Solve 21/8/4frac{3{2}}+21/4

$$\frac { 2 \frac { 1 } { 8 } } { 4 \frac { 3 } { 2 } } + 2 \frac { 1 } { 4 }$$

Evaluate

$$\frac{29}{11}\approx 2.636363636$$

Solution Steps

Divide \frac{2\times 8+1}{8} by \frac{4\times 2+3}{2} by multiplying \frac{2\times 8+1}{8} by the reciprocal of \frac{4\times 2+3}{2}.

$$\frac{\left(2\times 8+1\right)\times 2}{8\left(4\times 2+3\right)}+\frac{2\times 4+1}{4}$$

Cancel out 2 in both numerator and denominator.

$$\frac{1+2\times 8}{4\left(3+2\times 4\right)}+\frac{2\times 4+1}{4}$$

Multiply 2 and 8 to get 16.

$$\frac{1+16}{4\left(3+2\times 4\right)}+\frac{2\times 4+1}{4}$$

Add 1 and 16 to get 17.

$$\frac{17}{4\left(3+2\times 4\right)}+\frac{2\times 4+1}{4}$$

Multiply 2 and 4 to get 8.

$$\frac{17}{4\left(3+8\right)}+\frac{2\times 4+1}{4}$$

Add 3 and 8 to get 11.

$$\frac{17}{4\times 11}+\frac{2\times 4+1}{4}$$

Multiply 4 and 11 to get 44.

$$\frac{17}{44}+\frac{2\times 4+1}{4}$$

Multiply 2 and 4 to get 8.

$$\frac{17}{44}+\frac{8+1}{4}$$

Add 8 and 1 to get 9.

$$\frac{17}{44}+\frac{9}{4}$$

Least common multiple of 44 and 4 is 44. Convert \frac{17}{44} and \frac{9}{4} to fractions with denominator 44.

$$\frac{17}{44}+\frac{99}{44}$$

Since \frac{17}{44} and \frac{99}{44} have the same denominator, add them by adding their numerators.

$$\frac{17+99}{44}$$

Add 17 and 99 to get 116.

$$\frac{116}{44}$$

Reduce the fraction \frac{116}{44} to lowest terms by extracting and canceling out 4.

$$\frac{29}{11}$$

Factor

$$\frac{29}{11} = 2\frac{7}{11} = 2.6363636363636362$$