Question

Reduce: 2 · 3 · 3 · 5 2 · 2 · 2 · 3 3 · 5 · 5

Answer 1

The given expression is :

`3(1)/(3)-1(3)/(5)`

The general form to simplify the mixed fraction is :

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

Simplify the given fraction :

`\begin{gathered} 3(1)/(3)=(3*3+1)/(3) \\ 3(1)/(3)=(10)/(3) \end{gathered}`
`\begin{gathered} 1(3)/(5)=(1*5+3)/(5) \\ 1(3)/(5)=(8)/(5) \end{gathered}`

Substitute the value and simplify :

`\begin{gathered} 3(1)/(3)-1(3)/(5)=(10)/(3)-(8)/(5) \\ 3(1)/(3)-1(3)/(5)=(5*10-3*8)/(15) \\ 3(1)/(3)-1(3)/(5)=(50-24)/(15) \\ 3(1)/(3)-1(3)/(5)=(26)/(15) \end{gathered}`

To express the fraction 26/15 into mixed fraction :

Divide 26 by 15 :

Mixed Fraction is written as : Quotient Remainder/Divisor

Here Quotient = 1, Remainder = 11 and dividor = 15

`(26)/(15)=1(11)/(15)`

Thus :

`3(1)/(3)-1(3)/(5)=1(11)/(15)`

Answer :

`3(1)/(3)-1(3)/(5)=1(11)/(15)`