Pre-Algebra Examples

$7 \frac{5}{9} - (- 2 \frac{2}{9}) - 1 \frac{7}{9}$

Step 1

Convert $7 \frac{5}{9}$ to an improper fraction.

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Step 1.1

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

$7 + \frac{5}{9} - (- 2 \frac{2}{9}) - 1 \frac{7}{9}$

Step 1.2

Add $7$ and $\frac{5}{9}$ .

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Step 1.2.1

To write $7$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$7 \cdot \frac{9}{9} + \frac{5}{9} - (- 2 \frac{2}{9}) - 1 \frac{7}{9}$

Step 1.2.2

Combine $7$ and $\frac{9}{9}$ .

$\frac{7 \cdot 9}{9} + \frac{5}{9} - (- 2 \frac{2}{9}) - 1 \frac{7}{9}$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{7 \cdot 9 + 5}{9} - (- 2 \frac{2}{9}) - 1 \frac{7}{9}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $7$ by $9$ .

$\frac{63 + 5}{9} - (- 2 \frac{2}{9}) - 1 \frac{7}{9}$

Step 1.2.4.2

Add $63$ and $5$ .

$\frac{68}{9} - (- 2 \frac{2}{9}) - 1 \frac{7}{9}$

Step 2

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

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Step 2.1

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

$\frac{68}{9} - - (2 + \frac{2}{9}) - 1 \frac{7}{9}$

Step 2.2

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

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Step 2.2.1

To write $2$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$\frac{68}{9} - - (2 \cdot \frac{9}{9} + \frac{2}{9}) - 1 \frac{7}{9}$

Step 2.2.2

Combine $2$ and $\frac{9}{9}$ .

$\frac{68}{9} - - (\frac{2 \cdot 9}{9} + \frac{2}{9}) - 1 \frac{7}{9}$

Step 2.2.3

Combine the numerators over the common denominator.

$\frac{68}{9} - - \frac{2 \cdot 9 + 2}{9} - 1 \frac{7}{9}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply $2$ by $9$ .

$\frac{68}{9} - - \frac{18 + 2}{9} - 1 \frac{7}{9}$

Step 2.2.4.2

Add $18$ and $2$ .

$\frac{68}{9} - - \frac{20}{9} - 1 \frac{7}{9}$

Step 3

Convert $1 \frac{7}{9}$ to an improper fraction.

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Step 3.1

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

$\frac{68}{9} - - \frac{20}{9} - (1 + \frac{7}{9})$

Step 3.2

Add $1$ and $\frac{7}{9}$ .

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Step 3.2.1

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

$\frac{68}{9} - - \frac{20}{9} - (\frac{9}{9} + \frac{7}{9})$

Step 3.2.2

Combine the numerators over the common denominator.

$\frac{68}{9} - - \frac{20}{9} - \frac{9 + 7}{9}$

Step 3.2.3

Add $9$ and $7$ .

$\frac{68}{9} - - \frac{20}{9} - \frac{16}{9}$

Step 4

Combine the numerators over the common denominator.

$- - \frac{20}{9} + \frac{68 - 16}{9}$

Step 5

Subtract $16$ from $68$ .

$- - \frac{20}{9} + \frac{52}{9}$

Step 6

Multiply $- - \frac{20}{9}$ .

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Step 6.1

Multiply $- 1$ by $- 1$ .

$1 (\frac{20}{9}) + \frac{52}{9}$

Step 6.2

Multiply $\frac{20}{9}$ by $1$ .

$\frac{20}{9} + \frac{52}{9}$

Step 7

Combine the numerators over the common denominator.

$\frac{20 + 52}{9}$

Step 8

Simplify the expression.

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Step 8.1

Add $20$ and $52$ .

$\frac{72}{9}$

Step 8.2

Divide $72$ by $9$ .

$8$