Question

asked Apr 8, 2022 111k views

2 Answers

Pandawan · Answer 1 · 2022-04-09T12:21:38+0000

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

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.

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

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

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.

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

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

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.

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

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