Basic Math Examples

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

Step 1

Remove parentheses.

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

Step 2

Find the common denominator.

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Step 2.1

Multiply $\frac{1}{2}$ by $\frac{30}{30}$ .

$\frac{1}{2} \cdot \frac{30}{30} + \frac{2}{3} - \frac{5}{4} + \frac{3}{5}$

Step 2.2

Multiply $\frac{1}{2}$ by $\frac{30}{30}$ .

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

Step 2.3

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

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

Step 2.4

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

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

Step 2.5

Multiply $\frac{5}{4}$ by $\frac{15}{15}$ .

$\frac{30}{2 \cdot 30} + \frac{2 \cdot 20}{3 \cdot 20} - (\frac{5}{4} \cdot \frac{15}{15}) + \frac{3}{5}$

Step 2.6

Multiply $\frac{5}{4}$ by $\frac{15}{15}$ .

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

Step 2.7

Multiply $\frac{3}{5}$ by $\frac{12}{12}$ .

$\frac{30}{2 \cdot 30} + \frac{2 \cdot 20}{3 \cdot 20} - \frac{5 \cdot 15}{4 \cdot 15} + \frac{3}{5} \cdot \frac{12}{12}$

Step 2.8

Multiply $\frac{3}{5}$ by $\frac{12}{12}$ .

$\frac{30}{2 \cdot 30} + \frac{2 \cdot 20}{3 \cdot 20} - \frac{5 \cdot 15}{4 \cdot 15} + \frac{3 \cdot 12}{5 \cdot 12}$

Step 2.9

Multiply $2$ by $30$ .

$\frac{30}{60} + \frac{2 \cdot 20}{3 \cdot 20} - \frac{5 \cdot 15}{4 \cdot 15} + \frac{3 \cdot 12}{5 \cdot 12}$

Step 2.10

Multiply $3$ by $20$ .

$\frac{30}{60} + \frac{2 \cdot 20}{60} - \frac{5 \cdot 15}{4 \cdot 15} + \frac{3 \cdot 12}{5 \cdot 12}$

Step 2.11

Multiply $4$ by $15$ .

$\frac{30}{60} + \frac{2 \cdot 20}{60} - \frac{5 \cdot 15}{60} + \frac{3 \cdot 12}{5 \cdot 12}$

Step 2.12

Multiply $5$ by $12$ .

$\frac{30}{60} + \frac{2 \cdot 20}{60} - \frac{5 \cdot 15}{60} + \frac{3 \cdot 12}{60}$

Step 3

Combine the numerators over the common denominator.

$\frac{30 + 2 \cdot 20 - 5 \cdot 15 + 3 \cdot 12}{60}$

Step 4

Simplify each term.

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Step 4.1

Multiply $2$ by $20$ .

$\frac{30 + 40 - 5 \cdot 15 + 3 \cdot 12}{60}$

Step 4.2

Multiply $- 5$ by $15$ .

$\frac{30 + 40 - 75 + 3 \cdot 12}{60}$

Step 4.3

Multiply $3$ by $12$ .

$\frac{30 + 40 - 75 + 36}{60}$

Step 5

Simplify by adding and subtracting.

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Step 5.1

Add $30$ and $40$ .

$\frac{70 - 75 + 36}{60}$

Step 5.2

Subtract $75$ from $70$ .

$\frac{- 5 + 36}{60}$

Step 5.3

Add $- 5$ and $36$ .

$\frac{31}{60}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{31}{60}$

Decimal Form:

$0.51\overline{6}$