Solve 11.21/4+51/2+103/4=

$$11.2 \frac { 1 } { 4 } + 5 \frac { 1 } { 2 } + 10 \frac { 3 } { 4 } =$$

Evaluate

$$27.7$$

Solution Steps

Multiply 11.2 and 4 to get 44.8.

$$\frac{44.8+1}{4}+\frac{5\times 2+1}{2}+\frac{10\times 4+3}{4}$$

Add 44.8 and 1 to get 45.8.

$$\frac{45.8}{4}+\frac{5\times 2+1}{2}+\frac{10\times 4+3}{4}$$

Expand \frac{45.8}{4} by multiplying both numerator and the denominator by 10.

$$\frac{458}{40}+\frac{5\times 2+1}{2}+\frac{10\times 4+3}{4}$$

Reduce the fraction \frac{458}{40} to lowest terms by extracting and canceling out 2.

$$\frac{229}{20}+\frac{5\times 2+1}{2}+\frac{10\times 4+3}{4}$$

Multiply 5 and 2 to get 10.

$$\frac{229}{20}+\frac{10+1}{2}+\frac{10\times 4+3}{4}$$

Add 10 and 1 to get 11.

$$\frac{229}{20}+\frac{11}{2}+\frac{10\times 4+3}{4}$$

Least common multiple of 20 and 2 is 20. Convert \frac{229}{20} and \frac{11}{2} to fractions with denominator 20.

$$\frac{229}{20}+\frac{110}{20}+\frac{10\times 4+3}{4}$$

Since \frac{229}{20} and \frac{110}{20} have the same denominator, add them by adding their numerators.

$$\frac{229+110}{20}+\frac{10\times 4+3}{4}$$

Add 229 and 110 to get 339.

$$\frac{339}{20}+\frac{10\times 4+3}{4}$$

Multiply 10 and 4 to get 40.

$$\frac{339}{20}+\frac{40+3}{4}$$

Add 40 and 3 to get 43.

$$\frac{339}{20}+\frac{43}{4}$$

Least common multiple of 20 and 4 is 20. Convert \frac{339}{20} and \frac{43}{4} to fractions with denominator 20.

$$\frac{339}{20}+\frac{215}{20}$$

Since \frac{339}{20} and \frac{215}{20} have the same denominator, add them by adding their numerators.

$$\frac{339+215}{20}$$

Add 339 and 215 to get 554.

$$\frac{554}{20}$$

Reduce the fraction \frac{554}{20} to lowest terms by extracting and canceling out 2.

$$\frac{277}{10}$$

Factor

$$\frac{277}{2 \cdot 5} = 27\frac{7}{10} = 27.7$$