2)(7-(2)/(15))+(3)/(10)`

Wee need to start with the parenthesis.

`7-(2)/(15)=(7)/(1)-(2)/(15)`

We the numerator will be 7 times 15 minus 2 (2x1), and the denominator will be 15 (15x1)

`(105-2)/(15)=(103)/(15)`

Now, the expression to solve is:

`(1)/(3)-(1)/(2)\cdot(103)/(15)+(3)/(10)`

We need to perform the multiplication first (the second term)

`(1)/(2)\cdot(103)/(15)=(103)/(2\cdot15)=(103)/(30)`

Now, the expression to solve will be:

`(1)/(3)-(103)/(30)+(3)/(10)`

Now we can solve either the substraction or the sum. Let's go first with the substraction:

`(1)/(3)-(103)/(30)=(1\cdot30-3\cdot103)/(3\cdot30)=(30-309)/(90)=(-279)/(90)`
`\begin{gathered} (-279)/(90)\text{ can be simplified since both numerator and denominator are divisible by 3} \\ \end{gathered}`
`(-279)/(90)=(-93)/(30)=(-31)/(10)`

Note that it could be simplified twice, dividing both numerator and denominator by 3.

Then, the expression to solve is reduced to:

`-(31)/(10)+(3)/(10)=(3)/(10)-(31)/(10)`

We can make that substraction easily since they have the same denominator. 3 - 31 = -28

Then, the first expressions equals to:

`(-28)/(10)=(-14)/(5)`

Then, the full answer will be:

`(1)/(3)-(1)/(2)\cdot(7-(2)/(15))+(3)/(10)=-(14)/(5)`