Algebra Examples

$\frac{10}{\frac{3}{\frac{1}{6}}} - (2.8 + 1.2)$

Step 1

Simplify each term.

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Step 1.1

Multiply the numerator by the reciprocal of the denominator.

$10 \frac{\frac{1}{6}}{3} - (2.8 + 1.2)$

Step 1.2

Multiply the numerator by the reciprocal of the denominator.

$10 (\frac{1}{6} \cdot \frac{1}{3}) - (2.8 + 1.2)$

Step 1.3

Multiply $\frac{1}{6} \cdot \frac{1}{3}$ .

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Step 1.3.1

Multiply $\frac{1}{6}$ by $\frac{1}{3}$ .

$10 \frac{1}{6 \cdot 3} - (2.8 + 1.2)$

Step 1.3.2

Multiply $6$ by $3$ .

$10 (\frac{1}{18}) - (2.8 + 1.2)$

Step 1.4

Cancel the common factor of $2$ .

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Step 1.4.1

Factor $2$ out of $10$ .

$2 (5) \frac{1}{18} - (2.8 + 1.2)$

Step 1.4.2

Factor $2$ out of $18$ .

$2 \cdot 5 \frac{1}{2 \cdot 9} - (2.8 + 1.2)$

Step 1.4.3

Cancel the common factor.

$2 \cdot 5 \frac{1}{2 \cdot 9} - (2.8 + 1.2)$

Step 1.4.4

Rewrite the expression.

$5 (\frac{1}{9}) - (2.8 + 1.2)$

Step 1.5

Combine $5$ and $\frac{1}{9}$ .

$\frac{5}{9} - (2.8 + 1.2)$

Step 1.6

Add $2.8$ and $1.2$ .

$\frac{5}{9} - 1 \cdot 4$

Step 1.7

Multiply $- 1$ by $4$ .

$\frac{5}{9} - 4$

Step 2

To write $- 4$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$\frac{5}{9} - 4 \cdot \frac{9}{9}$

Step 3

Combine $- 4$ and $\frac{9}{9}$ .

$\frac{5}{9} + \frac{- 4 \cdot 9}{9}$

Step 4

Combine the numerators over the common denominator.

$\frac{5 - 4 \cdot 9}{9}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $- 4$ by $9$ .

$\frac{5 - 36}{9}$

Step 5.2

Subtract $36$ from $5$ .

$\frac{- 31}{9}$

Step 6

Cancel the common factor of $- 31$ and $9$ .

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Step 6.1

Rewrite $- 31$ as $1 (- 31)$ .

$\frac{1 (- 31)}{9}$

Step 6.2

Cancel the common factors.

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Step 6.2.1

Rewrite $9$ as $1 (9)$ .

$\frac{1 \cdot - 31}{1 \cdot 9}$

Step 6.2.2

Cancel the common factor.

$\frac{1 \cdot - 31}{1 \cdot 9}$

Step 6.2.3

Rewrite the expression.

$\frac{- 31}{9}$

Step 7

Move the negative in front of the fraction.

$- \frac{31}{9}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$- \frac{31}{9}$

Decimal Form:

$- 3.\overline{4}$

Mixed Number Form:

$- 3 \frac{4}{9}$