Solve \{9 / (3/10 - 2/10 + 1/5)\} * 3 + 1/5

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Question

$$\{9\div(\frac{3}{10}-\frac{2}{10}+\frac{1}{5})\}\times3+\frac{1}{5}$$

Evaluate

$\frac{451}{5}=90.2$

Solution Steps

Since $\frac{3}{10}$ and $\frac{2}{10}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{9}{\frac{3-2}{10}+\frac{1}{5}}\times 3+\frac{1}{5}$$

Subtract $2$ from $3$ to get $1$.

$$\frac{9}{\frac{1}{10}+\frac{1}{5}}\times 3+\frac{1}{5}$$

Least common multiple of $10$ and $5$ is $10$. Convert $\frac{1}{10}$ and $\frac{1}{5}$ to fractions with denominator $10$.

$$\frac{9}{\frac{1}{10}+\frac{2}{10}}\times 3+\frac{1}{5}$$

Since $\frac{1}{10}$ and $\frac{2}{10}$ have the same denominator, add them by adding their numerators.

$$\frac{9}{\frac{1+2}{10}}\times 3+\frac{1}{5}$$

Add $1$ and $2$ to get $3$.

$$\frac{9}{\frac{3}{10}}\times 3+\frac{1}{5}$$

Divide $9$ by $\frac{3}{10}$ by multiplying $9$ by the reciprocal of $\frac{3}{10}$.

$$9\times \frac{10}{3}\times 3+\frac{1}{5}$$

Express $9\times \frac{10}{3}$ as a single fraction.

$$\frac{9\times 10}{3}\times 3+\frac{1}{5}$$

Multiply $9$ and $10$ to get $90$.

$$\frac{90}{3}\times 3+\frac{1}{5}$$

Divide $90$ by $3$ to get $30$.

$$30\times 3+\frac{1}{5}$$

Multiply $30$ and $3$ to get $90$.

$$90+\frac{1}{5}$$

Convert $90$ to fraction $\frac{450}{5}$.

$$\frac{450}{5}+\frac{1}{5}$$

Since $\frac{450}{5}$ and $\frac{1}{5}$ have the same denominator, add them by adding their numerators.

$$\frac{450+1}{5}$$

Add $450$ and $1$ to get $451$.

$$\frac{451}{5}$$

Show Solution

Factor

$\frac{11 \cdot 41}{5} = 90\frac{1}{5} = 90.2$