Basic Math Examples

$(\frac{7}{2} + \frac{3}{4}) \div (\frac{5}{6} - \frac{1}{4})$

Step 1

Rewrite the division as a fraction.

$\frac{\frac{7}{2} + \frac{3}{4}}{\frac{5}{6} - \frac{1}{4}}$

Step 2

Multiply the numerator and denominator of the fraction by $12$ .

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Step 2.1

Multiply $\frac{\frac{7}{2} + \frac{3}{4}}{\frac{5}{6} - \frac{1}{4}}$ by $\frac{12}{12}$ .

$\frac{12}{12} \cdot \frac{\frac{7}{2} + \frac{3}{4}}{\frac{5}{6} - \frac{1}{4}}$

Step 2.2

Combine.

$\frac{12 (\frac{7}{2} + \frac{3}{4})}{12 (\frac{5}{6} - \frac{1}{4})}$

Step 3

Apply the distributive property.

$\frac{12 (\frac{7}{2}) + 12 (\frac{3}{4})}{12 (\frac{5}{6}) + 12 (- \frac{1}{4})}$

Step 4

Simplify by cancelling.

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Step 4.1

Cancel the common factor of $2$ .

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Step 4.1.1

Factor $2$ out of $12$ .

$\frac{2 (6) \frac{7}{2} + 12 (\frac{3}{4})}{12 (\frac{5}{6}) + 12 (- \frac{1}{4})}$

Step 4.1.2

Cancel the common factor.

$\frac{2 \cdot 6 \frac{7}{2} + 12 (\frac{3}{4})}{12 (\frac{5}{6}) + 12 (- \frac{1}{4})}$

Step 4.1.3

Rewrite the expression.

$\frac{6 \cdot 7 + 12 (\frac{3}{4})}{12 (\frac{5}{6}) + 12 (- \frac{1}{4})}$

Step 4.2

Multiply $6$ by $7$ .

$\frac{42 + 12 (\frac{3}{4})}{12 (\frac{5}{6}) + 12 (- \frac{1}{4})}$

Step 4.3

Cancel the common factor of $4$ .

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Step 4.3.1

Factor $4$ out of $12$ .

$\frac{42 + 4 (3) \frac{3}{4}}{12 (\frac{5}{6}) + 12 (- \frac{1}{4})}$

Step 4.3.2

Cancel the common factor.

$\frac{42 + 4 \cdot 3 \frac{3}{4}}{12 (\frac{5}{6}) + 12 (- \frac{1}{4})}$

Step 4.3.3

Rewrite the expression.

$\frac{42 + 3 \cdot 3}{12 (\frac{5}{6}) + 12 (- \frac{1}{4})}$

Step 4.4

Multiply $3$ by $3$ .

$\frac{42 + 9}{12 (\frac{5}{6}) + 12 (- \frac{1}{4})}$

Step 4.5

Cancel the common factor of $6$ .

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Step 4.5.1

Factor $6$ out of $12$ .

$\frac{42 + 9}{6 (2) \frac{5}{6} + 12 (- \frac{1}{4})}$

Step 4.5.2

Cancel the common factor.

$\frac{42 + 9}{6 \cdot 2 \frac{5}{6} + 12 (- \frac{1}{4})}$

Step 4.5.3

Rewrite the expression.

$\frac{42 + 9}{2 \cdot 5 + 12 (- \frac{1}{4})}$

Step 4.6

Multiply $2$ by $5$ .

$\frac{42 + 9}{10 + 12 (- \frac{1}{4})}$

Step 4.7

Cancel the common factor of $4$ .

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Step 4.7.1

Move the leading negative in $- \frac{1}{4}$ into the numerator.

$\frac{42 + 9}{10 + 12 (\frac{- 1}{4})}$

Step 4.7.2

Factor $4$ out of $12$ .

$\frac{42 + 9}{10 + 4 (3) \frac{- 1}{4}}$

Step 4.7.3

Cancel the common factor.

$\frac{42 + 9}{10 + 4 \cdot 3 \frac{- 1}{4}}$

Step 4.7.4

Rewrite the expression.

$\frac{42 + 9}{10 + 3 \cdot - 1}$

Step 4.8

Multiply $3$ by $- 1$ .

$\frac{42 + 9}{10 - 3}$

Step 5

Simplify by adding and subtracting.

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Step 5.1

Add $42$ and $9$ .

$\frac{51}{10 - 3}$

Step 5.2

Subtract $3$ from $10$ .

$\frac{51}{7}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{51}{7}$

Decimal Form:

$7.\overline{285714}$

Mixed Number Form:

$7 \frac{2}{7}$