Solve 219/4-1/18+61/72-1/364

$$2 \frac { 19 } { 4 } - \frac { 1 } { 18 } + \frac { 61 } { 72 } - \frac { 1 } { 36 } 4$$

Evaluate

$$\frac{535}{72}\approx 7.430555556$$

Solution Steps

Multiply 2 and 4 to get 8.

$$\frac{8+19}{4}-\frac{1}{18}+\frac{61}{72}-\frac{1}{36}\times 4$$

Add 8 and 19 to get 27.

$$\frac{27}{4}-\frac{1}{18}+\frac{61}{72}-\frac{1}{36}\times 4$$

Least common multiple of 4 and 18 is 36. Convert \frac{27}{4} and \frac{1}{18} to fractions with denominator 36.

$$\frac{243}{36}-\frac{2}{36}+\frac{61}{72}-\frac{1}{36}\times 4$$

Since \frac{243}{36} and \frac{2}{36} have the same denominator, subtract them by subtracting their numerators.

$$\frac{243-2}{36}+\frac{61}{72}-\frac{1}{36}\times 4$$

Subtract 2 from 243 to get 241.

$$\frac{241}{36}+\frac{61}{72}-\frac{1}{36}\times 4$$

Least common multiple of 36 and 72 is 72. Convert \frac{241}{36} and \frac{61}{72} to fractions with denominator 72.

$$\frac{482}{72}+\frac{61}{72}-\frac{1}{36}\times 4$$

Since \frac{482}{72} and \frac{61}{72} have the same denominator, add them by adding their numerators.

$$\frac{482+61}{72}-\frac{1}{36}\times 4$$

Add 482 and 61 to get 543.

$$\frac{543}{72}-\frac{1}{36}\times 4$$

Reduce the fraction \frac{543}{72} to lowest terms by extracting and canceling out 3.

$$\frac{181}{24}-\frac{1}{36}\times 4$$

Multiply \frac{1}{36} and 4 to get \frac{4}{36}.

$$\frac{181}{24}-\frac{4}{36}$$

Reduce the fraction \frac{4}{36} to lowest terms by extracting and canceling out 4.

$$\frac{181}{24}-\frac{1}{9}$$

Least common multiple of 24 and 9 is 72. Convert \frac{181}{24} and \frac{1}{9} to fractions with denominator 72.

$$\frac{543}{72}-\frac{8}{72}$$

Since \frac{543}{72} and \frac{8}{72} have the same denominator, subtract them by subtracting their numerators.

$$\frac{543-8}{72}$$

Subtract 8 from 543 to get 535.

$$\frac{535}{72}$$

Factor

$$\frac{5 \cdot 107}{2 ^ {3} \cdot 3 ^ {2}} = 7\frac{31}{72} = 7.430555555555555$$