Basic Math Examples

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

Step 1

Remove parentheses.

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

Step 2

Find the common denominator.

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Step 2.1

Multiply $\frac{3}{2}$ by $\frac{30}{30}$ .

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

Step 2.2

Multiply $\frac{3}{2}$ by $\frac{30}{30}$ .

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

Step 2.3

Multiply $\frac{2}{5}$ by $\frac{12}{12}$ .

$\frac{3 \cdot 30}{2 \cdot 30} - (\frac{2}{5} \cdot \frac{12}{12}) + \frac{5}{4} - \frac{2}{3}$

Step 2.4

Multiply $\frac{2}{5}$ by $\frac{12}{12}$ .

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

Step 2.5

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

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

Step 2.6

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

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

Step 2.7

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

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

Step 2.8

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

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

Step 2.9

Multiply $2$ by $30$ .

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

Step 2.10

Multiply $5$ by $12$ .

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

Step 2.11

Multiply $4$ by $15$ .

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

Step 2.12

Multiply $3$ by $20$ .

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

Step 3

Combine the numerators over the common denominator.

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

Step 4

Simplify each term.

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Step 4.1

Multiply $3$ by $30$ .

$\frac{90 - 2 \cdot 12 + 5 \cdot 15 - 2 \cdot 20}{60}$

Step 4.2

Multiply $- 2$ by $12$ .

$\frac{90 - 24 + 5 \cdot 15 - 2 \cdot 20}{60}$

Step 4.3

Multiply $5$ by $15$ .

$\frac{90 - 24 + 75 - 2 \cdot 20}{60}$

Step 4.4

Multiply $- 2$ by $20$ .

$\frac{90 - 24 + 75 - 40}{60}$

Step 5

Simplify by adding and subtracting.

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Step 5.1

Subtract $24$ from $90$ .

$\frac{66 + 75 - 40}{60}$

Step 5.2

Add $66$ and $75$ .

$\frac{141 - 40}{60}$

Step 5.3

Subtract $40$ from $141$ .

$\frac{101}{60}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{101}{60}$

Decimal Form:

$1.68\overline{3}$

Mixed Number Form:

$1 \frac{41}{60}$