Question

What is 1 2/5 × 2
what is 1/4 × 1​

Answer 1

12/5x2=25

1/4x1=1/4

Explanation:

Answer 2

`1).`
`2(4)/(5)`

`2).`
`(1)/(4)`

Explanation:

`1).`
`1(2)/(5)*2`

Convert mixed number to improper fraction:
`a(b)/(c) =(a*c+b)/(c)`

`1(x2)/(5) =(1*5+2)/(5) =(7)/(5)`

`(7)/(5) *2`

`(7)/(5) *2`

Apply the fraction rule:
`(a)/(b)*c =(a*c)/(b)`

`(7)/(5) *2=(7*2)/(5)`

`=(7*2)/(5)`

Multiply the numbers:
`7*2=14`

`=(14)/(5)`

Convert improper fractions to mixed numbers:
`(14)/(5)`

`(14)/(5)`

Write the problem in long division format:

`\begin{matrix}5\overline\smallspace14\space\space\space\space\space\space\space\space\space\space\space\space\end{matrix}`

Divide
`14` by
`5` to get
`2`

`\begin{matrix}\space\space\space\space\space\space\emptyspace2\space\space\space\space\space\space\space\space\space\space\space\space\\ 5\overline\space\space\space\space\space\space\space\space\space\space\space\space\end{matrix}`

Multiply the quotient digit
`(2)` by the divisor
`5`

`\begin{matrix}\space\space\space\space\space\space\emptyspace2\space\space\space\space\space\space\space\space\space\space\space\space\\ 5\overline\space\space\space\space\space\space\space\space\space\space\space\space\\ \space\space\space\space\underline{\emptyspace1\emptyspace0}\space\space\space\space\space\space\space\space\space\space\space\space\end{matrix}`

Subtract
`10` from
`14`

`\begin{matrix}\space\space\space\space\space\space\emptyspace2\space\space\space\space\space\space\space\space\space\space\space\space\\ 5\overline\smallspace14\space\space\space\space\space\space\space\space\space\space\space\space\\ \space\space\space\space\underline{\emptyspace1\emptyspace0}\space\space\space\space\space\space\space\space\space\space\space\space\\ \space\space\space\space\space\space\emptyspace4\space\space\space\space\space\space\space\space\space\space\space\space\end{matrix}`

The solution for long division of
`(14)/(5)` is
`2` with a remainder of
`4`

`2\quad \mathrm{Remainder}\quad \:4`

Convert to mixed number:
`Quotient(Remainder)/(Divisor)`

`(14)/(5) =2(4)/(5)`

`=2(4)/(5)`

`2(4)/(5)`

Convert
`(4)/(5)` to decimal using long division

`(4)/(5)`

Divide
`4` by
`5` to get
`0`

`\begin{matrix}\space\space\space\space\emptyspace0\space\space\space\space\space\space\space\space\space\space\space\space\\ 5\overline\smallspace4\space\space\space\space\space\space\space\space\space\space\space\space\end{matrix}`

Multiply the quotient digit
`(0)` by the divisor
`5`

`\begin{matrix}\space\space\space\space\emptyspace0\space\space\space\space\space\space\space\space\space\space\space\space\\ 5\overline\space\space\space\space\space\space\space\space\space\space\space\space\\ \space\space\space\space\underline{\emptyspace0}\space\space\space\space\space\space\space\space\space\space\space\space\end{matrix}`

Subtract
`0` from
`4`

`\begin{matrix}\space\space\space\space\emptyspace0\space\space\space\space\space\space\space\space\space\space\space\space\\ 5\overline\smallspace4\space\space\space\space\space\space\space\space\space\space\space\space\\ \space\space\space\space\underline{\emptyspace0}\space\space\space\space\space\space\space\space\space\space\space\space\\ \space\space\space\space\emptyspace4\space\space\space\space\space\space\space\space\space\space\space\space\end{matrix}`

Add a decimal place and a zero to the dividend

Bring down the zero from the dividend

`\begin{matrix}\space\space\space\space\emptyspace0.\space\space\space\space\space\space\space\space\space\space\space\\ 5\overline\smallspace4.0\space\space\space\space\space\space\space\space\space\\ \space\space\space\space\underline{\emptyspace0}\space\space\space\space\space\space\space\space\space\space\space\space\\ \space\space\space\space\emptyspace4\emptyspace0\space\space\space\space\space\space\space\space\space\space\end{matrix}`

Divide
`40` by
`5` to get
`8`

`(40)/(5) =8`

The solution for long division of
`(4)/(5)` is
`0.8`

`=2+0.8`

Add
`2+0.8=2.8`

`2).`
`(1)/(4) *1`

Multiply
`(1)/(4) *1=(1)/(4)`

`=(1)/(4)`

Anything multiplied by
`1` is the same number.

Divide the the numbers
`(1)/(4)` to get decimal form

Divide
`1` by
`4`

`(1)/(4) =0.25`

`=0.25`