Answer:
[tex]1).[/tex] [tex]2\frac{4}{5}[/tex]
[tex]2).[/tex] [tex]\frac{1}{4}[/tex]
Step-by-step explanation:
[tex]1).[/tex] [tex]1\frac{2}{5}*2[/tex]
Convert mixed number to improper fraction: [tex]a\frac{b}{c} =\frac{a*c+b}{c}[/tex]
[tex]1\frac{x2}{5} =\frac{1*5+2}{5} =\frac{7}{5}[/tex]
[tex]\frac{7}{5} *2[/tex]
[tex]\frac{7}{5} *2[/tex]
Apply the fraction rule: [tex]\frac{a}{b}*c =\frac{a*c}{b}[/tex]
[tex]\frac{7}{5} *2=\frac{7*2}{5}[/tex]
[tex]=\frac{7*2}{5}[/tex]
Multiply the numbers: [tex]7*2=14[/tex]
[tex]=\frac{14}{5}[/tex]
Convert improper fractions to mixed numbers: [tex]\frac{14}{5}[/tex]
[tex]\frac{14}{5}[/tex]
Write the problem in long division format:
[tex]\begin{matrix}5\overline{|\smallspace14}\space\space\space\space\space\space\space\space\space\space\space\space\end{matrix}[/tex]
Divide [tex]14[/tex] by [tex]5[/tex] to get [tex]2[/tex]
[tex]\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\end{matrix}[/tex]
Multiply the quotient digit [tex](2)[/tex] by the divisor [tex]5[/tex]
[tex]\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\end{matrix}[/tex]
Subtract [tex]10[/tex] from [tex]14[/tex]
[tex]\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}[/tex]
The solution for long division of [tex]\frac{14}{5}[/tex] is [tex]2[/tex] with a remainder of [tex]4[/tex]
[tex]2\quad \mathrm{Remainder}\quad \:4[/tex]
Convert to mixed number: [tex]Quotient\frac{Remainder}{Divisor}[/tex]
[tex]\frac{14}{5} =2\frac{4}{5}[/tex]
[tex]=2\frac{4}{5}[/tex]
[tex]2\frac{4}{5}[/tex]
Convert [tex]\frac{4}{5}[/tex] to decimal using long division
[tex]\frac{4}{5}[/tex]
Divide [tex]4[/tex] by [tex]5[/tex] to get [tex]0[/tex]
[tex]\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}[/tex]
Multiply the quotient digit [tex](0)[/tex] by the divisor [tex]5[/tex]
[tex]\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\end{matrix}[/tex]
Subtract [tex]0[/tex] from [tex]4[/tex]
[tex]\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}[/tex]
Add a decimal place and a zero to the dividend
Bring down the zero from the dividend
[tex]\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}[/tex]
Divide [tex]40[/tex] by [tex]5[/tex] to get [tex]8[/tex]
[tex]\frac{40}{5} =8[/tex]
The solution for long division of [tex]\frac{4}{5}[/tex] is [tex]0.8[/tex]
[tex]=2+0.8[/tex]
Add [tex]2+0.8=2.8[/tex]
[tex]2).[/tex] [tex]\frac{1}{4} *1[/tex]
Multiply [tex]\frac{1}{4} *1=\frac{1}{4}[/tex]
[tex]=\frac{1}{4}[/tex]
Anything multiplied by [tex]1[/tex] is the same number.
Divide the the numbers [tex]\frac{1}{4}[/tex] to get decimal form
Divide [tex]1[/tex] by [tex]4[/tex]
[tex]\frac{1}{4} =0.25[/tex]
[tex]=0.25[/tex]
