Solve 31/4-(1-9/224)*21/3

$$3 \frac { 1 } { 4 } - ( 1 - \frac { 9 } { 224 } ) \times 2 \frac { 1 } { 3 }$$

Evaluate

$$\frac{97}{96}\approx 1.010416667$$

Solution Steps

Multiply 3 and 4 to get 12.

$$\frac{12+1}{4}-\left(1-\frac{9}{224}\right)\times \frac{2\times 3+1}{3}$$

Add 12 and 1 to get 13.

$$\frac{13}{4}-\left(1-\frac{9}{224}\right)\times \frac{2\times 3+1}{3}$$

Convert 1 to fraction \frac{224}{224}.

$$\frac{13}{4}-\left(\frac{224}{224}-\frac{9}{224}\right)\times \frac{2\times 3+1}{3}$$

Since \frac{224}{224} and \frac{9}{224} have the same denominator, subtract them by subtracting their numerators.

$$\frac{13}{4}-\frac{224-9}{224}\times \frac{2\times 3+1}{3}$$

Subtract 9 from 224 to get 215.

$$\frac{13}{4}-\frac{215}{224}\times \frac{2\times 3+1}{3}$$

Multiply 2 and 3 to get 6.

$$\frac{13}{4}-\frac{215}{224}\times \frac{6+1}{3}$$

Add 6 and 1 to get 7.

$$\frac{13}{4}-\frac{215}{224}\times \frac{7}{3}$$

Multiply \frac{215}{224} times \frac{7}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{13}{4}-\frac{215\times 7}{224\times 3}$$

Do the multiplications in the fraction \frac{215\times 7}{224\times 3}.

$$\frac{13}{4}-\frac{1505}{672}$$

Reduce the fraction \frac{1505}{672} to lowest terms by extracting and canceling out 7.

$$\frac{13}{4}-\frac{215}{96}$$

Least common multiple of 4 and 96 is 96. Convert \frac{13}{4} and \frac{215}{96} to fractions with denominator 96.

$$\frac{312}{96}-\frac{215}{96}$$

Since \frac{312}{96} and \frac{215}{96} have the same denominator, subtract them by subtracting their numerators.

$$\frac{312-215}{96}$$

Subtract 215 from 312 to get 97.

$$\frac{97}{96}$$

Factor

$$\frac{97}{2 ^ {5} \cdot 3} = 1\frac{1}{96} = 1.0104166666666667$$