Solve a=(43/4-11/8):3/8-1/2:(1frac{1}{4}-frac{3}{4})

$$a = ( 4 \frac { 3 } { 4 } - 1 \frac { 1 } { 8 } ) : \frac { 3 } { 8 } - \frac { 1 } { 2 } : ( 1 \frac { 1 } { 4 } - \frac { 3 } { 4 } )$$

Solve for a

$$a = \frac{26}{3} = 8\frac{2}{3} \approx 8.666666667$$

Steps for Solving Linear Equation

Multiply 4 and 4 to get 16.

$$a=\frac{\frac{16+3}{4}-\frac{1\times 8+1}{8}}{\frac{3}{8}}-\frac{\frac{1}{2}}{\frac{1\times 4+1}{4}-\frac{3}{4}}$$

Add 16 and 3 to get 19.

$$a=\frac{\frac{19}{4}-\frac{1\times 8+1}{8}}{\frac{3}{8}}-\frac{\frac{1}{2}}{\frac{1\times 4+1}{4}-\frac{3}{4}}$$

Multiply 1 and 8 to get 8.

$$a=\frac{\frac{19}{4}-\frac{8+1}{8}}{\frac{3}{8}}-\frac{\frac{1}{2}}{\frac{1\times 4+1}{4}-\frac{3}{4}}$$

Add 8 and 1 to get 9.

$$a=\frac{\frac{19}{4}-\frac{9}{8}}{\frac{3}{8}}-\frac{\frac{1}{2}}{\frac{1\times 4+1}{4}-\frac{3}{4}}$$

Least common multiple of 4 and 8 is 8. Convert \frac{19}{4} and \frac{9}{8} to fractions with denominator 8.

$$a=\frac{\frac{38}{8}-\frac{9}{8}}{\frac{3}{8}}-\frac{\frac{1}{2}}{\frac{1\times 4+1}{4}-\frac{3}{4}}$$

Since \frac{38}{8} and \frac{9}{8} have the same denominator, subtract them by subtracting their numerators.

$$a=\frac{\frac{38-9}{8}}{\frac{3}{8}}-\frac{\frac{1}{2}}{\frac{1\times 4+1}{4}-\frac{3}{4}}$$

Subtract 9 from 38 to get 29.

$$a=\frac{\frac{29}{8}}{\frac{3}{8}}-\frac{\frac{1}{2}}{\frac{1\times 4+1}{4}-\frac{3}{4}}$$

Divide \frac{29}{8} by \frac{3}{8} by multiplying \frac{29}{8} by the reciprocal of \frac{3}{8}.

$$a=\frac{29}{8}\times \frac{8}{3}-\frac{\frac{1}{2}}{\frac{1\times 4+1}{4}-\frac{3}{4}}$$

Multiply \frac{29}{8} times \frac{8}{3} by multiplying numerator times numerator and denominator times denominator.

$$a=\frac{29\times 8}{8\times 3}-\frac{\frac{1}{2}}{\frac{1\times 4+1}{4}-\frac{3}{4}}$$

Cancel out 8 in both numerator and denominator.

$$a=\frac{29}{3}-\frac{\frac{1}{2}}{\frac{1\times 4+1}{4}-\frac{3}{4}}$$

Multiply 1 and 4 to get 4.

$$a=\frac{29}{3}-\frac{\frac{1}{2}}{\frac{4+1}{4}-\frac{3}{4}}$$

Add 4 and 1 to get 5.

$$a=\frac{29}{3}-\frac{\frac{1}{2}}{\frac{5}{4}-\frac{3}{4}}$$

Since \frac{5}{4} and \frac{3}{4} have the same denominator, subtract them by subtracting their numerators.

$$a=\frac{29}{3}-\frac{\frac{1}{2}}{\frac{5-3}{4}}$$

Subtract 3 from 5 to get 2.

$$a=\frac{29}{3}-\frac{\frac{1}{2}}{\frac{2}{4}}$$

Reduce the fraction \frac{2}{4} to lowest terms by extracting and canceling out 2.

$$a=\frac{29}{3}-\frac{\frac{1}{2}}{\frac{1}{2}}$$

Divide \frac{1}{2} by \frac{1}{2} to get 1.

$$a=\frac{29}{3}-1$$

Convert 1 to fraction \frac{3}{3}.

$$a=\frac{29}{3}-\frac{3}{3}$$

Since \frac{29}{3} and \frac{3}{3} have the same denominator, subtract them by subtracting their numerators.

$$a=\frac{29-3}{3}$$

Subtract 3 from 29 to get 26.

$$a=\frac{26}{3}$$

Assign a

$$a≔\frac{26}{3}$$