Solve 23/30div(23/5+13/10-32/15)

$$\frac { 23 } { 30 } \div ( 2 \frac { 3 } { 5 } + 1 \frac { 3 } { 10 } - 3 \frac { 2 } { 15 } )$$

Evaluate

$$1$$

Solution Steps

Multiply 2 and 5 to get 10.

$$\frac{\frac{23}{30}}{\frac{10+3}{5}+\frac{1\times 10+3}{10}-\frac{3\times 15+2}{15}}$$

Add 10 and 3 to get 13.

$$\frac{\frac{23}{30}}{\frac{13}{5}+\frac{1\times 10+3}{10}-\frac{3\times 15+2}{15}}$$

Multiply 1 and 10 to get 10.

$$\frac{\frac{23}{30}}{\frac{13}{5}+\frac{10+3}{10}-\frac{3\times 15+2}{15}}$$

Add 10 and 3 to get 13.

$$\frac{\frac{23}{30}}{\frac{13}{5}+\frac{13}{10}-\frac{3\times 15+2}{15}}$$

Least common multiple of 5 and 10 is 10. Convert \frac{13}{5} and \frac{13}{10} to fractions with denominator 10.

$$\frac{\frac{23}{30}}{\frac{26}{10}+\frac{13}{10}-\frac{3\times 15+2}{15}}$$

Since \frac{26}{10} and \frac{13}{10} have the same denominator, add them by adding their numerators.

$$\frac{\frac{23}{30}}{\frac{26+13}{10}-\frac{3\times 15+2}{15}}$$

Add 26 and 13 to get 39.

$$\frac{\frac{23}{30}}{\frac{39}{10}-\frac{3\times 15+2}{15}}$$

Multiply 3 and 15 to get 45.

$$\frac{\frac{23}{30}}{\frac{39}{10}-\frac{45+2}{15}}$$

Add 45 and 2 to get 47.

$$\frac{\frac{23}{30}}{\frac{39}{10}-\frac{47}{15}}$$

Least common multiple of 10 and 15 is 30. Convert \frac{39}{10} and \frac{47}{15} to fractions with denominator 30.

$$\frac{\frac{23}{30}}{\frac{117}{30}-\frac{94}{30}}$$

Since \frac{117}{30} and \frac{94}{30} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{23}{30}}{\frac{117-94}{30}}$$

Subtract 94 from 117 to get 23.

$$\frac{\frac{23}{30}}{\frac{23}{30}}$$

Divide \frac{23}{30} by \frac{23}{30} to get 1.

$$1$$

Factor

$$1$$