Questions: Select the fully reduced form of the fraction: (16x-24)/(18x-27) a) (8x-8)/(9x-9) b) (x-8)/(x-9) c) 8/9 d) -(8/9) e) (8x)/(9x)

$Select the fully reduced form of the fraction: (16x-24)/(18x-27) a) (8x-8)/(9x-9) b) (x-8)/(x-9) c) 8/9 d) -(8/9) e) (8x)/(9x)$

Transcript text: 10. (L52) Select the fully reduced form of the fraction: $\frac{16 x-24}{18 x-27}$ a) $\frac{8 x-8}{9 x-9}$ b) $\frac{x-8}{x-9}$ c) $\frac{8}{9}$ d) $-\frac{8}{9}$ e) $\frac{8 x}{9 x}$

Solution

Solution Steps

Step 1: Factor the numerator and denominator

The given fraction is: \[ \frac{16x - 24}{18x - 27} \] First, factor out the greatest common factor (GCF) from both the numerator and the denominator.

The numerator $16x - 24$ can be factored as $8(2x - 3)$.
The denominator $18x - 27$ can be factored as $9(2x - 3)$.

Thus, the fraction becomes: \[ \frac{8(2x - 3)}{9(2x - 3)} \]

Step 2: Simplify the fraction

Since $2x - 3$ appears in both the numerator and the denominator, it can be canceled out (assuming $2x - 3 \neq 0$): \[ \frac{8(2x - 3)}{9(2x - 3)} = \frac{8}{9} \]

Step 3: Compare with the options

The simplified form of the fraction is $\frac{8}{9}$. Now, compare this with the given options:

a) $\frac{8x-8}{9x-9}$
b) $\frac{x-8}{x-9}$
c) $\frac{8}{9}$
d) $-\frac{8}{9}$
e) $\frac{8x}{9x}$

The correct answer is option c) $\frac{8}{9}$.