Respuesta :

Answer:

Answer: 35/18

Step-by-step explanation:

[tex] \frac{ \{ \frac{3}{4} - \frac{5}{2} \} }{ \{ \frac{3}{5} - \frac{3}{2} \}} = \frac{( - \frac{7}{4} )}{ (- \frac{9}{10} )} \\ \\ = \frac{7}{4} \div \frac{9}{10} [/tex]

use the reciprocal of 9/10 :

[tex] = \frac{7}{4} \times \frac{10}{9} \\ \\ = \frac{35}{18} [/tex]

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[tex] \huge \boxed{\mathfrak{Question} \downarrow}[/tex]

  • Simplify [tex]\huge \sf\frac { \frac { 3 } { 4 } - \frac { 5 } { 2 } } { \frac { 3 } { 5 } - \frac { 3 } { 2 } } \\ [/tex]

[tex] \large \boxed{\mathfrak{Answer \: with \: Explanation} \downarrow}[/tex]

[tex] \huge \sf\frac { \frac { 3 } { 4 } - \frac { 5 } { 2 } } { \frac { 3 } { 5 } - \frac { 3 } { 2 } } \\ [/tex]

  • The least common multiple of 4 and 2 is 4. Convert [tex]\sf\frac{3}{4} [/tex]and [tex]\sf\frac{5}{2} [/tex]to fractions with denominator 4.

[tex] \huge \sf \frac{\frac{3}{4}-\frac{10}{4}}{\frac{3}{5}-\frac{3}{2}} \\ [/tex]

  • Because [tex]\sf\frac{3}{4} [/tex]and [tex]\sf \frac{10}{4}[/tex] have the same denominator, subtract them by subtracting their numerators.

[tex] \huge \sf\frac{\frac{3-10}{4}}{\frac{3}{5}-\frac{3}{2}} \\ [/tex]

  • Subtract 10 from 3 to get -7.

[tex] \huge \sf\frac{-\frac{7}{4}}{\frac{3}{5}-\frac{3}{2}} \\ [/tex]

  • The least common multiple of 5 and 2 is 10. Convert [tex]\sf\frac{3}{5}[/tex] and [tex]\sf \frac{3}{2}[/tex] to fractions with denominator 10.

[tex] \huge \sf\frac{-\frac{7}{4}}{\frac{6}{10}-\frac{15}{10}} \\ [/tex]

  • Because [tex]\sf \frac{6}{10}[/tex] and [tex]\sf \frac{15}{10}[/tex] have the same denominator, subtract them by subtracting their numerators.

[tex] \huge \sf\frac{-\frac{7}{4}}{\frac{6-15}{10}} \\ [/tex]

  • Subtract 15 from 6 to get -9.

[tex] \huge \sf\frac{-\frac{7}{4}}{-\frac{9}{10}} \\ [/tex]

  • Divide [tex]\sf-\frac{7}{4}[/tex] by [tex]\sf-\frac{9}{10}[/tex] by multiplying [tex]\sf-\frac{7}{4}[/tex] by the reciprocal of [tex]\sf-\frac{9}{10}[/tex].

[tex] \huge \sf-\frac{7}{4}\left(-\frac{10}{9}\right) [/tex]

  • Multiply [tex]\sf-\frac{7}{4}[/tex] by [tex]\sf-\frac{10}{9}[/tex] by multiplying the numerator by the numerator and the denominator by the denominator.

[tex] \huge \sf\frac{-7\left(-10\right)}{4\times 9} [/tex]

  • Carry out the multiplications in the fraction [tex]\sf\frac{-7\left(-10\right)}{4\times 9}[/tex].

[tex] \huge \sf\frac{70}{36} [/tex]

  • Reduce the fraction [tex]\sf\frac{70}{36}[/tex] to its lowest terms by extracting and cancelling out 2.

[tex] \huge \boxed{ \bf\frac{35}{18}\approx 1.944..}[/tex]

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