Answer:
[tex]4\frac{5}{8}\div \:\:2\frac{3}{4}=\frac{37}{22}[/tex]
Step-by-step explanation:
Given
[tex]4\frac{5}{8}\div \:2\frac{3}{4}[/tex]
[tex]\mathrm{Convert\:mixed\:numbers\:to\:improper\:fractions}:\quad 4\frac{5}{8}=\frac{37}{8}[/tex]
[tex]=\frac{37}{8}\div \:2\frac{3}{4}[/tex]
[tex]\mathrm{Convert\:mixed\:numbers\:to\:improper\:fractions}:\quad 2\frac{3}{4}=\frac{11}{4}[/tex]
[tex]=\frac{37}{8}\div \frac{11}{4}[/tex]
[tex]\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{a}{b}\div \frac{c}{d}=\frac{a}{b}\times \frac{d}{c}[/tex]
[tex]=\frac{37}{8}\times \frac{4}{11}[/tex]
[tex]\mathrm{Cross-cancel\:common\:factor:}\:4[/tex]
[tex]=\frac{37}{2}\times \frac{1}{11}[/tex]
[tex]\mathrm{Multiply\:fractions}:\quad \frac{a}{b}\times \frac{c}{d}=\frac{a\:\times \:c}{b\:\times \:d}[/tex]
[tex]=\frac{37\times \:1}{2\times \:11}[/tex]
[tex]\mathrm{Multiply\:the\:numbers:}\:37\times \:1=37[/tex]
[tex]=\frac{37}{2\times \:11}[/tex]
[tex]\mathrm{Multiply\:the\:numbers:}\:2\times \:11=22[/tex]
[tex]=\frac{37}{22}[/tex]
Therefore,
[tex]4\frac{5}{8}\div \:\:2\frac{3}{4}=\frac{37}{22}[/tex]
