Solve 41/2*8/9+51/3:102/3

$$4 \frac { 1 } { 2 } \cdot \frac { 8 } { 9 } + 5 \frac { 1 } { 3 } : 10 \frac { 2 } { 3 }$$

Evaluate

$$\frac{9}{2}=4.5$$

Solution Steps

Multiply 4 and 2 to get 8.

$$\frac{8+1}{2}\times \frac{8}{9}+\frac{\frac{5\times 3+1}{3}}{\frac{10\times 3+2}{3}}$$

Add 8 and 1 to get 9.

$$\frac{9}{2}\times \frac{8}{9}+\frac{\frac{5\times 3+1}{3}}{\frac{10\times 3+2}{3}}$$

Multiply \frac{9}{2} times \frac{8}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{9\times 8}{2\times 9}+\frac{\frac{5\times 3+1}{3}}{\frac{10\times 3+2}{3}}$$

Cancel out 9 in both numerator and denominator.

$$\frac{8}{2}+\frac{\frac{5\times 3+1}{3}}{\frac{10\times 3+2}{3}}$$

Divide 8 by 2 to get 4.

$$4+\frac{\frac{5\times 3+1}{3}}{\frac{10\times 3+2}{3}}$$

Divide \frac{5\times 3+1}{3} by \frac{10\times 3+2}{3} by multiplying \frac{5\times 3+1}{3} by the reciprocal of \frac{10\times 3+2}{3}.

$$4+\frac{\left(5\times 3+1\right)\times 3}{3\left(10\times 3+2\right)}$$

Cancel out 3 in both numerator and denominator.

$$4+\frac{1+3\times 5}{2+3\times 10}$$

Multiply 3 and 5 to get 15.

$$4+\frac{1+15}{2+3\times 10}$$

Add 1 and 15 to get 16.

$$4+\frac{16}{2+3\times 10}$$

Multiply 3 and 10 to get 30.

$$4+\frac{16}{2+30}$$

Add 2 and 30 to get 32.

$$4+\frac{16}{32}$$

Reduce the fraction \frac{16}{32} to lowest terms by extracting and canceling out 16.

$$4+\frac{1}{2}$$

Convert 4 to fraction \frac{8}{2}.

$$\frac{8}{2}+\frac{1}{2}$$

Since \frac{8}{2} and \frac{1}{2} have the same denominator, add them by adding their numerators.

$$\frac{8+1}{2}$$

Add 8 and 1 to get 9.

$$\frac{9}{2}$$

Factor

$$\frac{3 ^ {2}}{2} = 4\frac{1}{2} = 4.5$$