Basic Math Examples

$(\frac{7}{8} - \frac{3}{16}) \div (\frac{1}{3} - \frac{1}{4})$

Step 1

Rewrite the division as a fraction.

$\frac{\frac{7}{8} - \frac{3}{16}}{\frac{1}{3} - \frac{1}{4}}$

Step 2

Multiply the numerator and denominator of the fraction by $48$ .

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Step 2.1

Multiply $\frac{\frac{7}{8} - \frac{3}{16}}{\frac{1}{3} - \frac{1}{4}}$ by $\frac{48}{48}$ .

$\frac{48}{48} \cdot \frac{\frac{7}{8} - \frac{3}{16}}{\frac{1}{3} - \frac{1}{4}}$

Step 2.2

Combine.

$\frac{48 (\frac{7}{8} - \frac{3}{16})}{48 (\frac{1}{3} - \frac{1}{4})}$

Step 3

Apply the distributive property.

$\frac{48 (\frac{7}{8}) + 48 (- \frac{3}{16})}{48 (\frac{1}{3}) + 48 (- \frac{1}{4})}$

Step 4

Simplify by cancelling.

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Step 4.1

Cancel the common factor of $8$ .

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Step 4.1.1

Factor $8$ out of $48$ .

$\frac{8 (6) \frac{7}{8} + 48 (- \frac{3}{16})}{48 (\frac{1}{3}) + 48 (- \frac{1}{4})}$

Step 4.1.2

Cancel the common factor.

$\frac{8 \cdot 6 \frac{7}{8} + 48 (- \frac{3}{16})}{48 (\frac{1}{3}) + 48 (- \frac{1}{4})}$

Step 4.1.3

Rewrite the expression.

$\frac{6 \cdot 7 + 48 (- \frac{3}{16})}{48 (\frac{1}{3}) + 48 (- \frac{1}{4})}$

Step 4.2

Multiply $6$ by $7$ .

$\frac{42 + 48 (- \frac{3}{16})}{48 (\frac{1}{3}) + 48 (- \frac{1}{4})}$

Step 4.3

Cancel the common factor of $16$ .

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Step 4.3.1

Move the leading negative in $- \frac{3}{16}$ into the numerator.

$\frac{42 + 48 (\frac{- 3}{16})}{48 (\frac{1}{3}) + 48 (- \frac{1}{4})}$

Step 4.3.2

Factor $16$ out of $48$ .

$\frac{42 + 16 (3) \frac{- 3}{16}}{48 (\frac{1}{3}) + 48 (- \frac{1}{4})}$

Step 4.3.3

Cancel the common factor.

$\frac{42 + 16 \cdot 3 \frac{- 3}{16}}{48 (\frac{1}{3}) + 48 (- \frac{1}{4})}$

Step 4.3.4

Rewrite the expression.

$\frac{42 + 3 \cdot - 3}{48 (\frac{1}{3}) + 48 (- \frac{1}{4})}$

Step 4.4

Multiply $3$ by $- 3$ .

$\frac{42 - 9}{48 (\frac{1}{3}) + 48 (- \frac{1}{4})}$

Step 4.5

Cancel the common factor of $3$ .

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Step 4.5.1

Factor $3$ out of $48$ .

$\frac{42 - 9}{3 (16) \frac{1}{3} + 48 (- \frac{1}{4})}$

Step 4.5.2

Cancel the common factor.

$\frac{42 - 9}{3 \cdot 16 \frac{1}{3} + 48 (- \frac{1}{4})}$

Step 4.5.3

Rewrite the expression.

$\frac{42 - 9}{16 + 48 (- \frac{1}{4})}$

Step 4.6

Cancel the common factor of $4$ .

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Step 4.6.1

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

$\frac{42 - 9}{16 + 48 (\frac{- 1}{4})}$

Step 4.6.2

Factor $4$ out of $48$ .

$\frac{42 - 9}{16 + 4 (12) \frac{- 1}{4}}$

Step 4.6.3

Cancel the common factor.

$\frac{42 - 9}{16 + 4 \cdot 12 \frac{- 1}{4}}$

Step 4.6.4

Rewrite the expression.

$\frac{42 - 9}{16 + 12 \cdot - 1}$

Step 4.7

Multiply $12$ by $- 1$ .

$\frac{42 - 9}{16 - 12}$

Step 5

Simplify by subtracting numbers.

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Step 5.1

Subtract $9$ from $42$ .

$\frac{33}{16 - 12}$

Step 5.2

Subtract $12$ from $16$ .

$\frac{33}{4}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{33}{4}$

Decimal Form:

$8.25$

Mixed Number Form:

$8 \frac{1}{4}$