Solve (7 1/3) / (2/3); 2 1/5 + (1 3/8) / (2 3/4) - 1 1/2 of | 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

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

Evaluate

$\frac{116}{5}=23.2$

Solution Steps

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

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

Cancel out $3$ in both numerator and denominator.

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

Multiply $3$ and $7$ to get $21$.

$$\frac{1+21}{2}\times \frac{2\times 5+1}{5}+\frac{\frac{1\times 8+3}{8}}{\frac{2\times 4+3}{4}}-\frac{1\times 2+1}{2}$$

Add $1$ and $21$ to get $22$.

$$\frac{22}{2}\times \frac{2\times 5+1}{5}+\frac{\frac{1\times 8+3}{8}}{\frac{2\times 4+3}{4}}-\frac{1\times 2+1}{2}$$

Divide $22$ by $2$ to get $11$.

$$11\times \frac{2\times 5+1}{5}+\frac{\frac{1\times 8+3}{8}}{\frac{2\times 4+3}{4}}-\frac{1\times 2+1}{2}$$

Multiply $2$ and $5$ to get $10$.

$$11\times \frac{10+1}{5}+\frac{\frac{1\times 8+3}{8}}{\frac{2\times 4+3}{4}}-\frac{1\times 2+1}{2}$$

Add $10$ and $1$ to get $11$.

$$11\times \frac{11}{5}+\frac{\frac{1\times 8+3}{8}}{\frac{2\times 4+3}{4}}-\frac{1\times 2+1}{2}$$

Express $11\times \frac{11}{5}$ as a single fraction.

$$\frac{11\times 11}{5}+\frac{\frac{1\times 8+3}{8}}{\frac{2\times 4+3}{4}}-\frac{1\times 2+1}{2}$$

Multiply $11$ and $11$ to get $121$.

$$\frac{121}{5}+\frac{\frac{1\times 8+3}{8}}{\frac{2\times 4+3}{4}}-\frac{1\times 2+1}{2}$$

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

$$\frac{121}{5}+\frac{\left(1\times 8+3\right)\times 4}{8\left(2\times 4+3\right)}-\frac{1\times 2+1}{2}$$

Cancel out $4$ in both numerator and denominator.

$$\frac{121}{5}+\frac{3+8}{2\left(3+2\times 4\right)}-\frac{1\times 2+1}{2}$$

Add $3$ and $8$ to get $11$.

$$\frac{121}{5}+\frac{11}{2\left(3+2\times 4\right)}-\frac{1\times 2+1}{2}$$

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

$$\frac{121}{5}+\frac{11}{2\left(3+8\right)}-\frac{1\times 2+1}{2}$$

Add $3$ and $8$ to get $11$.

$$\frac{121}{5}+\frac{11}{2\times 11}-\frac{1\times 2+1}{2}$$

Multiply $2$ and $11$ to get $22$.

$$\frac{121}{5}+\frac{11}{22}-\frac{1\times 2+1}{2}$$

Reduce the fraction $\frac{11}{22}$ to lowest terms by extracting and canceling out $11$.

$$\frac{121}{5}+\frac{1}{2}-\frac{1\times 2+1}{2}$$

Least common multiple of $5$ and $2$ is $10$. Convert $\frac{121}{5}$ and $\frac{1}{2}$ to fractions with denominator $10$.

$$\frac{242}{10}+\frac{5}{10}-\frac{1\times 2+1}{2}$$

Since $\frac{242}{10}$ and $\frac{5}{10}$ have the same denominator, add them by adding their numerators.

$$\frac{242+5}{10}-\frac{1\times 2+1}{2}$$

Add $242$ and $5$ to get $247$.

$$\frac{247}{10}-\frac{1\times 2+1}{2}$$

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

$$\frac{247}{10}-\frac{2+1}{2}$$

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

$$\frac{247}{10}-\frac{3}{2}$$

Least common multiple of $10$ and $2$ is $10$. Convert $\frac{247}{10}$ and $\frac{3}{2}$ to fractions with denominator $10$.

$$\frac{247}{10}-\frac{15}{10}$$

Since $\frac{247}{10}$ and $\frac{15}{10}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{247-15}{10}$$

Subtract $15$ from $247$ to get $232$.

$$\frac{232}{10}$$

Reduce the fraction $\frac{232}{10}$ to lowest terms by extracting and canceling out $2$.

$$\frac{116}{5}$$

Factor

$\frac{2 ^ {2} \cdot 29}{5} = 23\frac{1}{5} = 23.2$