Solve valuate the fc (2 7/8 * 1 1/5 / (3/40))/(3 + (- 2 1/4) / (1 1/2)) | 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

$$\left. \begin{array} { l } { \frac { 2 \frac { 7 } { 8 } \times 1 \frac { 1 } { 5 } \div \frac { 3 } { 40 } } { 3 - 2 \frac { 1 } { 4 } \div 1 \frac { 1 } { 2 } } } \end{array} \right.$$

Evaluate

$\frac{92}{3}\approx 30.666666667$

Solution Steps

Multiply $2$ and $8$ to get $16$.

$$\frac{\frac{\frac{16+7}{8}\times \frac{1\times 5+1}{5}}{\frac{3}{40}}}{3-\frac{\frac{2\times 4+1}{4}}{\frac{1\times 2+1}{2}}}$$

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

$$\frac{\frac{\frac{23}{8}\times \frac{1\times 5+1}{5}}{\frac{3}{40}}}{3-\frac{\frac{2\times 4+1}{4}}{\frac{1\times 2+1}{2}}}$$

Multiply $1$ and $5$ to get $5$.

$$\frac{\frac{\frac{23}{8}\times \frac{5+1}{5}}{\frac{3}{40}}}{3-\frac{\frac{2\times 4+1}{4}}{\frac{1\times 2+1}{2}}}$$

Add $5$ and $1$ to get $6$.

$$\frac{\frac{\frac{23}{8}\times \frac{6}{5}}{\frac{3}{40}}}{3-\frac{\frac{2\times 4+1}{4}}{\frac{1\times 2+1}{2}}}$$

Multiply $\frac{23}{8}$ times $\frac{6}{5}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{\frac{23\times 6}{8\times 5}}{\frac{3}{40}}}{3-\frac{\frac{2\times 4+1}{4}}{\frac{1\times 2+1}{2}}}$$

Do the multiplications in the fraction $\frac{23\times 6}{8\times 5}$.

$$\frac{\frac{\frac{138}{40}}{\frac{3}{40}}}{3-\frac{\frac{2\times 4+1}{4}}{\frac{1\times 2+1}{2}}}$$

Reduce the fraction $\frac{138}{40}$ to lowest terms by extracting and canceling out $2$.

$$\frac{\frac{\frac{69}{20}}{\frac{3}{40}}}{3-\frac{\frac{2\times 4+1}{4}}{\frac{1\times 2+1}{2}}}$$

Divide $\frac{69}{20}$ by $\frac{3}{40}$ by multiplying $\frac{69}{20}$ by the reciprocal of $\frac{3}{40}$.

$$\frac{\frac{69}{20}\times \frac{40}{3}}{3-\frac{\frac{2\times 4+1}{4}}{\frac{1\times 2+1}{2}}}$$

Multiply $\frac{69}{20}$ times $\frac{40}{3}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{69\times 40}{20\times 3}}{3-\frac{\frac{2\times 4+1}{4}}{\frac{1\times 2+1}{2}}}$$

Do the multiplications in the fraction $\frac{69\times 40}{20\times 3}$.

$$\frac{\frac{2760}{60}}{3-\frac{\frac{2\times 4+1}{4}}{\frac{1\times 2+1}{2}}}$$

Divide $2760$ by $60$ to get $46$.

$$\frac{46}{3-\frac{\frac{2\times 4+1}{4}}{\frac{1\times 2+1}{2}}}$$

Divide $\frac{2\times 4+1}{4}$ by $\frac{1\times 2+1}{2}$ by multiplying $\frac{2\times 4+1}{4}$ by the reciprocal of $\frac{1\times 2+1}{2}$.

$$\frac{46}{3-\frac{\left(2\times 4+1\right)\times 2}{4\left(1\times 2+1\right)}}$$

Cancel out $2$ in both numerator and denominator.

$$\frac{46}{3-\frac{1+2\times 4}{2\left(1+2\right)}}$$

Multiply $2$ and $4$ to get $8$.

$$\frac{46}{3-\frac{1+8}{2\left(1+2\right)}}$$

Add $1$ and $8$ to get $9$.

$$\frac{46}{3-\frac{9}{2\left(1+2\right)}}$$

Add $1$ and $2$ to get $3$.

$$\frac{46}{3-\frac{9}{2\times 3}}$$

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

$$\frac{46}{3-\frac{9}{6}}$$

Reduce the fraction $\frac{9}{6}$ to lowest terms by extracting and canceling out $3$.

$$\frac{46}{3-\frac{3}{2}}$$

Convert $3$ to fraction $\frac{6}{2}$.

$$\frac{46}{\frac{6}{2}-\frac{3}{2}}$$

Since $\frac{6}{2}$ and $\frac{3}{2}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{46}{\frac{6-3}{2}}$$

Subtract $3$ from $6$ to get $3$.

$$\frac{46}{\frac{3}{2}}$$

Divide $46$ by $\frac{3}{2}$ by multiplying $46$ by the reciprocal of $\frac{3}{2}$.

$$46\times \frac{2}{3}$$

Express $46\times \frac{2}{3}$ as a single fraction.

$$\frac{46\times 2}{3}$$

Multiply $46$ and $2$ to get $92$.

$$\frac{92}{3}$$

Factor

$\frac{2 ^ {2} \cdot 23}{3} = 30\frac{2}{3} = 30.666666666666668$