Solve (11)/(5)+(4)/(21)\times42-(18)/(5)\div(27)/(45)

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Question

$$\frac{ 11 }{ 5 } + \frac{ 4 }{ 21 } \times 42- \frac{ 18 }{ 5 } \div \frac{ 27 }{ 45 }$$

Evaluate

$\frac{21}{5}=4.2$

Solution Steps

Express $\frac{4}{21}\times 42$ as a single fraction.

$$\frac{11}{5}+\frac{4\times 42}{21}-\frac{\frac{18}{5}}{\frac{27}{45}}$$

Multiply $4$ and $42$ to get $168$.

$$\frac{11}{5}+\frac{168}{21}-\frac{\frac{18}{5}}{\frac{27}{45}}$$

Divide $168$ by $21$ to get $8$.

$$\frac{11}{5}+8-\frac{\frac{18}{5}}{\frac{27}{45}}$$

Convert $8$ to fraction $\frac{40}{5}$.

$$\frac{11}{5}+\frac{40}{5}-\frac{\frac{18}{5}}{\frac{27}{45}}$$

Since $\frac{11}{5}$ and $\frac{40}{5}$ have the same denominator, add them by adding their numerators.

$$\frac{11+40}{5}-\frac{\frac{18}{5}}{\frac{27}{45}}$$

Add $11$ and $40$ to get $51$.

$$\frac{51}{5}-\frac{\frac{18}{5}}{\frac{27}{45}}$$

Divide $\frac{18}{5}$ by $\frac{27}{45}$ by multiplying $\frac{18}{5}$ by the reciprocal of $\frac{27}{45}$.

$$\frac{51}{5}-\frac{18\times 45}{5\times 27}$$

Cancel out $3\times 5\times 9$ in both numerator and denominator.

$$\frac{51}{5}-2\times 3$$

Multiply $2$ and $3$ to get $6$.

$$\frac{51}{5}-6$$

Convert $6$ to fraction $\frac{30}{5}$.

$$\frac{51}{5}-\frac{30}{5}$$

Since $\frac{51}{5}$ and $\frac{30}{5}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{51-30}{5}$$

Subtract $30$ from $51$ to get $21$.

$$\frac{21}{5}$$

Show Solution

Factor

$\frac{3 \cdot 7}{5} = 4\frac{1}{5} = 4.2$