Solve 7 1/2 - [(2 1/4) / \{1 1/4 - 1/2 * (3/2 - 1/3 - 1/6)\}]

Question

$$7\frac{1}{2}-[2\frac{1}{4}\div\{1\frac{1}{4}-\frac{1}{2}(\frac{3}{2}-\frac{1}{3}-\frac{1}{6})\}]$$

Evaluate

$\frac{9}{2}=4.5$

Solution Steps

Multiply $7$ and $2$ to get $14$.

$$\frac{14+1}{2}-\frac{\frac{2\times 4+1}{4}}{\frac{1\times 4+1}{4}-\frac{1}{2}\left(\frac{3}{2}-\frac{1}{3}-\frac{1}{6}\right)}$$

Add $14$ and $1$ to get $15$.

$$\frac{15}{2}-\frac{\frac{2\times 4+1}{4}}{\frac{1\times 4+1}{4}-\frac{1}{2}\left(\frac{3}{2}-\frac{1}{3}-\frac{1}{6}\right)}$$

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

$$\frac{15}{2}-\frac{\frac{8+1}{4}}{\frac{1\times 4+1}{4}-\frac{1}{2}\left(\frac{3}{2}-\frac{1}{3}-\frac{1}{6}\right)}$$

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

$$\frac{15}{2}-\frac{\frac{9}{4}}{\frac{1\times 4+1}{4}-\frac{1}{2}\left(\frac{3}{2}-\frac{1}{3}-\frac{1}{6}\right)}$$

Multiply $1$ and $4$ to get $4$.

$$\frac{15}{2}-\frac{\frac{9}{4}}{\frac{4+1}{4}-\frac{1}{2}\left(\frac{3}{2}-\frac{1}{3}-\frac{1}{6}\right)}$$

Add $4$ and $1$ to get $5$.

$$\frac{15}{2}-\frac{\frac{9}{4}}{\frac{5}{4}-\frac{1}{2}\left(\frac{3}{2}-\frac{1}{3}-\frac{1}{6}\right)}$$

Least common multiple of $2$ and $3$ is $6$. Convert $\frac{3}{2}$ and $\frac{1}{3}$ to fractions with denominator $6$.

$$\frac{15}{2}-\frac{\frac{9}{4}}{\frac{5}{4}-\frac{1}{2}\left(\frac{9}{6}-\frac{2}{6}-\frac{1}{6}\right)}$$

Since $\frac{9}{6}$ and $\frac{2}{6}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{15}{2}-\frac{\frac{9}{4}}{\frac{5}{4}-\frac{1}{2}\left(\frac{9-2}{6}-\frac{1}{6}\right)}$$

Subtract $2$ from $9$ to get $7$.

$$\frac{15}{2}-\frac{\frac{9}{4}}{\frac{5}{4}-\frac{1}{2}\left(\frac{7}{6}-\frac{1}{6}\right)}$$

Since $\frac{7}{6}$ and $\frac{1}{6}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{15}{2}-\frac{\frac{9}{4}}{\frac{5}{4}-\frac{1}{2}\times \frac{7-1}{6}}$$

Subtract $1$ from $7$ to get $6$.

$$\frac{15}{2}-\frac{\frac{9}{4}}{\frac{5}{4}-\frac{1}{2}\times \frac{6}{6}}$$

Divide $6$ by $6$ to get $1$.

$$\frac{15}{2}-\frac{\frac{9}{4}}{\frac{5}{4}-\frac{1}{2}\times 1}$$

Multiply $\frac{1}{2}$ and $1$ to get $\frac{1}{2}$.

$$\frac{15}{2}-\frac{\frac{9}{4}}{\frac{5}{4}-\frac{1}{2}}$$

Least common multiple of $4$ and $2$ is $4$. Convert $\frac{5}{4}$ and $\frac{1}{2}$ to fractions with denominator $4$.

$$\frac{15}{2}-\frac{\frac{9}{4}}{\frac{5}{4}-\frac{2}{4}}$$

Since $\frac{5}{4}$ and $\frac{2}{4}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{15}{2}-\frac{\frac{9}{4}}{\frac{5-2}{4}}$$

Subtract $2$ from $5$ to get $3$.

$$\frac{15}{2}-\frac{\frac{9}{4}}{\frac{3}{4}}$$

Divide $\frac{9}{4}$ by $\frac{3}{4}$ by multiplying $\frac{9}{4}$ by the reciprocal of $\frac{3}{4}$.

$$\frac{15}{2}-\frac{9}{4}\times \frac{4}{3}$$

Multiply $\frac{9}{4}$ times $\frac{4}{3}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{15}{2}-\frac{9\times 4}{4\times 3}$$

Cancel out $4$ in both numerator and denominator.

$$\frac{15}{2}-\frac{9}{3}$$

Divide $9$ by $3$ to get $3$.

$$\frac{15}{2}-3$$

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

$$\frac{15}{2}-\frac{6}{2}$$

Since $\frac{15}{2}$ and $\frac{6}{2}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{15-6}{2}$$

Subtract $6$ from $15$ to get $9$.

$$\frac{9}{2}$$

Show Solution

Factor

$\frac{3 ^ {2}}{2} = 4\frac{1}{2} = 4.5$

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