Hello,
Question:
Divide. −4 3/5÷1 1/5 Enter your answer as a mixed number, in simplified form, in the box.
Solution:
Turn into improper fraction,
-4 3/5 = 23/5
1 1/5 = 6/5
Use Copy Dot Flip,
-23/5 x 5/6
Multiply Across,
-23 x 5 = -115
5 x 6 = 30
= -115/30
Turn into Mixed Number,
-115/30 = -3 25/30
Simplify,
-3 25/30 = -3 5/6
Answer:
-3 5/6
Answer by Mimiwhatsup:
[tex]-4\frac{3}{5}\div \:1\frac{1}{5}\\\mathrm{Convert\:mixed\:numbers\:to\:improper\:fractions}:\quad 4\frac{3}{5}=\frac{23}{5}\\-4\frac{3}{5}\div \:1\frac{1}{5}\\\mathrm{Convert\:mixed\:numbers\:to\:improper\:fraction:}\:a\frac{b}{c}=\frac{a\times \:c+b}{c}\\4\frac{3}{5}=\frac{4\times 5+3}{5}=\frac{23}{5}\\\\-\frac{23}{5}\div \:1\times \frac{1}{5}\\=-\frac{23}{5}\div \:1\frac{1}{5}\\\mathrm{Convert\:mixed\:numbers\:to\:improper\:fractions}:\quad 1\frac{1}{5}=\frac{6}{5}\\\\[/tex]
[tex]-\frac{23}{5}\div \:1\frac{1}{5}\\\mathrm{Convert\:mixed\:numbers\:to\:improper\:fraction:}\:a\frac{b}{c}=\frac{a\times \:c+b}{c}\\1\frac{1}{5}=\frac{1\times 5+1}{5}=\frac{6}{5}\\-\frac{23}{5}\div \frac{6}{5}\\=-\frac{23}{5}\div \frac{6}{5}\\\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{a}{b}\div \frac{c}{d}=\frac{a}{b}\times \frac{d}{c}\\=-\frac{23}{5}\times \frac{5}{6}\\\mathrm{Cross-cancel:}\:5\\=-\frac{23}{6}\\\mathrm{Convert\:improper\:fractions\:to\:mixed\:numbers}:\quad \frac{23}{6}\\[/tex]
[tex]\mathrm{Convert\:improper\:fractions\:to\:mixed\:numbers}:\quad \frac{23}{6}=3\frac{5}{6}\\\mathrm{Long\:Division}\:\frac{23}{6}:\quad 3\quad \mathrm{Remainder}\quad \:5\\\frac{23}{6}\\Write\:the\:problem\:in\:long\:division\:format\\6\overline{|\smallspace23}\\\mathrm{Divide}\:23\:\mathrm{by}\:6\:\mathrm{to\:get}\:3\\[/tex][tex]\begin{matrix}\space\space\space\space\space\space\emptyspace3\space\space\space\space\space\space\space\space\space\space\space\space\\ 6\overline{|\smallspace23}\space\space\space\space\space\space\space\space\space\space\space\space\end{matrix}\\\mathrm{Multiply\:the\:quotient\:digit}\:\left(3\right)\:\mathrm{by\:the\:divisor}\:6\\[/tex][tex]\begin{matrix}\space\space\space\space\space\space\emptyspace3\space\space\space\space\space\space\space\space\space\space\space\space\\ 6\overline{|\smallspace23}\space\space\space\space\space\space\space\space\space\space\space\space\\ \space\space\space\space\underline{\emptyspace1\emptyspace8}\space\space\space\space\space\space\space\space\space\space\space\space\end{matrix}\\\mathrm{Subtract}\:18\:\mathrm{from}\:23\\[/tex]
[tex]\begin{matrix}\space\space\space\space\space\space\emptyspace3\space\space\space\space\space\space\space\space\space\space\space\space\\ 6\overline{|\smallspace23}\space\space\space\space\space\space\space\space\space\space\space\space\\ \space\space\space\space\underline{\emptyspace1\emptyspace8}\space\space\space\space\space\space\space\space\space\space\space\space\\ \space\space\space\space\space\space\emptyspace5\space\space\space\space\space\space\space\space\space\space\space\space\end{matrix}\\[/tex]
[tex]\mathrm{The\:solution\:for\:Long\:Division\:of}\:\frac{23}{6}\:\mathrm{is}\:3\:\mathrm{with\:remainder\:of}\:5\\3\quad \mathrm{Remainder}\quad \:5\\Convert\:to\:mixed\:number:\:Quotient\frac{Remainder}{Divisor}\\\frac{23}{6}=3\frac{5}{6}\\Answer: -3\frac{5}{6}[/tex]
