Evaluate 2/3+1/4*2/5-3/4+5/2

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

Step 1

Simplify each term.

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

$\frac{2}{3} + \frac{1}{2 (2)} \cdot \frac{2}{5} - \frac{3}{4} + \frac{5}{2}$

Cancel the common factor.

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

Rewrite the expression.

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

Multiply $\frac{1}{2}$ by $\frac{1}{5}$ .

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

Multiply $2$ by $5$ .

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

Step 2

Find the common denominator.

Multiply $\frac{2}{3}$ by $\frac{20}{20}$ .

$\frac{2}{3} \cdot \frac{20}{20} + \frac{1}{10} - \frac{3}{4} + \frac{5}{2}$

Multiply $\frac{2}{3}$ by $\frac{20}{20}$ .

$\frac{2 \cdot 20}{3 \cdot 20} + \frac{1}{10} - \frac{3}{4} + \frac{5}{2}$

Multiply $\frac{1}{10}$ by $\frac{6}{6}$ .

$\frac{2 \cdot 20}{3 \cdot 20} + \frac{1}{10} \cdot \frac{6}{6} - \frac{3}{4} + \frac{5}{2}$

Multiply $\frac{1}{10}$ by $\frac{6}{6}$ .

$\frac{2 \cdot 20}{3 \cdot 20} + \frac{6}{10 \cdot 6} - \frac{3}{4} + \frac{5}{2}$

Multiply $\frac{3}{4}$ by $\frac{15}{15}$ .

$\frac{2 \cdot 20}{3 \cdot 20} + \frac{6}{10 \cdot 6} - (\frac{3}{4} \cdot \frac{15}{15}) + \frac{5}{2}$

Multiply $\frac{3}{4}$ by $\frac{15}{15}$ .

$\frac{2 \cdot 20}{3 \cdot 20} + \frac{6}{10 \cdot 6} - \frac{3 \cdot 15}{4 \cdot 15} + \frac{5}{2}$

Multiply $\frac{5}{2}$ by $\frac{30}{30}$ .

$\frac{2 \cdot 20}{3 \cdot 20} + \frac{6}{10 \cdot 6} - \frac{3 \cdot 15}{4 \cdot 15} + \frac{5}{2} \cdot \frac{30}{30}$

Multiply $\frac{5}{2}$ by $\frac{30}{30}$ .

$\frac{2 \cdot 20}{3 \cdot 20} + \frac{6}{10 \cdot 6} - \frac{3 \cdot 15}{4 \cdot 15} + \frac{5 \cdot 30}{2 \cdot 30}$

Multiply $3$ by $20$ .

$\frac{2 \cdot 20}{60} + \frac{6}{10 \cdot 6} - \frac{3 \cdot 15}{4 \cdot 15} + \frac{5 \cdot 30}{2 \cdot 30}$

Reorder the factors of $10 \cdot 6$ .

$\frac{2 \cdot 20}{60} + \frac{6}{6 \cdot 10} - \frac{3 \cdot 15}{4 \cdot 15} + \frac{5 \cdot 30}{2 \cdot 30}$

Multiply $6$ by $10$ .

$\frac{2 \cdot 20}{60} + \frac{6}{60} - \frac{3 \cdot 15}{4 \cdot 15} + \frac{5 \cdot 30}{2 \cdot 30}$

Multiply $4$ by $15$ .

$\frac{2 \cdot 20}{60} + \frac{6}{60} - \frac{3 \cdot 15}{60} + \frac{5 \cdot 30}{2 \cdot 30}$

Multiply $2$ by $30$ .

$\frac{2 \cdot 20}{60} + \frac{6}{60} - \frac{3 \cdot 15}{60} + \frac{5 \cdot 30}{60}$

Step 3

Combine the numerators over the common denominator.

$\frac{2 \cdot 20 + 6 - 3 \cdot 15 + 5 \cdot 30}{60}$

Step 4

Simplify each term.

Multiply $2$ by $20$ .

$\frac{40 + 6 - 3 \cdot 15 + 5 \cdot 30}{60}$

Multiply $- 3$ by $15$ .

$\frac{40 + 6 - 45 + 5 \cdot 30}{60}$

Multiply $5$ by $30$ .

$\frac{40 + 6 - 45 + 150}{60}$

Step 5

Simplify by adding and subtracting.

Add $40$ and $6$ .

$\frac{46 - 45 + 150}{60}$

Subtract $45$ from $46$ .

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

Add $1$ and $150$ .

$\frac{151}{60}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{151}{60}$

Decimal Form:

$2.51\overline{6}$

Mixed Number Form:

$2 \frac{31}{60}$

Evaluate 2/3+1/4*2/5-3/4+5/2

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