Solve 9/4-3/41/3+4/33-2(frac{2}{3})

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

Evaluate

$$\frac{14}{3}\approx 4.666666667$$

Solution Steps

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

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

Cancel out 3 in both numerator and denominator.

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

Since \frac{9}{4} and \frac{1}{4} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 1 from 9 to get 8.

$$\frac{8}{4}+\frac{4}{3}\times 3-2\times \frac{2}{3}$$

Divide 8 by 4 to get 2.

$$2+\frac{4}{3}\times 3-2\times \frac{2}{3}$$

Cancel out 3 and 3.

$$2+4-2\times \frac{2}{3}$$

Add 2 and 4 to get 6.

$$6-2\times \frac{2}{3}$$

Express 2\times \frac{2}{3} as a single fraction.

$$6-\frac{2\times 2}{3}$$

Multiply 2 and 2 to get 4.

$$6-\frac{4}{3}$$

Convert 6 to fraction \frac{18}{3}.

$$\frac{18}{3}-\frac{4}{3}$$

Since \frac{18}{3} and \frac{4}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{18-4}{3}$$

Subtract 4 from 18 to get 14.

$$\frac{14}{3}$$

Factor

$$\frac{2 \cdot 7}{3} = 4\frac{2}{3} = 4.666666666666667$$