Question

Which expressions have a quotient of 3/4?Select all that apply.a. 2/8 ÷ 1/3b. 2/3 ÷ 2c. 1/2 ÷ 3/8d. 1 1/4 ÷ 1 2/3e. 4 2/3 ÷ 3 1/2

Answer 1

To determine which expression gives as a result 3/4 you have to solve them:

When you divide two fractions, you have to invert the denominator of the division (reciprocal fraction) and multiply the numerator of the division by the reciprocal fraction.

a.

`(2)/(8)/(1)/(3)`

Reverse the denominator

`(1)/(3)\to(3)/(1)`

And multiply both fractions

`(2)/(8)\cdot(3)/(1)=(2\cdot3)/(8\cdot1)=(6)/(8)`

Both 6 and 8 are divisible by 2, so you can simplify the result as

`(6/2)/(8/2)=(3)/(4)`

b.

`(2)/(3)/2`

Determine the reciprocal of the denominator

`(2)/(1)=(1)/(2)`

And multiply it by the numerator of the division

`(2)/(3)\cdot(1)/(2)=(2\cdot1)/(3\cdot2)=(2)/(6)`

Both values are divisible by 2, so you can simplify the result as:

`(2/2)/(6/2)=(1)/(3)`

c.

`(1)/(2)/(3)/(8)`

Determine the reciprocal fraction

`(3)/(8)\to(8)/(3)`

Multiply both fractions

`(1)/(2)\cdot(8)/(3)=(1\cdot8)/(2\cdot3)=(8)/(6)`

Divide the numerator and denominator by 2 to simplify the fractions

`(8/2)/(6/2)=(4)/(3)`

d.

`1(1)/(4)/1(2)/(3)`

Express both mixed fractions as improper fractions

`1(1)/(4)=(4)/(4)+(1)/(4)=(5)/(4)`
`1(2)/(3)=(3)/(3)+(2)/(3)=(5)/(3)`

So the division is

`(5)/(4)/(5)/(3)`

Determine the reciprocal fraction

`(5)/(3)\to(3)/(5)`

And multiply both fractions

`(5)/(4)\cdot(3)/(5)=(5\cdot3)/(4\cdot5)=(15)/(20)`

Both values 15 and 20 are divisible by 5, you can simplify the result

`(15/5)/(20/5)=(3)/(4)`

e.

`4(2)/(3)/3(1)/(2)`

Convert the fractions from mixed to improper

`(4\cdot3)/(1\cdot3)+(2)/(3)=(12)/(3)+(2)/(3)=(14)/(3)`
`(3\cdot2)/(1\cdot2)+(1)/(2)=(6)/(2)+(1)/(2)=(7)/(2)`
`(14)/(3)/(7)/(2)`

Determine the reciprocal fraction

`(7)/(2)\to(2)/(7)`

And multiply both fractions

`(14)/(3)\cdot(2)/(7)=(14\cdot2)/(3\cdot7)=(28)/(21)=(4)/(3)`

From the given quotients, those that have 3/4, as a result, are "a." and "d."