Evaluate 10 7/9+(-9 2/3)

$10 \frac{7}{9} + (- 9 \frac{2}{3})$

Step 1

Remove parentheses.

$10 \frac{7}{9} - 9 \frac{2}{3}$

Step 2

Convert $10 \frac{7}{9}$ to an improper fraction.

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

$10 + \frac{7}{9} - 9 \frac{2}{3}$

Add $10$ and $\frac{7}{9}$ .

To write $10$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$10 \cdot \frac{9}{9} + \frac{7}{9} - 9 \frac{2}{3}$

Combine $10$ and $\frac{9}{9}$ .

$\frac{10 \cdot 9}{9} + \frac{7}{9} - 9 \frac{2}{3}$

Combine the numerators over the common denominator.

$\frac{10 \cdot 9 + 7}{9} - 9 \frac{2}{3}$

Simplify the numerator.

Multiply $10$ by $9$ .

$\frac{90 + 7}{9} - 9 \frac{2}{3}$

Add $90$ and $7$ .

$\frac{97}{9} - 9 \frac{2}{3}$

Step 3

Convert $9 \frac{2}{3}$ to an improper fraction.

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

$\frac{97}{9} - (9 + \frac{2}{3})$

Add $9$ and $\frac{2}{3}$ .

To write $9$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{97}{9} - (9 \cdot \frac{3}{3} + \frac{2}{3})$

Combine $9$ and $\frac{3}{3}$ .

$\frac{97}{9} - (\frac{9 \cdot 3}{3} + \frac{2}{3})$

Combine the numerators over the common denominator.

$\frac{97}{9} - \frac{9 \cdot 3 + 2}{3}$

Simplify the numerator.

Multiply $9$ by $3$ .

$\frac{97}{9} - \frac{27 + 2}{3}$

Add $27$ and $2$ .

$\frac{97}{9} - \frac{29}{3}$

Step 4

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

$\frac{97}{9} - \frac{29}{3} \cdot \frac{3}{3}$

Step 5

Write each expression with a common denominator of $9$ , by multiplying each by an appropriate factor of $1$ .

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

$\frac{97}{9} - \frac{29 \cdot 3}{3 \cdot 3}$

Multiply $3$ by $3$ .

$\frac{97}{9} - \frac{29 \cdot 3}{9}$

Step 6

Combine the numerators over the common denominator.

$\frac{97 - 29 \cdot 3}{9}$

Step 7

Simplify the numerator.

Multiply $- 29$ by $3$ .

$\frac{97 - 87}{9}$

Subtract $87$ from $97$ .

$\frac{10}{9}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{10}{9}$

Decimal Form:

$1.\overline{1}$

Mixed Number Form:

$1 \frac{1}{9}$

Evaluate 10 7/9+(-9 2/3)

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