Solve 7/8+23/4div31/2

$$\frac { 7 } { 8 } + 2 \frac { 3 } { 4 } \div 3 \frac { 1 } { 2 }$$

Evaluate

$$\frac{93}{56}\approx 1.660714286$$

Solution Steps

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

$$\frac{7}{8}+\frac{\left(2\times 4+3\right)\times 2}{4\left(3\times 2+1\right)}$$

Cancel out 2 in both numerator and denominator.

$$\frac{7}{8}+\frac{3+2\times 4}{2\left(1+2\times 3\right)}$$

Multiply 2 and 4 to get 8.

$$\frac{7}{8}+\frac{3+8}{2\left(1+2\times 3\right)}$$

Add 3 and 8 to get 11.

$$\frac{7}{8}+\frac{11}{2\left(1+2\times 3\right)}$$

Multiply 2 and 3 to get 6.

$$\frac{7}{8}+\frac{11}{2\left(1+6\right)}$$

Add 1 and 6 to get 7.

$$\frac{7}{8}+\frac{11}{2\times 7}$$

Multiply 2 and 7 to get 14.

$$\frac{7}{8}+\frac{11}{14}$$

Least common multiple of 8 and 14 is 56. Convert \frac{7}{8} and \frac{11}{14} to fractions with denominator 56.

$$\frac{49}{56}+\frac{44}{56}$$

Since \frac{49}{56} and \frac{44}{56} have the same denominator, add them by adding their numerators.

$$\frac{49+44}{56}$$

Add 49 and 44 to get 93.

$$\frac{93}{56}$$

Factor

$$\frac{3 \cdot 31}{2 ^ {3} \cdot 7} = 1\frac{37}{56} = 1.6607142857142858$$