Question

Using complete sentences, explain how to find the quotient of 4 5/8 ÷ 2 3/4 . Make sure to include the quotient in your answer.

Answer 1

Answer:

$4\frac{5}{8}\div \:\:2\frac{3}{4}=\frac{37}{22}$

Step-by-step explanation:

Given

$4\frac{5}{8}\div \:2\frac{3}{4}$

$\mathrm{Convert\:mixed\:numbers\:to\:improper\:fractions}:\quad 4\frac{5}{8}=\frac{37}{8}$

$=\frac{37}{8}\div \:2\frac{3}{4}$

$\mathrm{Convert\:mixed\:numbers\:to\:improper\:fractions}:\quad 2\frac{3}{4}=\frac{11}{4}$

$=\frac{37}{8}\div \frac{11}{4}$

$\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{a}{b}\div \frac{c}{d}=\frac{a}{b}\times \frac{d}{c}$

$=\frac{37}{8}\times \frac{4}{11}$

$\mathrm{Cross-cancel\:common\:factor:}\:4$

$=\frac{37}{2}\times \frac{1}{11}$

$\mathrm{Multiply\:fractions}:\quad \frac{a}{b}\times \frac{c}{d}=\frac{a\:\times \:c}{b\:\times \:d}$

$=\frac{37\times \:1}{2\times \:11}$

$\mathrm{Multiply\:the\:numbers:}\:37\times \:1=37$

$=\frac{37}{2\times \:11}$

$\mathrm{Multiply\:the\:numbers:}\:2\times \:11=22$

$=\frac{37}{22}$        

Therefore,

$4\frac{5}{8}\div \:\:2\frac{3}{4}=\frac{37}{22}$