Basic Math Examples

$\frac{1}{2} + (\frac{2}{3} + \frac{3}{4}) - (\frac{4}{5} \cdot \frac{5}{6})$

Step 1

Remove parentheses.

$\frac{1}{2} + \frac{2}{3} + \frac{3}{4} - (\frac{4}{5} \cdot \frac{5}{6})$

Step 2

Simplify each term.

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Step 2.1

Cancel the common factor of $2$ .

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Step 2.1.1

Factor $2$ out of $4$ .

$\frac{1}{2} + \frac{2}{3} + \frac{3}{4} - (\frac{2 (2)}{5} \cdot \frac{5}{6})$

Step 2.1.2

Factor $2$ out of $6$ .

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

Step 2.1.3

Cancel the common factor.

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

Step 2.1.4

Rewrite the expression.

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

Step 2.2

Cancel the common factor of $5$ .

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Step 2.2.1

Cancel the common factor.

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

Step 2.2.2

Rewrite the expression.

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

Step 2.3

Combine $2$ and $\frac{1}{3}$ .

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

Step 3

Combine fractions.

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Step 3.1

Combine the numerators over the common denominator.

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

Step 3.2

Subtract $2$ from $2$ .

$\frac{1}{2} + \frac{0}{3} + \frac{3}{4}$

Step 4

Find the common denominator.

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Step 4.1

Multiply $\frac{1}{2}$ by $\frac{6}{6}$ .

$\frac{1}{2} \cdot \frac{6}{6} + \frac{0}{3} + \frac{3}{4}$

Step 4.2

Multiply $\frac{1}{2}$ by $\frac{6}{6}$ .

$\frac{6}{2 \cdot 6} + \frac{0}{3} + \frac{3}{4}$

Step 4.3

Multiply $\frac{0}{3}$ by $\frac{4}{4}$ .

$\frac{6}{2 \cdot 6} + \frac{0}{3} \cdot \frac{4}{4} + \frac{3}{4}$

Step 4.4

Multiply $\frac{0}{3}$ by $\frac{4}{4}$ .

$\frac{6}{2 \cdot 6} + \frac{0 \cdot 4}{3 \cdot 4} + \frac{3}{4}$

Step 4.5

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

$\frac{6}{2 \cdot 6} + \frac{0 \cdot 4}{3 \cdot 4} + \frac{3}{4} \cdot \frac{3}{3}$

Step 4.6

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

$\frac{6}{2 \cdot 6} + \frac{0 \cdot 4}{3 \cdot 4} + \frac{3 \cdot 3}{4 \cdot 3}$

Step 4.7

Multiply $2$ by $6$ .

$\frac{6}{12} + \frac{0 \cdot 4}{3 \cdot 4} + \frac{3 \cdot 3}{4 \cdot 3}$

Step 4.8

Multiply $3$ by $4$ .

$\frac{6}{12} + \frac{0 \cdot 4}{12} + \frac{3 \cdot 3}{4 \cdot 3}$

Step 4.9

Reorder the factors of $4 \cdot 3$ .

$\frac{6}{12} + \frac{0 \cdot 4}{12} + \frac{3 \cdot 3}{3 \cdot 4}$

Step 4.10

Multiply $3$ by $4$ .

$\frac{6}{12} + \frac{0 \cdot 4}{12} + \frac{3 \cdot 3}{12}$

Step 5

Combine the numerators over the common denominator.

$\frac{6 + 0 \cdot 4 + 3 \cdot 3}{12}$

Step 6

Simplify each term.

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Step 6.1

Multiply $0$ by $4$ .

$\frac{6 + 0 + 3 \cdot 3}{12}$

Step 6.2

Multiply $3$ by $3$ .

$\frac{6 + 0 + 9}{12}$

Step 7

Reduce the expression by cancelling the common factors.

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Step 7.1

Add $6$ and $0$ .

$\frac{6 + 9}{12}$

Step 7.2

Add $6$ and $9$ .

$\frac{15}{12}$

Step 7.3

Cancel the common factor of $15$ and $12$ .

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Step 7.3.1

Factor $3$ out of $15$ .

$\frac{3 (5)}{12}$

Step 7.3.2

Cancel the common factors.

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Step 7.3.2.1

Factor $3$ out of $12$ .

$\frac{3 \cdot 5}{3 \cdot 4}$

Step 7.3.2.2

Cancel the common factor.

$\frac{3 \cdot 5}{3 \cdot 4}$

Step 7.3.2.3

Rewrite the expression.

$\frac{5}{4}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{5}{4}$

Decimal Form:

$1.25$

Mixed Number Form:

$1 \frac{1}{4}$