Basic Math Examples

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

Step 1

Find the common denominator.

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Step 1.1

Write $3$ as a fraction with denominator $1$ .

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

Step 1.2

Multiply $\frac{3}{1}$ by $\frac{4}{4}$ .

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

Step 1.3

Multiply $\frac{3}{1}$ by $\frac{4}{4}$ .

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

Step 1.4

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

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

Step 1.5

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

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

Step 1.6

Multiply $2$ by $2$ .

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

Step 2

Combine the numerators over the common denominator.

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

Step 3

Simplify each term.

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Step 3.1

Multiply $3$ by $4$ .

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

Step 3.2

Multiply $\frac{2}{5} \cdot 2$ .

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Step 3.2.1

Combine $\frac{2}{5}$ and $2$ .

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

Step 3.2.2

Multiply $2$ by $2$ .

$\frac{12 + \frac{4}{5} - 3}{4}$

Step 4

Find the common denominator.

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Step 4.1

Write $12$ as a fraction with denominator $1$ .

$\frac{\frac{12}{1} + \frac{4}{5} - 3}{4}$

Step 4.2

Multiply $\frac{12}{1}$ by $\frac{5}{5}$ .

$\frac{\frac{12}{1} \cdot \frac{5}{5} + \frac{4}{5} - 3}{4}$

Step 4.3

Multiply $\frac{12}{1}$ by $\frac{5}{5}$ .

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

Step 4.4

Write $- 3$ as a fraction with denominator $1$ .

$\frac{\frac{12 \cdot 5}{5} + \frac{4}{5} + \frac{- 3}{1}}{4}$

Step 4.5

Multiply $\frac{- 3}{1}$ by $\frac{5}{5}$ .

$\frac{\frac{12 \cdot 5}{5} + \frac{4}{5} + \frac{- 3}{1} \cdot \frac{5}{5}}{4}$

Step 4.6

Multiply $\frac{- 3}{1}$ by $\frac{5}{5}$ .

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

Step 5

Combine the numerators over the common denominator.

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

Step 6

Simplify each term.

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Step 6.1

Multiply $12$ by $5$ .

$\frac{\frac{60 + 4 - 3 \cdot 5}{5}}{4}$

Step 6.2

Multiply $- 3$ by $5$ .

$\frac{\frac{60 + 4 - 15}{5}}{4}$

Step 7

Simplify by adding and subtracting.

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Step 7.1

Add $60$ and $4$ .

$\frac{\frac{64 - 15}{5}}{4}$

Step 7.2

Subtract $15$ from $64$ .

$\frac{\frac{49}{5}}{4}$

Step 8

Multiply the numerator by the reciprocal of the denominator.

$\frac{49}{5} \cdot \frac{1}{4}$

Step 9

Multiply $\frac{49}{5} \cdot \frac{1}{4}$ .

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Step 9.1

Multiply $\frac{49}{5}$ by $\frac{1}{4}$ .

$\frac{49}{5 \cdot 4}$

Step 9.2

Multiply $5$ by $4$ .

$\frac{49}{20}$

Step 10

The result can be shown in multiple forms.

Exact Form:

$\frac{49}{20}$

Decimal Form:

$2.45$

Mixed Number Form:

$2 \frac{9}{20}$