Question

NEED HELP ASAP. I don not understand why I'm wrong. What is the right answer???

Answer 1

`\huge \boxed{\mathfrak{Question} \downarrow}`

• Simplify
  `\huge \sf\frac { \frac { 3 } { 4 } - \frac { 5 } { 2 } } { \frac { 3 } { 5 } - \frac { 3 } { 2 } } \\`

`\large \boxed{\mathfrak{Answer \: with \: Explanation} \downarrow}`

`\huge \sf\frac { \frac { 3 } { 4 } - \frac { 5 } { 2 } } { \frac { 3 } { 5 } - \frac { 3 } { 2 } } \\`

• The least common multiple of 4 and 2 is 4. Convert
  `\sf(3)/(4)`and
  `\sf(5)/(2)`to fractions with denominator 4.

`\huge \sf ((3)/(4)-(10)/(4))/((3)/(5)-(3)/(2)) \\`

• Because
  `\sf(3)/(4)`and
  `\sf (10)/(4)` have the same denominator, subtract them by subtracting their numerators.

`\huge \sf((3-10)/(4))/((3)/(5)-(3)/(2)) \\`

• Subtract 10 from 3 to get -7.

`\huge \sf(-(7)/(4))/((3)/(5)-(3)/(2)) \\`

• The least common multiple of 5 and 2 is 10. Convert
  `\sf(3)/(5)` and
  `\sf (3)/(2)` to fractions with denominator 10.

`\huge \sf(-(7)/(4))/((6)/(10)-(15)/(10)) \\`

• Because
  `\sf (6)/(10)` and
  `\sf (15)/(10)` have the same denominator, subtract them by subtracting their numerators.

`\huge \sf(-(7)/(4))/((6-15)/(10)) \\`

• Subtract 15 from 6 to get -9.

`\huge \sf(-(7)/(4))/(-(9)/(10)) \\`

• Divide
  `\sf-(7)/(4)` by
  `\sf-(9)/(10)` by multiplying
  `\sf-(7)/(4)` by the reciprocal of
  `\sf-(9)/(10)`.

`\huge \sf-(7)/(4)\left(-(10)/(9)\right)`

• Multiply
  `\sf-(7)/(4)` by
  `\sf-(10)/(9)` by multiplying the numerator by the numerator and the denominator by the denominator.

`\huge \sf(-7\left(-10\right))/(4* 9)`

• Carry out the multiplications in the fraction
  `\sf(-7\left(-10\right))/(4* 9)`.

`\huge \sf(70)/(36)`

• Reduce the fraction
  `\sf(70)/(36)` to its lowest terms by extracting and cancelling out 2.

`\huge \boxed{ \bf(35)/(18)\approx 1.944..}`

Answer 2

Answer: 35/18

Explanation:

`\frac{ \{ (3)/(4) - (5)/(2) \} }{ \{ (3)/(5) - (3)/(2) \}} = (( - (7)/(4) ))/( (- (9)/(10) )) \\ \\ = (7)/(4) / (9)/(10)`

use the reciprocal of 9/10 :

`= (7)/(4) * (10)/(9) \\ \\ = (35)/(18)`