Solve 13/4x(4/9+1/3)div(21/5-1frac{1}{2})

$$1 \frac { 3 } { 4 } x ( \frac { 4 } { 9 } + \frac { 1 } { 3 } ) \div ( 2 \frac { 1 } { 5 } - 1 \frac { 1 } { 2 } )$$

Evaluate

$$\frac{35x}{18}$$

Solution Steps

Multiply 1 and 4 to get 4.

$$\frac{\frac{4+3}{4}x\left(\frac{4}{9}+\frac{1}{3}\right)}{\frac{2\times 5+1}{5}-\frac{1\times 2+1}{2}}$$

Add 4 and 3 to get 7.

$$\frac{\frac{7}{4}x\left(\frac{4}{9}+\frac{1}{3}\right)}{\frac{2\times 5+1}{5}-\frac{1\times 2+1}{2}}$$

Least common multiple of 9 and 3 is 9. Convert \frac{4}{9} and \frac{1}{3} to fractions with denominator 9.

$$\frac{\frac{7}{4}x\left(\frac{4}{9}+\frac{3}{9}\right)}{\frac{2\times 5+1}{5}-\frac{1\times 2+1}{2}}$$

Since \frac{4}{9} and \frac{3}{9} have the same denominator, add them by adding their numerators.

$$\frac{\frac{7}{4}x\times \frac{4+3}{9}}{\frac{2\times 5+1}{5}-\frac{1\times 2+1}{2}}$$

Add 4 and 3 to get 7.

$$\frac{\frac{7}{4}x\times \frac{7}{9}}{\frac{2\times 5+1}{5}-\frac{1\times 2+1}{2}}$$

Multiply \frac{7}{4} times \frac{7}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{7\times 7}{4\times 9}x}{\frac{2\times 5+1}{5}-\frac{1\times 2+1}{2}}$$

Do the multiplications in the fraction \frac{7\times 7}{4\times 9}.

$$\frac{\frac{49}{36}x}{\frac{2\times 5+1}{5}-\frac{1\times 2+1}{2}}$$

Multiply 2 and 5 to get 10.

$$\frac{\frac{49}{36}x}{\frac{10+1}{5}-\frac{1\times 2+1}{2}}$$

Add 10 and 1 to get 11.

$$\frac{\frac{49}{36}x}{\frac{11}{5}-\frac{1\times 2+1}{2}}$$

Multiply 1 and 2 to get 2.

$$\frac{\frac{49}{36}x}{\frac{11}{5}-\frac{2+1}{2}}$$

Add 2 and 1 to get 3.

$$\frac{\frac{49}{36}x}{\frac{11}{5}-\frac{3}{2}}$$

Least common multiple of 5 and 2 is 10. Convert \frac{11}{5} and \frac{3}{2} to fractions with denominator 10.

$$\frac{\frac{49}{36}x}{\frac{22}{10}-\frac{15}{10}}$$

Since \frac{22}{10} and \frac{15}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{49}{36}x}{\frac{22-15}{10}}$$

Subtract 15 from 22 to get 7.

$$\frac{\frac{49}{36}x}{\frac{7}{10}}$$

Divide \frac{49}{36}x by \frac{7}{10} by multiplying \frac{49}{36}x by the reciprocal of \frac{7}{10}.

$$\frac{\frac{49}{36}x\times 10}{7}$$

Express \frac{49}{36}\times 10 as a single fraction.

$$\frac{\frac{49\times 10}{36}x}{7}$$

Multiply 49 and 10 to get 490.

$$\frac{\frac{490}{36}x}{7}$$

Reduce the fraction \frac{490}{36} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{245}{18}x}{7}$$

Divide \frac{245}{18}x by 7 to get \frac{35}{18}x.

$$\frac{35}{18}x$$

Expand

$$\frac{35x}{18}$$

Solution Steps

Multiply 1 and 4 to get 4.

$$\frac{\frac{4+3}{4}x\left(\frac{4}{9}+\frac{1}{3}\right)}{\frac{2\times 5+1}{5}-\frac{1\times 2+1}{2}}$$

Add 4 and 3 to get 7.

$$\frac{\frac{7}{4}x\left(\frac{4}{9}+\frac{1}{3}\right)}{\frac{2\times 5+1}{5}-\frac{1\times 2+1}{2}}$$

Least common multiple of 9 and 3 is 9. Convert \frac{4}{9} and \frac{1}{3} to fractions with denominator 9.

$$\frac{\frac{7}{4}x\left(\frac{4}{9}+\frac{3}{9}\right)}{\frac{2\times 5+1}{5}-\frac{1\times 2+1}{2}}$$

Since \frac{4}{9} and \frac{3}{9} have the same denominator, add them by adding their numerators.

$$\frac{\frac{7}{4}x\times \frac{4+3}{9}}{\frac{2\times 5+1}{5}-\frac{1\times 2+1}{2}}$$

Add 4 and 3 to get 7.

$$\frac{\frac{7}{4}x\times \frac{7}{9}}{\frac{2\times 5+1}{5}-\frac{1\times 2+1}{2}}$$

Multiply \frac{7}{4} times \frac{7}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{7\times 7}{4\times 9}x}{\frac{2\times 5+1}{5}-\frac{1\times 2+1}{2}}$$

Do the multiplications in the fraction \frac{7\times 7}{4\times 9}.

$$\frac{\frac{49}{36}x}{\frac{2\times 5+1}{5}-\frac{1\times 2+1}{2}}$$

Multiply 2 and 5 to get 10.

$$\frac{\frac{49}{36}x}{\frac{10+1}{5}-\frac{1\times 2+1}{2}}$$

Add 10 and 1 to get 11.

$$\frac{\frac{49}{36}x}{\frac{11}{5}-\frac{1\times 2+1}{2}}$$

Multiply 1 and 2 to get 2.

$$\frac{\frac{49}{36}x}{\frac{11}{5}-\frac{2+1}{2}}$$

Add 2 and 1 to get 3.

$$\frac{\frac{49}{36}x}{\frac{11}{5}-\frac{3}{2}}$$

Least common multiple of 5 and 2 is 10. Convert \frac{11}{5} and \frac{3}{2} to fractions with denominator 10.

$$\frac{\frac{49}{36}x}{\frac{22}{10}-\frac{15}{10}}$$

Since \frac{22}{10} and \frac{15}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{49}{36}x}{\frac{22-15}{10}}$$

Subtract 15 from 22 to get 7.

$$\frac{\frac{49}{36}x}{\frac{7}{10}}$$

Divide \frac{49}{36}x by \frac{7}{10} by multiplying \frac{49}{36}x by the reciprocal of \frac{7}{10}.

$$\frac{\frac{49}{36}x\times 10}{7}$$

Express \frac{49}{36}\times 10 as a single fraction.

$$\frac{\frac{49\times 10}{36}x}{7}$$

Multiply 49 and 10 to get 490.

$$\frac{\frac{490}{36}x}{7}$$

Reduce the fraction \frac{490}{36} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{245}{18}x}{7}$$

Divide \frac{245}{18}x by 7 to get \frac{35}{18}x.

$$\frac{35}{18}x$$