Solve σ No. 5. Evaluate (3/4 + 1 5/7 + 4/7 * of * 2 1/3)/((1 3/7 - 5/8) * 2/3) th | 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

$$\frac { \frac { 3 } { 4 } + 1 \frac { 5 } { 7 } \div \frac { 4 } { 7 } 2 \frac { 1 } { 3 } } { ( 1 \frac { 3 } { 7 } - \frac { 5 } { 8 } ) \times \frac { 2 } { 3 } }$$

Evaluate

$\frac{217}{15}\approx 14.466666667$

Solution Steps

Divide $\frac{1\times 7+5}{7}$ by $\frac{4}{7}$ by multiplying $\frac{1\times 7+5}{7}$ by the reciprocal of $\frac{4}{7}$.

$$\frac{\frac{3}{4}+\frac{\left(1\times 7+5\right)\times 7}{7\times 4}\times \frac{2\times 3+1}{3}}{\left(\frac{1\times 7+3}{7}-\frac{5}{8}\right)\times \frac{2}{3}}$$

Cancel out $7$ in both numerator and denominator.

$$\frac{\frac{3}{4}+\frac{5+7}{4}\times \frac{2\times 3+1}{3}}{\left(\frac{1\times 7+3}{7}-\frac{5}{8}\right)\times \frac{2}{3}}$$

Add $5$ and $7$ to get $12$.

$$\frac{\frac{3}{4}+\frac{12}{4}\times \frac{2\times 3+1}{3}}{\left(\frac{1\times 7+3}{7}-\frac{5}{8}\right)\times \frac{2}{3}}$$

Divide $12$ by $4$ to get $3$.

$$\frac{\frac{3}{4}+3\times \frac{2\times 3+1}{3}}{\left(\frac{1\times 7+3}{7}-\frac{5}{8}\right)\times \frac{2}{3}}$$

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

$$\frac{\frac{3}{4}+3\times \frac{6+1}{3}}{\left(\frac{1\times 7+3}{7}-\frac{5}{8}\right)\times \frac{2}{3}}$$

Add $6$ and $1$ to get $7$.

$$\frac{\frac{3}{4}+3\times \frac{7}{3}}{\left(\frac{1\times 7+3}{7}-\frac{5}{8}\right)\times \frac{2}{3}}$$

Cancel out $3$ and $3$.

$$\frac{\frac{3}{4}+7}{\left(\frac{1\times 7+3}{7}-\frac{5}{8}\right)\times \frac{2}{3}}$$

Convert $7$ to fraction $\frac{28}{4}$.

$$\frac{\frac{3}{4}+\frac{28}{4}}{\left(\frac{1\times 7+3}{7}-\frac{5}{8}\right)\times \frac{2}{3}}$$

Since $\frac{3}{4}$ and $\frac{28}{4}$ have the same denominator, add them by adding their numerators.

$$\frac{\frac{3+28}{4}}{\left(\frac{1\times 7+3}{7}-\frac{5}{8}\right)\times \frac{2}{3}}$$

Add $3$ and $28$ to get $31$.

$$\frac{\frac{31}{4}}{\left(\frac{1\times 7+3}{7}-\frac{5}{8}\right)\times \frac{2}{3}}$$

Multiply $1$ and $7$ to get $7$.

$$\frac{\frac{31}{4}}{\left(\frac{7+3}{7}-\frac{5}{8}\right)\times \frac{2}{3}}$$

Add $7$ and $3$ to get $10$.

$$\frac{\frac{31}{4}}{\left(\frac{10}{7}-\frac{5}{8}\right)\times \frac{2}{3}}$$

Least common multiple of $7$ and $8$ is $56$. Convert $\frac{10}{7}$ and $\frac{5}{8}$ to fractions with denominator $56$.

$$\frac{\frac{31}{4}}{\left(\frac{80}{56}-\frac{35}{56}\right)\times \frac{2}{3}}$$

Since $\frac{80}{56}$ and $\frac{35}{56}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{31}{4}}{\frac{80-35}{56}\times \frac{2}{3}}$$

Subtract $35$ from $80$ to get $45$.

$$\frac{\frac{31}{4}}{\frac{45}{56}\times \frac{2}{3}}$$

Multiply $\frac{45}{56}$ times $\frac{2}{3}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{31}{4}}{\frac{45\times 2}{56\times 3}}$$

Do the multiplications in the fraction $\frac{45\times 2}{56\times 3}$.

$$\frac{\frac{31}{4}}{\frac{90}{168}}$$

Reduce the fraction $\frac{90}{168}$ to lowest terms by extracting and canceling out $6$.

$$\frac{\frac{31}{4}}{\frac{15}{28}}$$

Divide $\frac{31}{4}$ by $\frac{15}{28}$ by multiplying $\frac{31}{4}$ by the reciprocal of $\frac{15}{28}$.

$$\frac{31}{4}\times \frac{28}{15}$$

Multiply $\frac{31}{4}$ times $\frac{28}{15}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{31\times 28}{4\times 15}$$

Do the multiplications in the fraction $\frac{31\times 28}{4\times 15}$.

$$\frac{868}{60}$$

Reduce the fraction $\frac{868}{60}$ to lowest terms by extracting and canceling out $4$.

$$\frac{217}{15}$$

Factor

$\frac{7 \cdot 31}{3 \cdot 5} = 14\frac{7}{15} = 14.466666666666667$