Evaluate (2/5-1/6)+1÷(-4/5)

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

Step 1

Find the common denominator.

Multiply $\frac{2}{5}$ by $\frac{\frac{6 \cdot 4}{5}}{\frac{6 \cdot 4}{5}}$ .

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

Multiply $\frac{2}{5}$ by $\frac{\frac{6 \cdot 4}{5}}{\frac{6 \cdot 4}{5}}$ .

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

Multiply $\frac{1}{6}$ by $\frac{\frac{5 \cdot 4}{5}}{\frac{5 \cdot 4}{5}}$ .

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

Multiply $\frac{1}{6}$ by $\frac{\frac{5 \cdot 4}{5}}{\frac{5 \cdot 4}{5}}$ .

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

Multiply $1 \div (- \frac{4}{5})$ by $\frac{- 30}{- 30}$ .

$\frac{2 \frac{6 \cdot 4}{5}}{5 \frac{6 \cdot 4}{5}} - \frac{\frac{5 \cdot 4}{5}}{6 \frac{5 \cdot 4}{5}} + 1 \div (- \frac{4}{5}) \cdot \frac{- 30}{- 30}$

Multiply $1 \div (- \frac{4}{5})$ by $\frac{- 30}{- 30}$ .

$\frac{2 \frac{6 \cdot 4}{5}}{5 \frac{6 \cdot 4}{5}} - \frac{\frac{5 \cdot 4}{5}}{6 \frac{5 \cdot 4}{5}} + \frac{- 30}{- \frac{4}{5} \cdot - 30}$

Multiply $6$ by $4$ .

$\frac{2 \frac{6 \cdot 4}{5}}{5 (\frac{24}{5})} - \frac{\frac{5 \cdot 4}{5}}{6 \frac{5 \cdot 4}{5}} + \frac{- 30}{- \frac{4}{5} \cdot - 30}$

Combine $5$ and $\frac{24}{5}$ .

$\frac{2 \frac{6 \cdot 4}{5}}{\frac{5 \cdot 24}{5}} - \frac{\frac{5 \cdot 4}{5}}{6 \frac{5 \cdot 4}{5}} + \frac{- 30}{- \frac{4}{5} \cdot - 30}$

Multiply $5$ by $24$ .

$\frac{2 \frac{6 \cdot 4}{5}}{\frac{120}{5}} - \frac{\frac{5 \cdot 4}{5}}{6 \frac{5 \cdot 4}{5}} + \frac{- 30}{- \frac{4}{5} \cdot - 30}$

Multiply $5$ by $4$ .

$\frac{2 \frac{6 \cdot 4}{5}}{\frac{120}{5}} - \frac{\frac{5 \cdot 4}{5}}{6 (\frac{20}{5})} + \frac{- 30}{- \frac{4}{5} \cdot - 30}$

Combine $6$ and $\frac{20}{5}$ .

$\frac{2 \frac{6 \cdot 4}{5}}{\frac{120}{5}} - \frac{\frac{5 \cdot 4}{5}}{\frac{6 \cdot 20}{5}} + \frac{- 30}{- \frac{4}{5} \cdot - 30}$

Multiply $6$ by $20$ .

$\frac{2 \frac{6 \cdot 4}{5}}{\frac{120}{5}} - \frac{\frac{5 \cdot 4}{5}}{\frac{120}{5}} + \frac{- 30}{- \frac{4}{5} \cdot - 30}$

Reorder the factors of $- \frac{4}{5} \cdot - 30$ .

$\frac{2 \frac{6 \cdot 4}{5}}{\frac{120}{5}} - \frac{\frac{5 \cdot 4}{5}}{\frac{120}{5}} + \frac{- 30}{- 30 \cdot - 1 \frac{4}{5}}$

Multiply $- 30$ by $- 1$ .

$\frac{2 \frac{6 \cdot 4}{5}}{\frac{120}{5}} - \frac{\frac{5 \cdot 4}{5}}{\frac{120}{5}} + \frac{- 30}{30 (\frac{4}{5})}$

Combine $30$ and $\frac{4}{5}$ .

$\frac{2 \frac{6 \cdot 4}{5}}{\frac{120}{5}} - \frac{\frac{5 \cdot 4}{5}}{\frac{120}{5}} + \frac{- 30}{\frac{30 \cdot 4}{5}}$

Multiply $30$ by $4$ .

$\frac{2 \frac{6 \cdot 4}{5}}{\frac{120}{5}} - \frac{\frac{5 \cdot 4}{5}}{\frac{120}{5}} + \frac{- 30}{\frac{120}{5}}$

Step 2

Combine the numerators over the common denominator.

$\frac{2 \frac{6 \cdot 4}{5} - \frac{5 \cdot 4}{5} - 30}{\frac{120}{5}}$

Step 3

Simplify each term.

Multiply $6$ by $4$ .

$\frac{2 (\frac{24}{5}) - \frac{5 \cdot 4}{5} - 30}{\frac{120}{5}}$

Multiply $2 (\frac{24}{5})$ .

