Solve Determine the value of the following : ) (4 4/7 + 3 2/5)/(5 1/3 - 1 7/6) | 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

$$\left. \begin{array} { l } { \quad \frac { 4 \frac { 4 } { 7 } + 3 \frac { 2 } { 5 } } { 5 \frac { 2 } { 3 } - 1 \frac { 7 } { 6 } } } \end{array} \right.$$

Evaluate

$\frac{558}{245}\approx 2.27755102$

Solution Steps

Multiply $4$ and $7$ to get $28$.

$$\frac{\frac{28+4}{7}+\frac{3\times 5+2}{5}}{\frac{5\times 3+2}{3}-\frac{1\times 6+7}{6}}$$

Add $28$ and $4$ to get $32$.

$$\frac{\frac{32}{7}+\frac{3\times 5+2}{5}}{\frac{5\times 3+2}{3}-\frac{1\times 6+7}{6}}$$

Multiply $3$ and $5$ to get $15$.

$$\frac{\frac{32}{7}+\frac{15+2}{5}}{\frac{5\times 3+2}{3}-\frac{1\times 6+7}{6}}$$

Add $15$ and $2$ to get $17$.

$$\frac{\frac{32}{7}+\frac{17}{5}}{\frac{5\times 3+2}{3}-\frac{1\times 6+7}{6}}$$

Least common multiple of $7$ and $5$ is $35$. Convert $\frac{32}{7}$ and $\frac{17}{5}$ to fractions with denominator $35$.

$$\frac{\frac{160}{35}+\frac{119}{35}}{\frac{5\times 3+2}{3}-\frac{1\times 6+7}{6}}$$

Since $\frac{160}{35}$ and $\frac{119}{35}$ have the same denominator, add them by adding their numerators.

$$\frac{\frac{160+119}{35}}{\frac{5\times 3+2}{3}-\frac{1\times 6+7}{6}}$$

Add $160$ and $119$ to get $279$.

$$\frac{\frac{279}{35}}{\frac{5\times 3+2}{3}-\frac{1\times 6+7}{6}}$$

Multiply $5$ and $3$ to get $15$.

$$\frac{\frac{279}{35}}{\frac{15+2}{3}-\frac{1\times 6+7}{6}}$$

Add $15$ and $2$ to get $17$.

$$\frac{\frac{279}{35}}{\frac{17}{3}-\frac{1\times 6+7}{6}}$$

Multiply $1$ and $6$ to get $6$.

$$\frac{\frac{279}{35}}{\frac{17}{3}-\frac{6+7}{6}}$$

Add $6$ and $7$ to get $13$.

$$\frac{\frac{279}{35}}{\frac{17}{3}-\frac{13}{6}}$$

Least common multiple of $3$ and $6$ is $6$. Convert $\frac{17}{3}$ and $\frac{13}{6}$ to fractions with denominator $6$.

$$\frac{\frac{279}{35}}{\frac{34}{6}-\frac{13}{6}}$$

Since $\frac{34}{6}$ and $\frac{13}{6}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{279}{35}}{\frac{34-13}{6}}$$

Subtract $13$ from $34$ to get $21$.

$$\frac{\frac{279}{35}}{\frac{21}{6}}$$

Reduce the fraction $\frac{21}{6}$ to lowest terms by extracting and canceling out $3$.

$$\frac{\frac{279}{35}}{\frac{7}{2}}$$

Divide $\frac{279}{35}$ by $\frac{7}{2}$ by multiplying $\frac{279}{35}$ by the reciprocal of $\frac{7}{2}$.

$$\frac{279}{35}\times \frac{2}{7}$$

Multiply $\frac{279}{35}$ times $\frac{2}{7}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{279\times 2}{35\times 7}$$

Do the multiplications in the fraction $\frac{279\times 2}{35\times 7}$.

$$\frac{558}{245}$$

Factor

$\frac{2 \cdot 3 ^ {2} \cdot 31}{5 \cdot 7 ^ {2}} = 2\frac{68}{245} = 2.2775510204081635$