Solve 2 * x/8 * 1 1/3 / (3/10) (3-24)15 | 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

$$\frac { 2 \frac { 7 } { 8 } \times 1 \frac { 1 } { 3 } \div \frac { 3 } { 10 } } { ( 3 - 2 \frac { 1 } { 4 } ) \div 1 \frac { 1 } { 2 } }$$

Evaluate

$\frac{230}{9}\approx 25.555555556$

Solution Steps

Divide $\frac{\frac{2\times 8+7}{8}\times \frac{1\times 3+1}{3}}{\frac{3}{10}}$ by $\frac{3-\frac{2\times 4+1}{4}}{\frac{1\times 2+1}{2}}$ by multiplying $\frac{\frac{2\times 8+7}{8}\times \frac{1\times 3+1}{3}}{\frac{3}{10}}$ by the reciprocal of $\frac{3-\frac{2\times 4+1}{4}}{\frac{1\times 2+1}{2}}$.

$$\frac{\frac{2\times 8+7}{8}\times \frac{1\times 3+1}{3}\times \frac{1\times 2+1}{2}}{\frac{3}{10}\left(3-\frac{2\times 4+1}{4}\right)}$$

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

$$\frac{\frac{16+7}{8}\times \frac{1\times 3+1}{3}\times \frac{1\times 2+1}{2}}{\frac{3}{10}\left(3-\frac{2\times 4+1}{4}\right)}$$

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

$$\frac{\frac{23}{8}\times \frac{1\times 3+1}{3}\times \frac{1\times 2+1}{2}}{\frac{3}{10}\left(3-\frac{2\times 4+1}{4}\right)}$$

Multiply $1$ and $3$ to get $3$.

$$\frac{\frac{23}{8}\times \frac{3+1}{3}\times \frac{1\times 2+1}{2}}{\frac{3}{10}\left(3-\frac{2\times 4+1}{4}\right)}$$

Add $3$ and $1$ to get $4$.

$$\frac{\frac{23}{8}\times \frac{4}{3}\times \frac{1\times 2+1}{2}}{\frac{3}{10}\left(3-\frac{2\times 4+1}{4}\right)}$$

Multiply $\frac{23}{8}$ times $\frac{4}{3}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{23\times 4}{8\times 3}\times \frac{1\times 2+1}{2}}{\frac{3}{10}\left(3-\frac{2\times 4+1}{4}\right)}$$

Do the multiplications in the fraction $\frac{23\times 4}{8\times 3}$.

$$\frac{\frac{92}{24}\times \frac{1\times 2+1}{2}}{\frac{3}{10}\left(3-\frac{2\times 4+1}{4}\right)}$$

Reduce the fraction $\frac{92}{24}$ to lowest terms by extracting and canceling out $4$.

$$\frac{\frac{23}{6}\times \frac{1\times 2+1}{2}}{\frac{3}{10}\left(3-\frac{2\times 4+1}{4}\right)}$$

Multiply $1$ and $2$ to get $2$.

$$\frac{\frac{23}{6}\times \frac{2+1}{2}}{\frac{3}{10}\left(3-\frac{2\times 4+1}{4}\right)}$$

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

$$\frac{\frac{23}{6}\times \frac{3}{2}}{\frac{3}{10}\left(3-\frac{2\times 4+1}{4}\right)}$$

Multiply $\frac{23}{6}$ times $\frac{3}{2}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{23\times 3}{6\times 2}}{\frac{3}{10}\left(3-\frac{2\times 4+1}{4}\right)}$$

Do the multiplications in the fraction $\frac{23\times 3}{6\times 2}$.

$$\frac{\frac{69}{12}}{\frac{3}{10}\left(3-\frac{2\times 4+1}{4}\right)}$$

Reduce the fraction $\frac{69}{12}$ to lowest terms by extracting and canceling out $3$.

$$\frac{\frac{23}{4}}{\frac{3}{10}\left(3-\frac{2\times 4+1}{4}\right)}$$

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

$$\frac{\frac{23}{4}}{\frac{3}{10}\left(3-\frac{8+1}{4}\right)}$$

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

$$\frac{\frac{23}{4}}{\frac{3}{10}\left(3-\frac{9}{4}\right)}$$

Convert $3$ to fraction $\frac{12}{4}$.

$$\frac{\frac{23}{4}}{\frac{3}{10}\left(\frac{12}{4}-\frac{9}{4}\right)}$$

Since $\frac{12}{4}$ and $\frac{9}{4}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{23}{4}}{\frac{3}{10}\times \frac{12-9}{4}}$$

Subtract $9$ from $12$ to get $3$.

$$\frac{\frac{23}{4}}{\frac{3}{10}\times \frac{3}{4}}$$

Multiply $\frac{3}{10}$ times $\frac{3}{4}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{23}{4}}{\frac{3\times 3}{10\times 4}}$$

Do the multiplications in the fraction $\frac{3\times 3}{10\times 4}$.

$$\frac{\frac{23}{4}}{\frac{9}{40}}$$

Divide $\frac{23}{4}$ by $\frac{9}{40}$ by multiplying $\frac{23}{4}$ by the reciprocal of $\frac{9}{40}$.

$$\frac{23}{4}\times \frac{40}{9}$$

Multiply $\frac{23}{4}$ times $\frac{40}{9}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{23\times 40}{4\times 9}$$

Do the multiplications in the fraction $\frac{23\times 40}{4\times 9}$.

$$\frac{920}{36}$$

Reduce the fraction $\frac{920}{36}$ to lowest terms by extracting and canceling out $4$.

$$\frac{230}{9}$$

Factor

$\frac{2 \cdot 5 \cdot 23}{3 ^ {2}} = 25\frac{5}{9} = 25.555555555555557$