Solve {[(8diva+3):7div(3div15:5)*3]*2-(19-7):6}*2+20

$$\{ [ ( 8 \div a + 3 ) : 7 \div ( 3 \div 15 : 5 ) * 3 ] * 2 - ( 19 - 7 ) : 6 \} * 2 + 20$$

Evaluate

$$\frac{1012}{7}+\frac{2400}{7a}$$

Short Solution Steps

Divide \frac{\frac{8}{a}+3}{7} by \frac{\frac{3}{15}}{5} by multiplying \frac{\frac{8}{a}+3}{7} by the reciprocal of \frac{\frac{3}{15}}{5}.

$$\left(\frac{\left(\frac{8}{a}+3\right)\times 5}{7\times \frac{3}{15}}\times 3\times 2-\frac{19-7}{6}\right)\times 2+20$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 3 times \frac{a}{a}.

$$\left(\frac{\left(\frac{8}{a}+\frac{3a}{a}\right)\times 5}{7\times \frac{3}{15}}\times 3\times 2-\frac{19-7}{6}\right)\times 2+20$$

Since \frac{8}{a} and \frac{3a}{a} have the same denominator, add them by adding their numerators.

$$\left(\frac{\frac{8+3a}{a}\times 5}{7\times \frac{3}{15}}\times 3\times 2-\frac{19-7}{6}\right)\times 2+20$$

Express \frac{8+3a}{a}\times 5 as a single fraction.

$$\left(\frac{\frac{\left(8+3a\right)\times 5}{a}}{7\times \frac{3}{15}}\times 3\times 2-\frac{19-7}{6}\right)\times 2+20$$

Reduce the fraction \frac{3}{15} to lowest terms by extracting and canceling out 3.

$$\left(\frac{\frac{\left(8+3a\right)\times 5}{a}}{7\times \frac{1}{5}}\times 3\times 2-\frac{19-7}{6}\right)\times 2+20$$

Multiply 7 and \frac{1}{5} to get \frac{7}{5}.

$$\left(\frac{\frac{\left(8+3a\right)\times 5}{a}}{\frac{7}{5}}\times 3\times 2-\frac{19-7}{6}\right)\times 2+20$$

Divide \frac{\left(8+3a\right)\times 5}{a} by \frac{7}{5} by multiplying \frac{\left(8+3a\right)\times 5}{a} by the reciprocal of \frac{7}{5}.

$$\left(\frac{\left(8+3a\right)\times 5\times 5}{a\times 7}\times 3\times 2-\frac{19-7}{6}\right)\times 2+20$$

Multiply 5 and 5 to get 25.

$$\left(\frac{\left(8+3a\right)\times 25}{a\times 7}\times 3\times 2-\frac{19-7}{6}\right)\times 2+20$$

Multiply 3 and 2 to get 6.

$$\left(\frac{\left(8+3a\right)\times 25}{a\times 7}\times 6-\frac{19-7}{6}\right)\times 2+20$$

Express \frac{\left(8+3a\right)\times 25}{a\times 7}\times 6 as a single fraction.

$$\left(\frac{\left(8+3a\right)\times 25\times 6}{a\times 7}-\frac{19-7}{6}\right)\times 2+20$$

Subtract 7 from 19 to get 12.

$$\left(\frac{\left(8+3a\right)\times 25\times 6}{a\times 7}-\frac{12}{6}\right)\times 2+20$$

Divide 12 by 6 to get 2.

$$\left(\frac{\left(8+3a\right)\times 25\times 6}{a\times 7}-2\right)\times 2+20$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 2 times \frac{a\times 7}{a\times 7}.

$$\left(\frac{\left(8+3a\right)\times 25\times 6}{a\times 7}-\frac{2a\times 7}{a\times 7}\right)\times 2+20$$

Since \frac{\left(8+3a\right)\times 25\times 6}{a\times 7} and \frac{2a\times 7}{a\times 7} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\left(8+3a\right)\times 25\times 6-2a\times 7}{a\times 7}\times 2+20$$

Do the multiplications in \left(8+3a\right)\times 25\times 6-2a\times 7.

$$\frac{1200+450a-14a}{a\times 7}\times 2+20$$

Combine like terms in 1200+450a-14a.

$$\frac{1200+436a}{a\times 7}\times 2+20$$

Express \frac{1200+436a}{a\times 7}\times 2 as a single fraction.

$$\frac{\left(1200+436a\right)\times 2}{a\times 7}+20$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 20 times \frac{a\times 7}{a\times 7}.

$$\frac{\left(1200+436a\right)\times 2}{a\times 7}+\frac{20a\times 7}{a\times 7}$$

Since \frac{\left(1200+436a\right)\times 2}{a\times 7} and \frac{20a\times 7}{a\times 7} have the same denominator, add them by adding their numerators.

$$\frac{\left(1200+436a\right)\times 2+20a\times 7}{a\times 7}$$

Do the multiplications in \left(1200+436a\right)\times 2+20a\times 7.

