Solve 21/4+41/2div2/9

$$2 \frac { 1 } { 4 } + 4 \frac { 1 } { 2 } \div \frac { 2 } { 9 }$$

Evaluate

$$\frac{45}{2}=22.5$$

Solution Steps

Multiply 2 and 4 to get 8.

$$\frac{8+1}{4}+\frac{\frac{4\times 2+1}{2}}{\frac{2}{9}}$$

Add 8 and 1 to get 9.

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

Divide \frac{4\times 2+1}{2} by \frac{2}{9} by multiplying \frac{4\times 2+1}{2} by the reciprocal of \frac{2}{9}.

$$\frac{9}{4}+\frac{\left(4\times 2+1\right)\times 9}{2\times 2}$$

Multiply 4 and 2 to get 8.

$$\frac{9}{4}+\frac{\left(8+1\right)\times 9}{2\times 2}$$

Add 8 and 1 to get 9.

$$\frac{9}{4}+\frac{9\times 9}{2\times 2}$$

Multiply 9 and 9 to get 81.

$$\frac{9}{4}+\frac{81}{2\times 2}$$

Multiply 2 and 2 to get 4.

$$\frac{9}{4}+\frac{81}{4}$$

Since \frac{9}{4} and \frac{81}{4} have the same denominator, add them by adding their numerators.

$$\frac{9+81}{4}$$

Add 9 and 81 to get 90.

$$\frac{90}{4}$$

Reduce the fraction \frac{90}{4} to lowest terms by extracting and canceling out 2.

$$\frac{45}{2}$$

Factor

$$\frac{3 ^ {2} \cdot 5}{2} = 22\frac{1}{2} = 22.5$$