Question
Find the value of:$1.35 + 1.5$
✓
Answer
Let $x=1.3 \overline{5} $
$\Rightarrow 10 x=13 . \overline{5} .....(i)$
$\Rightarrow 100 x=135 . \overline{5} .....(ii)$
Subtracting $(i) a=$ from $(ii),$
$90 x =122 $
$\Rightarrow x =\frac{122}{90} $
$=\frac{61}{45}$
Let $y=1 . \overline{5} .....(iii)$
$\Rightarrow 10 y =15 . \overline{5} .....(iv)$
$\Rightarrow 9 y =14 $
$\Rightarrow y =\frac{14}{9} $
$\therefore 1.3 \overline{5}+1 . \overline{5}= x + y $
$=\frac{61}{45}+\frac{14}{9} $
$=\frac{61 \times 1+14 \times 5}{45} $
$=\frac{61+70}{45} $
$=\frac{131}{45} $
$=2.91$
$\Rightarrow 10 x=13 . \overline{5} .....(i)$
$\Rightarrow 100 x=135 . \overline{5} .....(ii)$
Subtracting $(i) a=$ from $(ii),$
$90 x =122 $
$\Rightarrow x =\frac{122}{90} $
$=\frac{61}{45}$
Let $y=1 . \overline{5} .....(iii)$
$\Rightarrow 10 y =15 . \overline{5} .....(iv)$
$\Rightarrow 9 y =14 $
$\Rightarrow y =\frac{14}{9} $
$\therefore 1.3 \overline{5}+1 . \overline{5}= x + y $
$=\frac{61}{45}+\frac{14}{9} $
$=\frac{61 \times 1+14 \times 5}{45} $
$=\frac{61+70}{45} $
$=\frac{131}{45} $
$=2.91$
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