Exercise 26
If \( a = \frac{1}{2} \), \( b = \frac{-1}{4} \), \( c = \frac{-1}{3} \) and \( d = \frac{1}{9} \), then the expression \( \cfrac{a}{b} - \cfrac{c}{d} \) equals:
-
\( 5\)
-
\(0\)
-
\(1\)
-
\(-5\)
-
\(-1\)
Try to solve it before checking the answer.
-
1
Indeed:
\[
\begin{aligned}
\frac{a}{b} – \frac{c}{d}
&=
\frac{ \frac{1}{2} }{ \frac{-1}{4} } – \frac{ \frac{-1}{3} }{ \frac{1}{9} }
\\[1em]
&=
\frac{1 \times 4}{ 2 \times (-1) } – \frac{ (-1) \times 9 }{ 3 \times 1 }
\\[1em]
&=
\frac{ 4 }{ -2 } – \frac{ -9 }{3}
\\[1em]
&= -2 – (-3)
\\[1em]
&= \boldsymbol{1}
\end{aligned}
\]