Evaluate 7/9-(3/4)÷(9/10)+2/9

$\frac{7}{9} - \frac{3}{4} \div \frac{9}{10} + \frac{2}{9}$

Step 1

Combine fractions.

Combine the numerators over the common denominator.

$\frac{7 + 2}{9} + \frac{- \frac{3}{4}}{\frac{9}{10}}$

Add $7$ and $2$ .

$\frac{9}{9} + \frac{- \frac{3}{4}}{\frac{9}{10}}$

Step 2

Simplify each term.

Divide $9$ by $9$ .

$1 + \frac{- \frac{3}{4}}{\frac{9}{10}}$

Multiply the numerator by the reciprocal of the denominator.

$1 - \frac{3}{4} \cdot \frac{10}{9}$

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{3}{4}$ into the numerator.

$1 + \frac{- 3}{4} \cdot \frac{10}{9}$

Factor $3$ out of $- 3$ .

$1 + \frac{3 (- 1)}{4} \cdot \frac{10}{9}$

Factor $3$ out of $9$ .

$1 + \frac{3 \cdot - 1}{4} \cdot \frac{10}{3 \cdot 3}$

Cancel the common factor.

$1 + \frac{3 \cdot - 1}{4} \cdot \frac{10}{3 \cdot 3}$

Rewrite the expression.

$1 + \frac{- 1}{4} \cdot \frac{10}{3}$

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

$1 + \frac{- 1}{2 (2)} \cdot \frac{10}{3}$

Factor $2$ out of $10$ .

$1 + \frac{- 1}{2 \cdot 2} \cdot \frac{2 \cdot 5}{3}$

Cancel the common factor.

$1 + \frac{- 1}{2 \cdot 2} \cdot \frac{2 \cdot 5}{3}$

Rewrite the expression.

$1 + \frac{- 1}{2} \cdot \frac{5}{3}$

Multiply $\frac{- 1}{2}$ by $\frac{5}{3}$ .

$1 + \frac{- 1 \cdot 5}{2 \cdot 3}$

Multiply $- 1$ by $5$ .

$1 + \frac{- 5}{2 \cdot 3}$

Multiply $2$ by $3$ .

$1 + \frac{- 5}{6}$

Move the negative in front of the fraction.

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

Step 3

Simplify the expression.

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

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

Combine the numerators over the common denominator.

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

Subtract $5$ from $6$ .

$\frac{1}{6}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{6}$

Decimal Form:

$0.1\overline{6}$

Evaluate 7/9-(3/4)÷(9/10)+2/9

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