Solve A. 14 + \{9/21 / (4/5 - 2/3) - 6\}

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Question

$$14 + \{ \frac { 9 } { 21 } \div ( \frac { 4 } { 5 } - \frac { 2 } { 3 } ) - 6 \}$$

Evaluate

$\frac{157}{14}\approx 11.214285714$

Solution Steps

Reduce the fraction $\frac{9}{21}$ to lowest terms by extracting and canceling out $3$.

$$14+\frac{\frac{3}{7}}{\frac{4}{5}-\frac{2}{3}}-6$$

Least common multiple of $5$ and $3$ is $15$. Convert $\frac{4}{5}$ and $\frac{2}{3}$ to fractions with denominator $15$.

$$14+\frac{\frac{3}{7}}{\frac{12}{15}-\frac{10}{15}}-6$$

Since $\frac{12}{15}$ and $\frac{10}{15}$ have the same denominator, subtract them by subtracting their numerators.

$$14+\frac{\frac{3}{7}}{\frac{12-10}{15}}-6$$

Subtract $10$ from $12$ to get $2$.

$$14+\frac{\frac{3}{7}}{\frac{2}{15}}-6$$

Divide $\frac{3}{7}$ by $\frac{2}{15}$ by multiplying $\frac{3}{7}$ by the reciprocal of $\frac{2}{15}$.

$$14+\frac{3}{7}\times \frac{15}{2}-6$$

Multiply $\frac{3}{7}$ times $\frac{15}{2}$ by multiplying numerator times numerator and denominator times denominator.

$$14+\frac{3\times 15}{7\times 2}-6$$

Do the multiplications in the fraction $\frac{3\times 15}{7\times 2}$.

$$14+\frac{45}{14}-6$$

Convert $14$ to fraction $\frac{196}{14}$.

$$\frac{196}{14}+\frac{45}{14}-6$$

Since $\frac{196}{14}$ and $\frac{45}{14}$ have the same denominator, add them by adding their numerators.

$$\frac{196+45}{14}-6$$

Add $196$ and $45$ to get $241$.

$$\frac{241}{14}-6$$

Convert $6$ to fraction $\frac{84}{14}$.

$$\frac{241}{14}-\frac{84}{14}$$

Since $\frac{241}{14}$ and $\frac{84}{14}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{241-84}{14}$$

Subtract $84$ from $241$ to get $157$.

$$\frac{157}{14}$$

Show Solution

Factor

$\frac{157}{2 \cdot 7} = 11\frac{3}{14} = 11.214285714285714$