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Question

Katrina rode her bicycle $$ 6\dfrac{1}{2} km $$ in the morning and $$ 8\dfrac{3}{4} km $$ in the evening. Find the distance traveled by her altogether on that day.

Solution
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Given
Distance traveled by Katrina in the morning
$$ = 6\dfrac 12 = \dfrac {( 6 \times 2) +1 }{2} = \dfrac { 12+1}{2}=\dfrac {13}{2}\ km $$
Distance traveled by Katrina in the evening
$$ = 8 \dfrac {3}{4} = \dfrac {( 8 \times 4) +3 }{4} = \dfrac { 32 +3}{4} = \dfrac {35}{4} \ km$$

$$ \therefore $$ Total distance traveled by her
$$ =\dfrac {13}{2} + \dfrac {35}{4}\\ = \dfrac { 13}{2}\times \dfrac 22+ \dfrac {35}{4}\times\dfrac 11 \hspace{1.5cm}[\because \text {LCM of }2 \text { and } 4=4]\\ =\dfrac {26}4+\dfrac {35}4\\ =\dfrac{26+35}4\\=\dfrac{61}4=15\dfrac 14 \ km$$

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