Solve 54/7:7+15/4*2/9-11/4=

$$\frac { 54 } { 7 } : 7 + \frac { 15 } { 4 } \cdot \frac { 2 } { 9 } - 1 \frac { 1 } { 4 } =$$

Evaluate

$$\frac{403}{588}\approx 0.68537415$$

Solution Steps

Express \frac{\frac{54}{7}}{7} as a single fraction.

$$\frac{54}{7\times 7}+\frac{15}{4}\times \frac{2}{9}-\frac{1\times 4+1}{4}$$

Multiply 7 and 7 to get 49.

$$\frac{54}{49}+\frac{15}{4}\times \frac{2}{9}-\frac{1\times 4+1}{4}$$

Multiply \frac{15}{4} times \frac{2}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{54}{49}+\frac{15\times 2}{4\times 9}-\frac{1\times 4+1}{4}$$

Do the multiplications in the fraction \frac{15\times 2}{4\times 9}.

$$\frac{54}{49}+\frac{30}{36}-\frac{1\times 4+1}{4}$$

Reduce the fraction \frac{30}{36} to lowest terms by extracting and canceling out 6.

$$\frac{54}{49}+\frac{5}{6}-\frac{1\times 4+1}{4}$$

Least common multiple of 49 and 6 is 294. Convert \frac{54}{49} and \frac{5}{6} to fractions with denominator 294.

$$\frac{324}{294}+\frac{245}{294}-\frac{1\times 4+1}{4}$$

Since \frac{324}{294} and \frac{245}{294} have the same denominator, add them by adding their numerators.

$$\frac{324+245}{294}-\frac{1\times 4+1}{4}$$

Add 324 and 245 to get 569.

$$\frac{569}{294}-\frac{1\times 4+1}{4}$$

Multiply 1 and 4 to get 4.

$$\frac{569}{294}-\frac{4+1}{4}$$

Add 4 and 1 to get 5.

$$\frac{569}{294}-\frac{5}{4}$$

Least common multiple of 294 and 4 is 588. Convert \frac{569}{294} and \frac{5}{4} to fractions with denominator 588.

$$\frac{1138}{588}-\frac{735}{588}$$

Since \frac{1138}{588} and \frac{735}{588} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1138-735}{588}$$

Subtract 735 from 1138 to get 403.

$$\frac{403}{588}$$

Factor

$$\frac{13 \cdot 31}{2 ^ {2} \cdot 3 \cdot 7 ^ {2}} = 0.685374149659864$$