Solve ( b ) 5 + [24/7 - \{2/21 + (1/7 + 1/14)\}]

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Question

$$5 + [ \frac { 24 } { 7 } - \{ \frac { 2 } { 21 } + ( \frac { 1 } { 7 } + \frac { 1 } { 14 } ) \} ]$$

Evaluate

$\frac{341}{42}\approx 8.119047619$

Solution Steps

Least common multiple of $21$ and $7$ is $21$. Convert $\frac{2}{21}$ and $\frac{1}{7}$ to fractions with denominator $21$.

$$5+\frac{24}{7}-\left(\frac{2}{21}+\frac{3}{21}+\frac{1}{14}\right)$$

Since $\frac{2}{21}$ and $\frac{3}{21}$ have the same denominator, add them by adding their numerators.

$$5+\frac{24}{7}-\left(\frac{2+3}{21}+\frac{1}{14}\right)$$

Add $2$ and $3$ to get $5$.

$$5+\frac{24}{7}-\left(\frac{5}{21}+\frac{1}{14}\right)$$

Least common multiple of $21$ and $14$ is $42$. Convert $\frac{5}{21}$ and $\frac{1}{14}$ to fractions with denominator $42$.

$$5+\frac{24}{7}-\left(\frac{10}{42}+\frac{3}{42}\right)$$

Since $\frac{10}{42}$ and $\frac{3}{42}$ have the same denominator, add them by adding their numerators.

$$5+\frac{24}{7}-\frac{10+3}{42}$$

Add $10$ and $3$ to get $13$.

$$5+\frac{24}{7}-\frac{13}{42}$$

Least common multiple of $7$ and $42$ is $42$. Convert $\frac{24}{7}$ and $\frac{13}{42}$ to fractions with denominator $42$.

$$5+\frac{144}{42}-\frac{13}{42}$$

Since $\frac{144}{42}$ and $\frac{13}{42}$ have the same denominator, subtract them by subtracting their numerators.

$$5+\frac{144-13}{42}$$

Subtract $13$ from $144$ to get $131$.

$$5+\frac{131}{42}$$

Convert $5$ to fraction $\frac{210}{42}$.

$$\frac{210}{42}+\frac{131}{42}$$

Since $\frac{210}{42}$ and $\frac{131}{42}$ have the same denominator, add them by adding their numerators.

$$\frac{210+131}{42}$$

Add $210$ and $131$ to get $341$.

$$\frac{341}{42}$$

Show Solution

Factor

$\frac{11 \cdot 31}{2 \cdot 3 \cdot 7} = 8\frac{5}{42} = 8.119047619047619$