$$\frac{2400+872a+140a}{a\times 7}$$

Combine like terms in 2400+872a+140a.

$$\frac{2400+1012a}{a\times 7}$$

Expand

$$\frac{1012}{7}+\frac{2400}{7a}$$

Short Solution Steps

Divide \frac{\frac{8}{a}+3}{7} by \frac{\frac{3}{15}}{5} by multiplying \frac{\frac{8}{a}+3}{7} by the reciprocal of \frac{\frac{3}{15}}{5}.

$$\left(\frac{\left(\frac{8}{a}+3\right)\times 5}{7\times \frac{3}{15}}\times 3\times 2-\frac{19-7}{6}\right)\times 2+20$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 3 times \frac{a}{a}.

$$\left(\frac{\left(\frac{8}{a}+\frac{3a}{a}\right)\times 5}{7\times \frac{3}{15}}\times 3\times 2-\frac{19-7}{6}\right)\times 2+20$$

Since \frac{8}{a} and \frac{3a}{a} have the same denominator, add them by adding their numerators.

$$\left(\frac{\frac{8+3a}{a}\times 5}{7\times \frac{3}{15}}\times 3\times 2-\frac{19-7}{6}\right)\times 2+20$$

Express \frac{8+3a}{a}\times 5 as a single fraction.

$$\left(\frac{\frac{\left(8+3a\right)\times 5}{a}}{7\times \frac{3}{15}}\times 3\times 2-\frac{19-7}{6}\right)\times 2+20$$

Reduce the fraction \frac{3}{15} to lowest terms by extracting and canceling out 3.

$$\left(\frac{\frac{\left(8+3a\right)\times 5}{a}}{7\times \frac{1}{5}}\times 3\times 2-\frac{19-7}{6}\right)\times 2+20$$

Multiply 7 and \frac{1}{5} to get \frac{7}{5}.

$$\left(\frac{\frac{\left(8+3a\right)\times 5}{a}}{\frac{7}{5}}\times 3\times 2-\frac{19-7}{6}\right)\times 2+20$$

Divide \frac{\left(8+3a\right)\times 5}{a} by \frac{7}{5} by multiplying \frac{\left(8+3a\right)\times 5}{a} by the reciprocal of \frac{7}{5}.

$$\left(\frac{\left(8+3a\right)\times 5\times 5}{a\times 7}\times 3\times 2-\frac{19-7}{6}\right)\times 2+20$$

Multiply 5 and 5 to get 25.

$$\left(\frac{\left(8+3a\right)\times 25}{a\times 7}\times 3\times 2-\frac{19-7}{6}\right)\times 2+20$$

Multiply 3 and 2 to get 6.

$$\left(\frac{\left(8+3a\right)\times 25}{a\times 7}\times 6-\frac{19-7}{6}\right)\times 2+20$$

Express \frac{\left(8+3a\right)\times 25}{a\times 7}\times 6 as a single fraction.

$$\left(\frac{\left(8+3a\right)\times 25\times 6}{a\times 7}-\frac{19-7}{6}\right)\times 2+20$$

Subtract 7 from 19 to get 12.

$$\left(\frac{\left(8+3a\right)\times 25\times 6}{a\times 7}-\frac{12}{6}\right)\times 2+20$$

Divide 12 by 6 to get 2.

$$\left(\frac{\left(8+3a\right)\times 25\times 6}{a\times 7}-2\right)\times 2+20$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 2 times \frac{a\times 7}{a\times 7}.

$$\left(\frac{\left(8+3a\right)\times 25\times 6}{a\times 7}-\frac{2a\times 7}{a\times 7}\right)\times 2+20$$

Since \frac{\left(8+3a\right)\times 25\times 6}{a\times 7} and \frac{2a\times 7}{a\times 7} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\left(8+3a\right)\times 25\times 6-2a\times 7}{a\times 7}\times 2+20$$

Do the multiplications in \left(8+3a\right)\times 25\times 6-2a\times 7.

$$\frac{1200+450a-14a}{a\times 7}\times 2+20$$

Combine like terms in 1200+450a-14a.

$$\frac{1200+436a}{a\times 7}\times 2+20$$

Express \frac{1200+436a}{a\times 7}\times 2 as a single fraction.

$$\frac{\left(1200+436a\right)\times 2}{a\times 7}+20$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 20 times \frac{a\times 7}{a\times 7}.

$$\frac{\left(1200+436a\right)\times 2}{a\times 7}+\frac{20a\times 7}{a\times 7}$$

Since \frac{\left(1200+436a\right)\times 2}{a\times 7} and \frac{20a\times 7}{a\times 7} have the same denominator, add them by adding their numerators.

$$\frac{\left(1200+436a\right)\times 2+20a\times 7}{a\times 7}$$

Do the multiplications in \left(1200+436a\right)\times 2+20a\times 7.

$$\frac{2400+872a+140a}{a\times 7}$$

Combine like terms in 2400+872a+140a.

$$\frac{2400+1012a}{a\times 7}$$