Solve 2/3+1/4*2/5-3/4+frac{5}{2}=

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

Evaluate

$$\frac{151}{60}\approx 2.516666667$$

Solution Steps

Multiply \frac{1}{4} times \frac{2}{5} by multiplying numerator times numerator and denominator times denominator.

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

Do the multiplications in the fraction \frac{1\times 2}{4\times 5}.

$$\frac{2}{3}+\frac{2}{20}-\frac{3}{4}+\frac{5}{2}$$

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

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

Least common multiple of 3 and 10 is 30. Convert \frac{2}{3} and \frac{1}{10} to fractions with denominator 30.

$$\frac{20}{30}+\frac{3}{30}-\frac{3}{4}+\frac{5}{2}$$

Since \frac{20}{30} and \frac{3}{30} have the same denominator, add them by adding their numerators.

$$\frac{20+3}{30}-\frac{3}{4}+\frac{5}{2}$$

Add 20 and 3 to get 23.

$$\frac{23}{30}-\frac{3}{4}+\frac{5}{2}$$

Least common multiple of 30 and 4 is 60. Convert \frac{23}{30} and \frac{3}{4} to fractions with denominator 60.

$$\frac{46}{60}-\frac{45}{60}+\frac{5}{2}$$

Since \frac{46}{60} and \frac{45}{60} have the same denominator, subtract them by subtracting their numerators.

$$\frac{46-45}{60}+\frac{5}{2}$$

Subtract 45 from 46 to get 1.

$$\frac{1}{60}+\frac{5}{2}$$

Least common multiple of 60 and 2 is 60. Convert \frac{1}{60} and \frac{5}{2} to fractions with denominator 60.

$$\frac{1}{60}+\frac{150}{60}$$

Since \frac{1}{60} and \frac{150}{60} have the same denominator, add them by adding their numerators.

$$\frac{1+150}{60}$$

Add 1 and 150 to get 151.

$$\frac{151}{60}$$

Factor

$$\frac{151}{2 ^ {2} \cdot 3 \cdot 5} = 2\frac{31}{60} = 2.5166666666666666$$