Solve 1+1/4.77/frac{0.2{0.1}+0.1/0.2}

$$\frac{ 1+ \frac{ 1 }{ 4.77 } }{ \frac{ 0.2 }{ 0.1 } + \frac{ 0.1 }{ 0.2 } }$$

Evaluate

$$\frac{1154}{2385}\approx 0.483857442$$

Solution Steps

Expand \frac{1}{4.77} by multiplying both numerator and the denominator by 100.

$$\frac{1+\frac{100}{477}}{\frac{0.2}{0.1}+\frac{0.1}{0.2}}$$

Convert 1 to fraction \frac{477}{477}.

$$\frac{\frac{477}{477}+\frac{100}{477}}{\frac{0.2}{0.1}+\frac{0.1}{0.2}}$$

Since \frac{477}{477} and \frac{100}{477} have the same denominator, add them by adding their numerators.

$$\frac{\frac{477+100}{477}}{\frac{0.2}{0.1}+\frac{0.1}{0.2}}$$

Add 477 and 100 to get 577.

$$\frac{\frac{577}{477}}{\frac{0.2}{0.1}+\frac{0.1}{0.2}}$$

Expand \frac{0.2}{0.1} by multiplying both numerator and the denominator by 10. Anything divided by one gives itself.

$$\frac{\frac{577}{477}}{2+\frac{0.1}{0.2}}$$

Expand \frac{0.1}{0.2} by multiplying both numerator and the denominator by 10.

$$\frac{\frac{577}{477}}{2+\frac{1}{2}}$$

Convert 2 to fraction \frac{4}{2}.

$$\frac{\frac{577}{477}}{\frac{4}{2}+\frac{1}{2}}$$

Since \frac{4}{2} and \frac{1}{2} have the same denominator, add them by adding their numerators.

$$\frac{\frac{577}{477}}{\frac{4+1}{2}}$$

Add 4 and 1 to get 5.

$$\frac{\frac{577}{477}}{\frac{5}{2}}$$

Divide \frac{577}{477} by \frac{5}{2} by multiplying \frac{577}{477} by the reciprocal of \frac{5}{2}.

$$\frac{577}{477}\times \frac{2}{5}$$

Multiply \frac{577}{477} times \frac{2}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{577\times 2}{477\times 5}$$

Do the multiplications in the fraction \frac{577\times 2}{477\times 5}.

$$\frac{1154}{2385}$$

Factor

$$\frac{2 \cdot 577}{5 \cdot 53 \cdot 3 ^ {2}} = 0.48385744234800837$$