Solve 2-2/9:2/3-6/5:3/2=2

$$2 - \frac { 2 } { 9 } : \frac { 2 } { 3 } - \frac { 6 } { 5 } : \frac { 3 } { 2 } = 2$$

Verify

Solution Steps

Divide \frac{2}{9} by \frac{2}{3} by multiplying \frac{2}{9} by the reciprocal of \frac{2}{3}.

$$2-\frac{2}{9}\times \frac{3}{2}-\frac{\frac{6}{5}}{\frac{3}{2}}=2$$

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

$$2-\frac{2\times 3}{9\times 2}-\frac{\frac{6}{5}}{\frac{3}{2}}=2$$

Cancel out 2 in both numerator and denominator.

$$2-\frac{3}{9}-\frac{\frac{6}{5}}{\frac{3}{2}}=2$$

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

$$2-\frac{1}{3}-\frac{\frac{6}{5}}{\frac{3}{2}}=2$$

Convert 2 to fraction \frac{6}{3}.

$$\frac{6}{3}-\frac{1}{3}-\frac{\frac{6}{5}}{\frac{3}{2}}=2$$

Since \frac{6}{3} and \frac{1}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{6-1}{3}-\frac{\frac{6}{5}}{\frac{3}{2}}=2$$

Subtract 1 from 6 to get 5.

$$\frac{5}{3}-\frac{\frac{6}{5}}{\frac{3}{2}}=2$$

Divide \frac{6}{5} by \frac{3}{2} by multiplying \frac{6}{5} by the reciprocal of \frac{3}{2}.

$$\frac{5}{3}-\frac{6}{5}\times \frac{2}{3}=2$$

Multiply \frac{6}{5} times \frac{2}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5}{3}-\frac{6\times 2}{5\times 3}=2$$

Do the multiplications in the fraction \frac{6\times 2}{5\times 3}.

$$\frac{5}{3}-\frac{12}{15}=2$$

Reduce the fraction \frac{12}{15} to lowest terms by extracting and canceling out 3.

$$\frac{5}{3}-\frac{4}{5}=2$$

Least common multiple of 3 and 5 is 15. Convert \frac{5}{3} and \frac{4}{5} to fractions with denominator 15.

$$\frac{25}{15}-\frac{12}{15}=2$$

Since \frac{25}{15} and \frac{12}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{25-12}{15}=2$$

Subtract 12 from 25 to get 13.

$$\frac{13}{15}=2$$

Convert 2 to fraction \frac{30}{15}.

$$\frac{13}{15}=\frac{30}{15}$$

Compare \frac{13}{15} and \frac{30}{15}.

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