Solve (152/3-71/2):11/2=

$$( 15 \frac { 2 } { 3 } - 7 \frac { 1 } { 2 } ) : 1 \frac { 1 } { 2 } =$$

Evaluate

$$\frac{49}{9}\approx 5.444444444$$

Solution Steps

Multiply 15 and 3 to get 45.

$$\frac{\frac{45+2}{3}-\frac{7\times 2+1}{2}}{\frac{1\times 2+1}{2}}$$

Add 45 and 2 to get 47.

$$\frac{\frac{47}{3}-\frac{7\times 2+1}{2}}{\frac{1\times 2+1}{2}}$$

Multiply 7 and 2 to get 14.

$$\frac{\frac{47}{3}-\frac{14+1}{2}}{\frac{1\times 2+1}{2}}$$

Add 14 and 1 to get 15.

$$\frac{\frac{47}{3}-\frac{15}{2}}{\frac{1\times 2+1}{2}}$$

Least common multiple of 3 and 2 is 6. Convert \frac{47}{3} and \frac{15}{2} to fractions with denominator 6.

$$\frac{\frac{94}{6}-\frac{45}{6}}{\frac{1\times 2+1}{2}}$$

Since \frac{94}{6} and \frac{45}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{94-45}{6}}{\frac{1\times 2+1}{2}}$$

Subtract 45 from 94 to get 49.

$$\frac{\frac{49}{6}}{\frac{1\times 2+1}{2}}$$

Multiply 1 and 2 to get 2.

$$\frac{\frac{49}{6}}{\frac{2+1}{2}}$$

Add 2 and 1 to get 3.

$$\frac{\frac{49}{6}}{\frac{3}{2}}$$

Divide \frac{49}{6} by \frac{3}{2} by multiplying \frac{49}{6} by the reciprocal of \frac{3}{2}.

$$\frac{49}{6}\times \frac{2}{3}$$

Multiply \frac{49}{6} times \frac{2}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{49\times 2}{6\times 3}$$

Do the multiplications in the fraction \frac{49\times 2}{6\times 3}.

$$\frac{98}{18}$$

Reduce the fraction \frac{98}{18} to lowest terms by extracting and canceling out 2.

$$\frac{49}{9}$$

Factor

$$\frac{7 ^ {2}}{3 ^ {2}} = 5\frac{4}{9} = 5.444444444444445$$