Solve 7X186 1260 34(7/8 + 8/4) + 8(12/6 + 6/14) + 7(12/4 - 2/4) | Equatix - Math Solver

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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$$4 ( \frac { 7 } { 8 } + \frac { 8 } { 4 } ) + 8 ( \frac { 18 } { 6 } + \frac { 6 } { 14 } ) + 7 ( \frac { 19 } { 4 } - \frac { 2 } { 4 } )$$

Evaluate

$\frac{1923}{28}\approx 68.678571429$

Solution Steps

Divide $8$ by $4$ to get $2$.

$$4\left(\frac{7}{8}+2\right)+8\left(\frac{18}{6}+\frac{6}{14}\right)+7\left(\frac{19}{4}-\frac{2}{4}\right)$$

Convert $2$ to fraction $\frac{16}{8}$.

$$4\left(\frac{7}{8}+\frac{16}{8}\right)+8\left(\frac{18}{6}+\frac{6}{14}\right)+7\left(\frac{19}{4}-\frac{2}{4}\right)$$

Since $\frac{7}{8}$ and $\frac{16}{8}$ have the same denominator, add them by adding their numerators.

$$4\times \frac{7+16}{8}+8\left(\frac{18}{6}+\frac{6}{14}\right)+7\left(\frac{19}{4}-\frac{2}{4}\right)$$

Add $7$ and $16$ to get $23$.

$$4\times \frac{23}{8}+8\left(\frac{18}{6}+\frac{6}{14}\right)+7\left(\frac{19}{4}-\frac{2}{4}\right)$$

Express $4\times \frac{23}{8}$ as a single fraction.

$$\frac{4\times 23}{8}+8\left(\frac{18}{6}+\frac{6}{14}\right)+7\left(\frac{19}{4}-\frac{2}{4}\right)$$

Multiply $4$ and $23$ to get $92$.

$$\frac{92}{8}+8\left(\frac{18}{6}+\frac{6}{14}\right)+7\left(\frac{19}{4}-\frac{2}{4}\right)$$

Reduce the fraction $\frac{92}{8}$ to lowest terms by extracting and canceling out $4$.

$$\frac{23}{2}+8\left(\frac{18}{6}+\frac{6}{14}\right)+7\left(\frac{19}{4}-\frac{2}{4}\right)$$

Divide $18$ by $6$ to get $3$.

$$\frac{23}{2}+8\left(3+\frac{6}{14}\right)+7\left(\frac{19}{4}-\frac{2}{4}\right)$$

Reduce the fraction $\frac{6}{14}$ to lowest terms by extracting and canceling out $2$.

$$\frac{23}{2}+8\left(3+\frac{3}{7}\right)+7\left(\frac{19}{4}-\frac{2}{4}\right)$$

Convert $3$ to fraction $\frac{21}{7}$.

$$\frac{23}{2}+8\left(\frac{21}{7}+\frac{3}{7}\right)+7\left(\frac{19}{4}-\frac{2}{4}\right)$$

Since $\frac{21}{7}$ and $\frac{3}{7}$ have the same denominator, add them by adding their numerators.

$$\frac{23}{2}+8\times \frac{21+3}{7}+7\left(\frac{19}{4}-\frac{2}{4}\right)$$

Add $21$ and $3$ to get $24$.

$$\frac{23}{2}+8\times \frac{24}{7}+7\left(\frac{19}{4}-\frac{2}{4}\right)$$

Express $8\times \frac{24}{7}$ as a single fraction.

$$\frac{23}{2}+\frac{8\times 24}{7}+7\left(\frac{19}{4}-\frac{2}{4}\right)$$

Multiply $8$ and $24$ to get $192$.

$$\frac{23}{2}+\frac{192}{7}+7\left(\frac{19}{4}-\frac{2}{4}\right)$$

Least common multiple of $2$ and $7$ is $14$. Convert $\frac{23}{2}$ and $\frac{192}{7}$ to fractions with denominator $14$.

$$\frac{161}{14}+\frac{384}{14}+7\left(\frac{19}{4}-\frac{2}{4}\right)$$

Since $\frac{161}{14}$ and $\frac{384}{14}$ have the same denominator, add them by adding their numerators.

$$\frac{161+384}{14}+7\left(\frac{19}{4}-\frac{2}{4}\right)$$

Add $161$ and $384$ to get $545$.

$$\frac{545}{14}+7\left(\frac{19}{4}-\frac{2}{4}\right)$$

Since $\frac{19}{4}$ and $\frac{2}{4}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{545}{14}+7\times \frac{19-2}{4}$$

Subtract $2$ from $19$ to get $17$.

$$\frac{545}{14}+7\times \frac{17}{4}$$

Express $7\times \frac{17}{4}$ as a single fraction.

$$\frac{545}{14}+\frac{7\times 17}{4}$$

Multiply $7$ and $17$ to get $119$.

$$\frac{545}{14}+\frac{119}{4}$$

Least common multiple of $14$ and $4$ is $28$. Convert $\frac{545}{14}$ and $\frac{119}{4}$ to fractions with denominator $28$.

$$\frac{1090}{28}+\frac{833}{28}$$

Since $\frac{1090}{28}$ and $\frac{833}{28}$ have the same denominator, add them by adding their numerators.

$$\frac{1090+833}{28}$$

Add $1090$ and $833$ to get $1923$.

$$\frac{1923}{28}$$

Factor

$\frac{3 \cdot 641}{2 ^ {2} \cdot 7} = 68\frac{19}{28} = 68.67857142857143$