Simplify: $\left(3\frac{1}{4} + 4.8 ight) \div 0.85 + \left(1.6 imes \frac{3}{4} ight)$

Question

Simplify: $\left(3\frac{1}{4} + 4.8ight) \div 0.85 + \left(1.6 	imes \frac{3}{4}ight)$

Accepted Answer

Solution:
First, convert the mixed fraction into an improper fraction:
$$ 3\frac{1}{4} = \frac{13}{4} $$
Now, convert the decimals into fractions:
$$ 4.8 = \frac{48}{10} = \frac{24}{5} $$
$$ 0.85 = \frac{85}{100} = \frac{17}{20} $$
$$ 1.6 = \frac{16}{10} = \frac{8}{5} $$
Now, simplify the first bracket:
$$ \frac{13}{4} + \frac{24}{5} $$
$$ = \frac{65}{20} + \frac{96}{20} $$
$$ = \frac{161}{20} $$
Now, divide by $0.85$:
$$ \frac{161}{20} \div \frac{17}{20} $$
$$ = \frac{161}{20} 	imes \frac{20}{17} $$
$$ = \frac{161}{17} $$
Now, simplify the second bracket:
$$ 1.6 	imes \frac{3}{4} $$
$$ = \frac{8}{5} 	imes \frac{3}{4} $$
$$ = \frac{24}{20} $$
$$ = \frac{6}{5} $$
Now, add both values:
$$ \frac{161}{17} + \frac{6}{5} $$
$$ = \frac{805}{85} + \frac{102}{85} $$
$$ = \frac{907}{85} $$
Therefore, the simplified value is:
$$ \boxed{\frac{907}{85}} $$
Final Answer: **Option (d) $\frac{907}{85}$**

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