Pre-Algebra Examples

$9 - 3 \div \frac{1}{3} + 1$

Step 1

Find the common denominator.

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Step 1.1

Write $9$ as a fraction with denominator $1$ .

$\frac{9}{1} - 3 \div \frac{1}{3} + 1$

Step 1.2

Multiply $\frac{9}{1}$ by $\frac{\frac{1}{3}}{\frac{1}{3}}$ .

$\frac{9}{1} \cdot \frac{\frac{1}{3}}{\frac{1}{3}} - 3 \div \frac{1}{3} + 1$

Step 1.3

Multiply $\frac{9}{1}$ by $\frac{\frac{1}{3}}{\frac{1}{3}}$ .

$\frac{9 (\frac{1}{3})}{\frac{1}{3}} - 3 \div \frac{1}{3} + 1$

Step 1.4

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

$\frac{9 (\frac{1}{3})}{\frac{1}{3}} - 3 \div \frac{1}{3} + \frac{1}{1}$

Step 1.5

Multiply $\frac{1}{1}$ by $\frac{\frac{1}{3}}{\frac{1}{3}}$ .

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

Step 1.6

Multiply $\frac{1}{1}$ by $\frac{\frac{1}{3}}{\frac{1}{3}}$ .

$\frac{9 (\frac{1}{3})}{\frac{1}{3}} - 3 \div \frac{1}{3} + \frac{\frac{1}{3}}{\frac{1}{3}}$

Step 2

Combine the numerators over the common denominator.

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

Step 3

Cancel the common factor of $3$ .

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Step 3.1

Factor $3$ out of $9$ .

$\frac{3 (3) \frac{1}{3} - 3 + \frac{1}{3}}{\frac{1}{3}}$

Step 3.2

Cancel the common factor.

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

Step 3.3

Rewrite the expression.

$\frac{3 - 3 + \frac{1}{3}}{\frac{1}{3}}$

Step 4

Find the common denominator.

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Step 4.1

Write $3$ as a fraction with denominator $1$ .

$\frac{\frac{3}{1} - 3 + \frac{1}{3}}{\frac{1}{3}}$

Step 4.2

Multiply $\frac{3}{1}$ by $\frac{3}{3}$ .

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

Step 4.3

Multiply $\frac{3}{1}$ by $\frac{3}{3}$ .

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

Step 4.4

Write $- 3$ as a fraction with denominator $1$ .

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

Step 4.5

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

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

Step 4.6

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

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

Step 5

Combine the numerators over the common denominator.

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

Step 6

Simplify each term.

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Step 6.1

Multiply $3$ by $3$ .

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

Step 6.2

Multiply $- 3$ by $3$ .

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

Step 7

Reduce the expression by cancelling the common factors.

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Step 7.1

Subtract $9$ from $9$ .

$\frac{\frac{0 + 1}{3}}{\frac{1}{3}}$

Step 7.2

Add $0$ and $1$ .

$\frac{\frac{1}{3}}{\frac{1}{3}}$

Step 7.3

Cancel the common factor of $\frac{1}{3}$ .

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Step 7.3.1

Cancel the common factor.

$\frac{\frac{1}{3}}{\frac{1}{3}}$

Step 7.3.2

Rewrite the expression.

$1$