Evaluate -7 5/6+(-7 1/4)

$- 7 \frac{5}{6} + (- 7 \frac{1}{4})$

Step 1

Remove parentheses.

$- 7 \frac{5}{6} - 7 \frac{1}{4}$

Step 2

Convert $7 \frac{5}{6}$ to an improper fraction.

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

$- (7 + \frac{5}{6}) - 7 \frac{1}{4}$

Add $7$ and $\frac{5}{6}$ .

To write $7$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$- (7 \cdot \frac{6}{6} + \frac{5}{6}) - 7 \frac{1}{4}$

Combine $7$ and $\frac{6}{6}$ .

$- (\frac{7 \cdot 6}{6} + \frac{5}{6}) - 7 \frac{1}{4}$

Combine the numerators over the common denominator.

$- \frac{7 \cdot 6 + 5}{6} - 7 \frac{1}{4}$

Simplify the numerator.

Multiply $7$ by $6$ .

$- \frac{42 + 5}{6} - 7 \frac{1}{4}$

Add $42$ and $5$ .

$- \frac{47}{6} - 7 \frac{1}{4}$

Step 3

Convert $7 \frac{1}{4}$ to an improper fraction.

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

$- \frac{47}{6} - (7 + \frac{1}{4})$

Add $7$ and $\frac{1}{4}$ .

To write $7$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$- \frac{47}{6} - (7 \cdot \frac{4}{4} + \frac{1}{4})$

Combine $7$ and $\frac{4}{4}$ .

$- \frac{47}{6} - (\frac{7 \cdot 4}{4} + \frac{1}{4})$

Combine the numerators over the common denominator.

$- \frac{47}{6} - \frac{7 \cdot 4 + 1}{4}$

Simplify the numerator.

Multiply $7$ by $4$ .

$- \frac{47}{6} - \frac{28 + 1}{4}$

Add $28$ and $1$ .

$- \frac{47}{6} - \frac{29}{4}$

Step 4

To write $- \frac{47}{6}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- \frac{47}{6} \cdot \frac{2}{2} - \frac{29}{4}$

Step 5

To write $- \frac{29}{4}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$- \frac{47}{6} \cdot \frac{2}{2} - \frac{29}{4} \cdot \frac{3}{3}$

Step 6

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

Multiply $\frac{47}{6}$ by $\frac{2}{2}$ .

$- \frac{47 \cdot 2}{6 \cdot 2} - \frac{29}{4} \cdot \frac{3}{3}$

Multiply $6$ by $2$ .

$- \frac{47 \cdot 2}{12} - \frac{29}{4} \cdot \frac{3}{3}$

Multiply $\frac{29}{4}$ by $\frac{3}{3}$ .

$- \frac{47 \cdot 2}{12} - \frac{29 \cdot 3}{4 \cdot 3}$

Multiply $4$ by $3$ .

$- \frac{47 \cdot 2}{12} - \frac{29 \cdot 3}{12}$

Step 7

Combine the numerators over the common denominator.

$\frac{- 47 \cdot 2 - 29 \cdot 3}{12}$

Step 8

Simplify the numerator.

Multiply $- 47$ by $2$ .

$\frac{- 94 - 29 \cdot 3}{12}$

Multiply $- 29$ by $3$ .

$\frac{- 94 - 87}{12}$

Subtract $87$ from $- 94$ .

$\frac{- 181}{12}$

Step 9

Move the negative in front of the fraction.

$- \frac{181}{12}$

Step 10

The result can be shown in multiple forms.

Exact Form:

$- \frac{181}{12}$

Decimal Form:

$- 15.08\overline{3}$

Mixed Number Form:

$- 15 \frac{1}{12}$

Evaluate -7 5/6+(-7 1/4)

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