Evaluate (-2 5/6)-(-1 1/4)

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

Step 1

Convert $2 \frac{5}{6}$ to an improper fraction.

A mixed number is an addition of its whole and fractional parts.

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

Add $2$ and $\frac{5}{6}$ .

To write $2$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

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

Combine $2$ and $\frac{6}{6}$ .

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply $2$ by $6$ .

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

Add $12$ and $5$ .

$- \frac{17}{6} - (- 1 \frac{1}{4})$

Step 2

Convert $1 \frac{1}{4}$ to an improper fraction.

A mixed number is an addition of its whole and fractional parts.

$- \frac{17}{6} - - (1 + \frac{1}{4})$

Add $1$ and $\frac{1}{4}$ .

Write $1$ as a fraction with a common denominator.

$- \frac{17}{6} - - (\frac{4}{4} + \frac{1}{4})$

Combine the numerators over the common denominator.

$- \frac{17}{6} - - \frac{4 + 1}{4}$

Add $4$ and $1$ .

$- \frac{17}{6} - - \frac{5}{4}$

Step 3

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

Multiply $- 1$ by $- 1$ .

$- \frac{17}{6} + 1 (\frac{5}{4})$

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

$- \frac{17}{6} + \frac{5}{4}$

Step 4

To write $- \frac{17}{6}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- \frac{17}{6} \cdot \frac{2}{2} + \frac{5}{4}$

Step 5

To write $\frac{5}{4}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$- \frac{17}{6} \cdot \frac{2}{2} + \frac{5}{4} \cdot \frac{3}{3}$

Step 6

Write each expression with a common denominator of $12$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{17}{6}$ by $\frac{2}{2}$ .

$- \frac{17 \cdot 2}{6 \cdot 2} + \frac{5}{4} \cdot \frac{3}{3}$

Multiply $6$ by $2$ .

$- \frac{17 \cdot 2}{12} + \frac{5}{4} \cdot \frac{3}{3}$

Multiply $\frac{5}{4}$ by $\frac{3}{3}$ .

$- \frac{17 \cdot 2}{12} + \frac{5 \cdot 3}{4 \cdot 3}$

Multiply $4$ by $3$ .

$- \frac{17 \cdot 2}{12} + \frac{5 \cdot 3}{12}$

Step 7

Combine the numerators over the common denominator.

$\frac{- 17 \cdot 2 + 5 \cdot 3}{12}$

Step 8

Simplify the numerator.

Multiply $- 17$ by $2$ .

$\frac{- 34 + 5 \cdot 3}{12}$

Multiply $5$ by $3$ .

$\frac{- 34 + 15}{12}$

Add $- 34$ and $15$ .

$\frac{- 19}{12}$

Step 9

Move the negative in front of the fraction.

$- \frac{19}{12}$

Step 10

The result can be shown in multiple forms.

Exact Form:

$- \frac{19}{12}$

Decimal Form:

$- 1.58\overline{3}$

Mixed Number Form:

$- 1 \frac{7}{12}$

Evaluate (-2 5/6)-(-1 1/4)

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