Solve (35/8-3/4)div(11/8-1/4)

$$(3 \frac{ 5 }{ 8 } - \frac{ 3 }{ 4 } ) \div (1 \frac{ 1 }{ 8 } - \frac{ 1 }{ 4 } )$$

Evaluate

$$\frac{23}{7}\approx 3.285714286$$

Solution Steps

Multiply 3 and 8 to get 24.

$$\frac{\frac{24+5}{8}-\frac{3}{4}}{\frac{1\times 8+1}{8}-\frac{1}{4}}$$

Add 24 and 5 to get 29.

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

Least common multiple of 8 and 4 is 8. Convert \frac{29}{8} and \frac{3}{4} to fractions with denominator 8.

$$\frac{\frac{29}{8}-\frac{6}{8}}{\frac{1\times 8+1}{8}-\frac{1}{4}}$$

Since \frac{29}{8} and \frac{6}{8} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{29-6}{8}}{\frac{1\times 8+1}{8}-\frac{1}{4}}$$

Subtract 6 from 29 to get 23.

$$\frac{\frac{23}{8}}{\frac{1\times 8+1}{8}-\frac{1}{4}}$$

Multiply 1 and 8 to get 8.

$$\frac{\frac{23}{8}}{\frac{8+1}{8}-\frac{1}{4}}$$

Add 8 and 1 to get 9.

$$\frac{\frac{23}{8}}{\frac{9}{8}-\frac{1}{4}}$$

Least common multiple of 8 and 4 is 8. Convert \frac{9}{8} and \frac{1}{4} to fractions with denominator 8.

$$\frac{\frac{23}{8}}{\frac{9}{8}-\frac{2}{8}}$$

Since \frac{9}{8} and \frac{2}{8} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{23}{8}}{\frac{9-2}{8}}$$

Subtract 2 from 9 to get 7.

$$\frac{\frac{23}{8}}{\frac{7}{8}}$$

Divide \frac{23}{8} by \frac{7}{8} by multiplying \frac{23}{8} by the reciprocal of \frac{7}{8}.

$$\frac{23}{8}\times \frac{8}{7}$$

Multiply \frac{23}{8} times \frac{8}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{23\times 8}{8\times 7}$$

Cancel out 8 in both numerator and denominator.

$$\frac{23}{7}$$

Factor

$$\frac{23}{7} = 3\frac{2}{7} = 3.2857142857142856$$