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

`4(5)/(8)/ \:\:2(3)/(4)=(37)/(22)`

Explanation:

Given

`4(5)/(8)/ \:2(3)/(4)`

`\mathrm{Convert\:mixed\:numbers\:to\:improper\:fractions}:\quad 4(5)/(8)=(37)/(8)`

`=(37)/(8)/ \:2(3)/(4)`

`\mathrm{Convert\:mixed\:numbers\:to\:improper\:fractions}:\quad 2(3)/(4)=(11)/(4)`

`=(37)/(8)/ (11)/(4)`

`\mathrm{Apply\:the\:fraction\:rule}:\quad (a)/(b)/ (c)/(d)=(a)/(b)* (d)/(c)`

`=(37)/(8)* (4)/(11)`

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

`=(37)/(2)* (1)/(11)`

`\mathrm{Multiply\:fractions}:\quad (a)/(b)* (c)/(d)=(a\:* \:c)/(b\:* \:d)`

`=(37* \:1)/(2* \:11)`

`\mathrm{Multiply\:the\:numbers:}\:37* \:1=37`

`=(37)/(2* \:11)`

`\mathrm{Multiply\:the\:numbers:}\:2* \:11=22`

`=(37)/(22)`

Therefore,

`4(5)/(8)/ \:\:2(3)/(4)=(37)/(22)`