Solve 12/3+23/4+33/4+12/5

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

Evaluate

$$\frac{287}{30}\approx 9.566666667$$

Solution Steps

Multiply 1 and 3 to get 3.

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

Add 3 and 2 to get 5.

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

Multiply 2 and 4 to get 8.

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

Add 8 and 3 to get 11.

$$\frac{5}{3}+\frac{11}{4}+\frac{3\times 4+3}{4}+\frac{1\times 5+2}{5}$$

Least common multiple of 3 and 4 is 12. Convert \frac{5}{3} and \frac{11}{4} to fractions with denominator 12.

$$\frac{20}{12}+\frac{33}{12}+\frac{3\times 4+3}{4}+\frac{1\times 5+2}{5}$$

Since \frac{20}{12} and \frac{33}{12} have the same denominator, add them by adding their numerators.

$$\frac{20+33}{12}+\frac{3\times 4+3}{4}+\frac{1\times 5+2}{5}$$

Add 20 and 33 to get 53.

$$\frac{53}{12}+\frac{3\times 4+3}{4}+\frac{1\times 5+2}{5}$$

Multiply 3 and 4 to get 12.

$$\frac{53}{12}+\frac{12+3}{4}+\frac{1\times 5+2}{5}$$

Add 12 and 3 to get 15.

$$\frac{53}{12}+\frac{15}{4}+\frac{1\times 5+2}{5}$$

Least common multiple of 12 and 4 is 12. Convert \frac{53}{12} and \frac{15}{4} to fractions with denominator 12.

$$\frac{53}{12}+\frac{45}{12}+\frac{1\times 5+2}{5}$$

Since \frac{53}{12} and \frac{45}{12} have the same denominator, add them by adding their numerators.

$$\frac{53+45}{12}+\frac{1\times 5+2}{5}$$

Add 53 and 45 to get 98.

$$\frac{98}{12}+\frac{1\times 5+2}{5}$$

Reduce the fraction \frac{98}{12} to lowest terms by extracting and canceling out 2.

$$\frac{49}{6}+\frac{1\times 5+2}{5}$$

Multiply 1 and 5 to get 5.

$$\frac{49}{6}+\frac{5+2}{5}$$

Add 5 and 2 to get 7.

$$\frac{49}{6}+\frac{7}{5}$$

Least common multiple of 6 and 5 is 30. Convert \frac{49}{6} and \frac{7}{5} to fractions with denominator 30.

$$\frac{245}{30}+\frac{42}{30}$$

Since \frac{245}{30} and \frac{42}{30} have the same denominator, add them by adding their numerators.

$$\frac{245+42}{30}$$

Add 245 and 42 to get 287.

$$\frac{287}{30}$$

Factor

$$\frac{7 \cdot 41}{2 \cdot 3 \cdot 5} = 9\frac{17}{30} = 9.566666666666666$$