Solve 11/2*1/4+51/2div3/4

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

Evaluate

$$\frac{185}{24}\approx 7.708333333$$

Solution Steps

Multiply 1 and 2 to get 2.

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

Add 2 and 1 to get 3.

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

Multiply \frac{3}{2} times \frac{1}{4} by multiplying numerator times numerator and denominator times denominator.

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

Do the multiplications in the fraction \frac{3\times 1}{2\times 4}.

$$\frac{3}{8}+\frac{\frac{5\times 2+1}{2}}{\frac{3}{4}}$$

Divide \frac{5\times 2+1}{2} by \frac{3}{4} by multiplying \frac{5\times 2+1}{2} by the reciprocal of \frac{3}{4}.

$$\frac{3}{8}+\frac{\left(5\times 2+1\right)\times 4}{2\times 3}$$

Cancel out 2 in both numerator and denominator.

$$\frac{3}{8}+\frac{2\left(1+2\times 5\right)}{3}$$

Multiply 2 and 5 to get 10.

$$\frac{3}{8}+\frac{2\left(1+10\right)}{3}$$

Add 1 and 10 to get 11.

$$\frac{3}{8}+\frac{2\times 11}{3}$$

Multiply 2 and 11 to get 22.

$$\frac{3}{8}+\frac{22}{3}$$

Least common multiple of 8 and 3 is 24. Convert \frac{3}{8} and \frac{22}{3} to fractions with denominator 24.

$$\frac{9}{24}+\frac{176}{24}$$

Since \frac{9}{24} and \frac{176}{24} have the same denominator, add them by adding their numerators.

$$\frac{9+176}{24}$$

Add 9 and 176 to get 185.

$$\frac{185}{24}$$

Factor

$$\frac{5 \cdot 37}{2 ^ {3} \cdot 3} = 7\frac{17}{24} = 7.708333333333333$$