Basic Math Examples

$(- \frac{5}{16} - \frac{4}{3}) + \frac{1}{12}$

Step 1

Find the common denominator.

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Step 1.1

Multiply $\frac{5}{16}$ by $\frac{3}{3}$ .

$- (\frac{5}{16} \cdot \frac{3}{3}) - \frac{4}{3} + \frac{1}{12}$

Step 1.2

Multiply $\frac{5}{16}$ by $\frac{3}{3}$ .

$- \frac{5 \cdot 3}{16 \cdot 3} - \frac{4}{3} + \frac{1}{12}$

Step 1.3

Multiply $\frac{4}{3}$ by $\frac{16}{16}$ .

$- \frac{5 \cdot 3}{16 \cdot 3} - (\frac{4}{3} \cdot \frac{16}{16}) + \frac{1}{12}$

Step 1.4

Multiply $\frac{4}{3}$ by $\frac{16}{16}$ .

$- \frac{5 \cdot 3}{16 \cdot 3} - \frac{4 \cdot 16}{3 \cdot 16} + \frac{1}{12}$

Step 1.5

Multiply $\frac{1}{12}$ by $\frac{4}{4}$ .

$- \frac{5 \cdot 3}{16 \cdot 3} - \frac{4 \cdot 16}{3 \cdot 16} + \frac{1}{12} \cdot \frac{4}{4}$

Step 1.6

Multiply $\frac{1}{12}$ by $\frac{4}{4}$ .

$- \frac{5 \cdot 3}{16 \cdot 3} - \frac{4 \cdot 16}{3 \cdot 16} + \frac{4}{12 \cdot 4}$

Step 1.7

Reorder the factors of $16 \cdot 3$ .

$- \frac{5 \cdot 3}{3 \cdot 16} - \frac{4 \cdot 16}{3 \cdot 16} + \frac{4}{12 \cdot 4}$

Step 1.8

Multiply $3$ by $16$ .

$- \frac{5 \cdot 3}{48} - \frac{4 \cdot 16}{3 \cdot 16} + \frac{4}{12 \cdot 4}$

Step 1.9

Multiply $3$ by $16$ .

$- \frac{5 \cdot 3}{48} - \frac{4 \cdot 16}{48} + \frac{4}{12 \cdot 4}$

Step 1.10

Reorder the factors of $12 \cdot 4$ .

$- \frac{5 \cdot 3}{48} - \frac{4 \cdot 16}{48} + \frac{4}{4 \cdot 12}$

Step 1.11

Multiply $4$ by $12$ .

$- \frac{5 \cdot 3}{48} - \frac{4 \cdot 16}{48} + \frac{4}{48}$

Step 2

Combine the numerators over the common denominator.

$\frac{- 5 \cdot 3 - 4 \cdot 16 + 4}{48}$

Step 3

Simplify each term.

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Step 3.1

Multiply $- 5$ by $3$ .

$\frac{- 15 - 4 \cdot 16 + 4}{48}$

Step 3.2

Multiply $- 4$ by $16$ .

$\frac{- 15 - 64 + 4}{48}$

Step 4

Reduce the expression by cancelling the common factors.

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Step 4.1

Subtract $64$ from $- 15$ .

$\frac{- 79 + 4}{48}$

Step 4.2

Add $- 79$ and $4$ .

$\frac{- 75}{48}$

Step 4.3

Cancel the common factor of $- 75$ and $48$ .

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Step 4.3.1

Factor $3$ out of $- 75$ .

$\frac{3 (- 25)}{48}$

Step 4.3.2

Cancel the common factors.

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Step 4.3.2.1

Factor $3$ out of $48$ .

$\frac{3 \cdot - 25}{3 \cdot 16}$

Step 4.3.2.2

Cancel the common factor.

$\frac{3 \cdot - 25}{3 \cdot 16}$

Step 4.3.2.3

Rewrite the expression.

$\frac{- 25}{16}$

Step 4.4

Move the negative in front of the fraction.

$- \frac{25}{16}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$- \frac{25}{16}$

Decimal Form:

$- 1.5625$

Mixed Number Form:

$- 1 \frac{9}{16}$