Solve a=7/5/2+1,5/frac{9{2}}-frac{3/4}{frac{2,5}{7}}

$$a = \frac { \frac { 7 } { 5 } } { 2 } + \frac { 1,5 } { \frac { 9 } { 2 } } - \frac { \frac { 3 } { 4 } } { \frac { 2,5 } { 7 } }$$

Solve for a

$$a=-\frac{16}{15}\approx -1,066666667$$

Steps for Solving Linear Equation

Express \frac{\frac{7}{5}}{2} as a single fraction.

$$a=\frac{7}{5\times 2}+\frac{1,5}{\frac{9}{2}}-\frac{\frac{3}{4}}{\frac{2,5}{7}}$$

Multiply 5 and 2 to get 10.

$$a=\frac{7}{10}+\frac{1,5}{\frac{9}{2}}-\frac{\frac{3}{4}}{\frac{2,5}{7}}$$

Divide 1,5 by \frac{9}{2} by multiplying 1,5 by the reciprocal of \frac{9}{2}.

$$a=\frac{7}{10}+1,5\times \frac{2}{9}-\frac{\frac{3}{4}}{\frac{2,5}{7}}$$

Convert decimal number 1,5 to fraction \frac{15}{10}. Reduce the fraction \frac{15}{10} to lowest terms by extracting and canceling out 5.

$$a=\frac{7}{10}+\frac{3}{2}\times \frac{2}{9}-\frac{\frac{3}{4}}{\frac{2,5}{7}}$$

Multiply \frac{3}{2} times \frac{2}{9} by multiplying numerator times numerator and denominator times denominator.

$$a=\frac{7}{10}+\frac{3\times 2}{2\times 9}-\frac{\frac{3}{4}}{\frac{2,5}{7}}$$

Cancel out 2 in both numerator and denominator.

$$a=\frac{7}{10}+\frac{3}{9}-\frac{\frac{3}{4}}{\frac{2,5}{7}}$$

Reduce the fraction \frac{3}{9} to lowest terms by extracting and canceling out 3.

$$a=\frac{7}{10}+\frac{1}{3}-\frac{\frac{3}{4}}{\frac{2,5}{7}}$$

Least common multiple of 10 and 3 is 30. Convert \frac{7}{10} and \frac{1}{3} to fractions with denominator 30.

$$a=\frac{21}{30}+\frac{10}{30}-\frac{\frac{3}{4}}{\frac{2,5}{7}}$$

Since \frac{21}{30} and \frac{10}{30} have the same denominator, add them by adding their numerators.

$$a=\frac{21+10}{30}-\frac{\frac{3}{4}}{\frac{2,5}{7}}$$

Add 21 and 10 to get 31.

$$a=\frac{31}{30}-\frac{\frac{3}{4}}{\frac{2,5}{7}}$$

Divide \frac{3}{4} by \frac{2,5}{7} by multiplying \frac{3}{4} by the reciprocal of \frac{2,5}{7}.

$$a=\frac{31}{30}-\frac{3\times 7}{4\times 2,5}$$

Multiply 3 and 7 to get 21.

$$a=\frac{31}{30}-\frac{21}{4\times 2,5}$$

Multiply 4 and 2,5 to get 10.

$$a=\frac{31}{30}-\frac{21}{10}$$

Least common multiple of 30 and 10 is 30. Convert \frac{31}{30} and \frac{21}{10} to fractions with denominator 30.

$$a=\frac{31}{30}-\frac{63}{30}$$

Since \frac{31}{30} and \frac{63}{30} have the same denominator, subtract them by subtracting their numerators.

$$a=\frac{31-63}{30}$$

Subtract 63 from 31 to get -32.

$$a=\frac{-32}{30}$$

Reduce the fraction \frac{-32}{30} to lowest terms by extracting and canceling out 2.

$$a=-\frac{16}{15}$$

Assign a

$$a≔-\frac{16}{15}$$