Solve 2/3+5/4-3/2/frac{1{5}xfrac{4}{3}}

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

Evaluate

$$\frac{25}{16x}$$

Solution Steps

Least common multiple of 3 and 4 is 12. Convert \frac{2}{3} and \frac{5}{4} to fractions with denominator 12.

$$\frac{\frac{8}{12}+\frac{15}{12}-\frac{3}{2}}{\frac{1}{5}x\times \frac{4}{3}}$$

Since \frac{8}{12} and \frac{15}{12} have the same denominator, add them by adding their numerators.

$$\frac{\frac{8+15}{12}-\frac{3}{2}}{\frac{1}{5}x\times \frac{4}{3}}$$

Add 8 and 15 to get 23.

$$\frac{\frac{23}{12}-\frac{3}{2}}{\frac{1}{5}x\times \frac{4}{3}}$$

Least common multiple of 12 and 2 is 12. Convert \frac{23}{12} and \frac{3}{2} to fractions with denominator 12.

$$\frac{\frac{23}{12}-\frac{18}{12}}{\frac{1}{5}x\times \frac{4}{3}}$$

Since \frac{23}{12} and \frac{18}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{23-18}{12}}{\frac{1}{5}x\times \frac{4}{3}}$$

Subtract 18 from 23 to get 5.

$$\frac{\frac{5}{12}}{\frac{1}{5}x\times \frac{4}{3}}$$

Multiply \frac{1}{5} times \frac{4}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{5}{12}}{\frac{1\times 4}{5\times 3}x}$$

Do the multiplications in the fraction \frac{1\times 4}{5\times 3}.

$$\frac{\frac{5}{12}}{\frac{4}{15}x}$$

Express \frac{\frac{5}{12}}{\frac{4}{15}x} as a single fraction.

$$\frac{5}{12\times \frac{4}{15}x}$$

Express 12\times \frac{4}{15} as a single fraction.

$$\frac{5}{\frac{12\times 4}{15}x}$$

Multiply 12 and 4 to get 48.

$$\frac{5}{\frac{48}{15}x}$$

Reduce the fraction \frac{48}{15} to lowest terms by extracting and canceling out 3.

$$\frac{5}{\frac{16}{5}x}$$

Expand

$$\frac{25}{16x}$$

Solution Steps

Least common multiple of 3 and 4 is 12. Convert \frac{2}{3} and \frac{5}{4} to fractions with denominator 12.

$$\frac{\frac{8}{12}+\frac{15}{12}-\frac{3}{2}}{\frac{1}{5}x\times \frac{4}{3}}$$

Since \frac{8}{12} and \frac{15}{12} have the same denominator, add them by adding their numerators.

$$\frac{\frac{8+15}{12}-\frac{3}{2}}{\frac{1}{5}x\times \frac{4}{3}}$$

Add 8 and 15 to get 23.

$$\frac{\frac{23}{12}-\frac{3}{2}}{\frac{1}{5}x\times \frac{4}{3}}$$

Least common multiple of 12 and 2 is 12. Convert \frac{23}{12} and \frac{3}{2} to fractions with denominator 12.

$$\frac{\frac{23}{12}-\frac{18}{12}}{\frac{1}{5}x\times \frac{4}{3}}$$

Since \frac{23}{12} and \frac{18}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{23-18}{12}}{\frac{1}{5}x\times \frac{4}{3}}$$

Subtract 18 from 23 to get 5.

$$\frac{\frac{5}{12}}{\frac{1}{5}x\times \frac{4}{3}}$$

Multiply \frac{1}{5} times \frac{4}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{5}{12}}{\frac{1\times 4}{5\times 3}x}$$

Do the multiplications in the fraction \frac{1\times 4}{5\times 3}.

$$\frac{\frac{5}{12}}{\frac{4}{15}x}$$

Express \frac{\frac{5}{12}}{\frac{4}{15}x} as a single fraction.

$$\frac{5}{12\times \frac{4}{15}x}$$

Express 12\times \frac{4}{15} as a single fraction.

$$\frac{5}{\frac{12\times 4}{15}x}$$

Multiply 12 and 4 to get 48.

$$\frac{5}{\frac{48}{15}x}$$

Reduce the fraction \frac{48}{15} to lowest terms by extracting and canceling out 3.

$$\frac{5}{\frac{16}{5}x}$$