Solve 7- 1 1 4 2 2 3 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

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

Evaluate

$-\frac{21}{2}=-10.5$

Solution Steps

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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 $-21$.

$$-\frac{21}{2}$$

Factor

$-\frac{21}{2} = -10\frac{1}{2} = -10.5$