Solve 8+21/4div11/2=

$$8 + 2 \frac { 1 } { 4 } \div 1 \frac { 1 } { 2 } =$$

Evaluate

$$\frac{19}{2}=9.5$$

Solution Steps

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

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

Cancel out 2 in both numerator and denominator.

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

Multiply 2 and 4 to get 8.

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

Add 1 and 8 to get 9.

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

Add 1 and 2 to get 3.

$$8+\frac{9}{2\times 3}$$

Multiply 2 and 3 to get 6.

$$8+\frac{9}{6}$$

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

$$8+\frac{3}{2}$$

Convert 8 to fraction \frac{16}{2}.

$$\frac{16}{2}+\frac{3}{2}$$

Since \frac{16}{2} and \frac{3}{2} have the same denominator, add them by adding their numerators.

$$\frac{16+3}{2}$$

Add 16 and 3 to get 19.

$$\frac{19}{2}$$

Factor

$$\frac{19}{2} = 9\frac{1}{2} = 9.5$$