Solve (11/2+21/3)*11/4=

$$( 1 \frac { 1 } { 2 } + 2 \frac { 1 } { 3 } ) \cdot 1 \frac { 1 } { 4 } =$$

Evaluate

$$\frac{115}{24}\approx 4.791666667$$

Solution Steps

Multiply 1 and 2 to get 2.

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

Add 2 and 1 to get 3.

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

Multiply 2 and 3 to get 6.

$$\left(\frac{3}{2}+\frac{6+1}{3}\right)\times \frac{1\times 4+1}{4}$$

Add 6 and 1 to get 7.

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

Least common multiple of 2 and 3 is 6. Convert \frac{3}{2} and \frac{7}{3} to fractions with denominator 6.

$$\left(\frac{9}{6}+\frac{14}{6}\right)\times \frac{1\times 4+1}{4}$$

Since \frac{9}{6} and \frac{14}{6} have the same denominator, add them by adding their numerators.

$$\frac{9+14}{6}\times \frac{1\times 4+1}{4}$$

Add 9 and 14 to get 23.

$$\frac{23}{6}\times \frac{1\times 4+1}{4}$$

Multiply 1 and 4 to get 4.

$$\frac{23}{6}\times \frac{4+1}{4}$$

Add 4 and 1 to get 5.

$$\frac{23}{6}\times \frac{5}{4}$$

Multiply \frac{23}{6} times \frac{5}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{23\times 5}{6\times 4}$$

Do the multiplications in the fraction \frac{23\times 5}{6\times 4}.

$$\frac{115}{24}$$

Factor

$$\frac{5 \cdot 23}{2 ^ {3} \cdot 3} = 4\frac{19}{24} = 4.791666666666667$$