Solve 1010/37-20/73-321/73-532/73+3frac{27}{37}=

$$10 \frac { 10 } { 37 } - \frac { 20 } { 73 } - 3 \frac { 21 } { 73 } - 5 \frac { 32 } { 73 } + 3 \frac { 27 } { 37 } =$$

Evaluate

$$5$$

Solution Steps

Multiply 10 and 37 to get 370.

$$\frac{370+10}{37}-\frac{20}{73}-\frac{3\times 73+21}{73}-\frac{5\times 73+32}{73}+\frac{3\times 37+27}{37}$$

Add 370 and 10 to get 380.

$$\frac{380}{37}-\frac{20}{73}-\frac{3\times 73+21}{73}-\frac{5\times 73+32}{73}+\frac{3\times 37+27}{37}$$

Least common multiple of 37 and 73 is 2701. Convert \frac{380}{37} and \frac{20}{73} to fractions with denominator 2701.

$$\frac{27740}{2701}-\frac{740}{2701}-\frac{3\times 73+21}{73}-\frac{5\times 73+32}{73}+\frac{3\times 37+27}{37}$$

Since \frac{27740}{2701} and \frac{740}{2701} have the same denominator, subtract them by subtracting their numerators.

$$\frac{27740-740}{2701}-\frac{3\times 73+21}{73}-\frac{5\times 73+32}{73}+\frac{3\times 37+27}{37}$$

Subtract 740 from 27740 to get 27000.

$$\frac{27000}{2701}-\frac{3\times 73+21}{73}-\frac{5\times 73+32}{73}+\frac{3\times 37+27}{37}$$

Multiply 3 and 73 to get 219.

$$\frac{27000}{2701}-\frac{219+21}{73}-\frac{5\times 73+32}{73}+\frac{3\times 37+27}{37}$$

Add 219 and 21 to get 240.

$$\frac{27000}{2701}-\frac{240}{73}-\frac{5\times 73+32}{73}+\frac{3\times 37+27}{37}$$

Least common multiple of 2701 and 73 is 2701. Convert \frac{27000}{2701} and \frac{240}{73} to fractions with denominator 2701.

$$\frac{27000}{2701}-\frac{8880}{2701}-\frac{5\times 73+32}{73}+\frac{3\times 37+27}{37}$$

Since \frac{27000}{2701} and \frac{8880}{2701} have the same denominator, subtract them by subtracting their numerators.

$$\frac{27000-8880}{2701}-\frac{5\times 73+32}{73}+\frac{3\times 37+27}{37}$$

Subtract 8880 from 27000 to get 18120.

$$\frac{18120}{2701}-\frac{5\times 73+32}{73}+\frac{3\times 37+27}{37}$$

Multiply 5 and 73 to get 365.

$$\frac{18120}{2701}-\frac{365+32}{73}+\frac{3\times 37+27}{37}$$

Add 365 and 32 to get 397.

$$\frac{18120}{2701}-\frac{397}{73}+\frac{3\times 37+27}{37}$$

Least common multiple of 2701 and 73 is 2701. Convert \frac{18120}{2701} and \frac{397}{73} to fractions with denominator 2701.

$$\frac{18120}{2701}-\frac{14689}{2701}+\frac{3\times 37+27}{37}$$

Since \frac{18120}{2701} and \frac{14689}{2701} have the same denominator, subtract them by subtracting their numerators.

$$\frac{18120-14689}{2701}+\frac{3\times 37+27}{37}$$

Subtract 14689 from 18120 to get 3431.

$$\frac{3431}{2701}+\frac{3\times 37+27}{37}$$

Reduce the fraction \frac{3431}{2701} to lowest terms by extracting and canceling out 73.

$$\frac{47}{37}+\frac{3\times 37+27}{37}$$

Multiply 3 and 37 to get 111.

$$\frac{47}{37}+\frac{111+27}{37}$$

Add 111 and 27 to get 138.

$$\frac{47}{37}+\frac{138}{37}$$

Since \frac{47}{37} and \frac{138}{37} have the same denominator, add them by adding their numerators.

$$\frac{47+138}{37}$$

Add 47 and 138 to get 185.

$$\frac{185}{37}$$

Divide 185 by 37 to get 5.

$$5$$

Factor

$$5$$