Solve 3*1/2:6/9+sqrt{9}

$$3 \times \frac { 1 } { 2 } : \frac { 6 } { 9 } + \sqrt { 9 }$$

Evaluate

$$\frac{21}{4}=5.25$$

Solution Steps

Multiply 3 and \frac{1}{2} to get \frac{3}{2}.

$$\frac{\frac{3}{2}}{\frac{6}{9}}+\sqrt{9}$$

Reduce the fraction \frac{6}{9} to lowest terms by extracting and canceling out 3.

$$\frac{\frac{3}{2}}{\frac{2}{3}}+\sqrt{9}$$

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

$$\frac{3}{2}\times \frac{3}{2}+\sqrt{9}$$

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

$$\frac{3\times 3}{2\times 2}+\sqrt{9}$$

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

$$\frac{9}{4}+\sqrt{9}$$

Calculate the square root of 9 and get 3.

$$\frac{9}{4}+3$$

Convert 3 to fraction \frac{12}{4}.

$$\frac{9}{4}+\frac{12}{4}$$

Since \frac{9}{4} and \frac{12}{4} have the same denominator, add them by adding their numerators.

$$\frac{9+12}{4}$$

Add 9 and 12 to get 21.

$$\frac{21}{4}$$

Factor

$$\frac{3 \cdot 7}{2 ^ {2}} = 5\frac{1}{4} = 5.25$$