Combine $2$ and $\frac{24}{5}$ .

$\frac{\frac{2 \cdot 24}{5} - \frac{5 \cdot 4}{5} - 30}{\frac{120}{5}}$

Multiply $2$ by $24$ .

$\frac{\frac{48}{5} - \frac{5 \cdot 4}{5} - 30}{\frac{120}{5}}$

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{\frac{48}{5} - \frac{5 \cdot 4}{5} - 30}{\frac{120}{5}}$

Divide $4$ by $1$ .

$\frac{\frac{48}{5} - 1 \cdot 4 - 30}{\frac{120}{5}}$

Multiply $- 1$ by $4$ .

$\frac{\frac{48}{5} - 4 - 30}{\frac{120}{5}}$

Step 4

Find the common denominator.

Write $- 4$ as a fraction with denominator $1$ .

$\frac{\frac{48}{5} + \frac{- 4}{1} - 30}{\frac{120}{5}}$

Multiply $\frac{- 4}{1}$ by $\frac{5}{5}$ .

$\frac{\frac{48}{5} + \frac{- 4}{1} \cdot \frac{5}{5} - 30}{\frac{120}{5}}$

Multiply $\frac{- 4}{1}$ by $\frac{5}{5}$ .

$\frac{\frac{48}{5} + \frac{- 4 \cdot 5}{5} - 30}{\frac{120}{5}}$

Write $- 30$ as a fraction with denominator $1$ .

$\frac{\frac{48}{5} + \frac{- 4 \cdot 5}{5} + \frac{- 30}{1}}{\frac{120}{5}}$

Multiply $\frac{- 30}{1}$ by $\frac{5}{5}$ .

$\frac{\frac{48}{5} + \frac{- 4 \cdot 5}{5} + \frac{- 30}{1} \cdot \frac{5}{5}}{\frac{120}{5}}$

Multiply $\frac{- 30}{1}$ by $\frac{5}{5}$ .

$\frac{\frac{48}{5} + \frac{- 4 \cdot 5}{5} + \frac{- 30 \cdot 5}{5}}{\frac{120}{5}}$

Step 5

Combine the numerators over the common denominator.

$\frac{\frac{48 - 4 \cdot 5 - 30 \cdot 5}{5}}{\frac{120}{5}}$

Step 6

Simplify each term.

Multiply $- 4$ by $5$ .

$\frac{\frac{48 - 20 - 30 \cdot 5}{5}}{\frac{120}{5}}$

Multiply $- 30$ by $5$ .

$\frac{\frac{48 - 20 - 150}{5}}{\frac{120}{5}}$

Step 7

Reduce the expression by cancelling the common factors.

Subtract $20$ from $48$ .

$\frac{\frac{28 - 150}{5}}{\frac{120}{5}}$

Simplify the expression.

Subtract $150$ from $28$ .

$\frac{\frac{- 122}{5}}{\frac{120}{5}}$

Move the negative in front of the fraction.

$\frac{- \frac{122}{5}}{\frac{120}{5}}$

Cancel the common factor of $120$ and $5$ .

Factor $5$ out of $120$ .

$\frac{- \frac{122}{5}}{\frac{5 \cdot 24}{5}}$

Cancel the common factors.

Factor $5$ out of $5$ .

$\frac{- \frac{122}{5}}{\frac{5 \cdot 24}{5 (1)}}$

Cancel the common factor.

$\frac{- \frac{122}{5}}{\frac{5 \cdot 24}{5 \cdot 1}}$

Rewrite the expression.

$\frac{- \frac{122}{5}}{\frac{24}{1}}$

Divide $24$ by $1$ .

$\frac{- \frac{122}{5}}{24}$

Step 8

Multiply the numerator by the reciprocal of the denominator.

$- \frac{122}{5} \cdot \frac{1}{24}$

Step 9

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{122}{5}$ into the numerator.

$\frac{- 122}{5} \cdot \frac{1}{24}$

Factor $2$ out of $- 122$ .

$\frac{2 (- 61)}{5} \cdot \frac{1}{24}$

Factor $2$ out of $24$ .

$\frac{2 \cdot - 61}{5} \cdot \frac{1}{2 \cdot 12}$

Cancel the common factor.

$\frac{2 \cdot - 61}{5} \cdot \frac{1}{2 \cdot 12}$

Rewrite the expression.

$\frac{- 61}{5} \cdot \frac{1}{12}$

Step 10

Multiply $\frac{- 61}{5}$ by $\frac{1}{12}$ .

$\frac{- 61}{5 \cdot 12}$

Step 11

Simplify the expression.

Multiply $5$ by $12$ .

$\frac{- 61}{60}$

Move the negative in front of the fraction.

$- \frac{61}{60}$

Step 12

The result can be shown in multiple forms.

Exact Form:

$- \frac{61}{60}$

Decimal Form:

$- 1.01\overline{6}$

Mixed Number Form:

$- 1 \frac{1}{60}$

Evaluate (2/5-1/6)+1÷(-4/5)

Related Questions