Basic Math Examples

2 \frac{1}{3} - 3 \frac{1}{3}

$2 \frac{1}{3} - 3 \frac{1}{3}$

Step 1

Convert

2 \frac{1}{3}

$2 \frac{1}{3}$ to an improper fraction.

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Step 1.1

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

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

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

Step 1.2

Add

2

$2$ and

\frac{1}{3}

$\frac{1}{3}$ .

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Step 1.2.1

To write

2

$2$ as a fraction with a common denominator, multiply by

\frac{3}{3}

$\frac{3}{3}$ .

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

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

Step 1.2.2

Combine

2

$2$ and

\frac{3}{3}

$\frac{3}{3}$ .

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

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

Step 1.2.3

Combine the numerators over the common denominator.

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

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

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply

2

$2$ by

3

$3$ .

\frac{6 + 1}{3} - 3 \frac{1}{3}

$\frac{6 + 1}{3} - 3 \frac{1}{3}$

Step 1.2.4.2

Add

6

$6$ and

1

$1$ .

\frac{7}{3} - 3 \frac{1}{3}

$\frac{7}{3} - 3 \frac{1}{3}$

\frac{7}{3} - 3 \frac{1}{3}

$\frac{7}{3} - 3 \frac{1}{3}$

\frac{7}{3} - 3 \frac{1}{3}

$\frac{7}{3} - 3 \frac{1}{3}$

\frac{7}{3} - 3 \frac{1}{3}

$\frac{7}{3} - 3 \frac{1}{3}$

Step 2

Convert

3 \frac{1}{3}

$3 \frac{1}{3}$ to an improper fraction.

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Step 2.1

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

\frac{7}{3} - (3 + \frac{1}{3})

$\frac{7}{3} - (3 + \frac{1}{3})$

Step 2.2

Add

3

$3$ and

\frac{1}{3}

$\frac{1}{3}$ .

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Step 2.2.1

To write

3

$3$ as a fraction with a common denominator, multiply by

\frac{3}{3}

$\frac{3}{3}$ .

\frac{7}{3} - (3 \cdot \frac{3}{3} + \frac{1}{3})

$\frac{7}{3} - (3 \cdot \frac{3}{3} + \frac{1}{3})$

Step 2.2.2

Combine

3

$3$ and

\frac{3}{3}

$\frac{3}{3}$ .

\frac{7}{3} - (\frac{3 \cdot 3}{3} + \frac{1}{3})

$\frac{7}{3} - (\frac{3 \cdot 3}{3} + \frac{1}{3})$

Step 2.2.3

Combine the numerators over the common denominator.

\frac{7}{3} - \frac{3 \cdot 3 + 1}{3}

$\frac{7}{3} - \frac{3 \cdot 3 + 1}{3}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply

3

$3$ by

3

$3$ .

\frac{7}{3} - \frac{9 + 1}{3}

$\frac{7}{3} - \frac{9 + 1}{3}$

Step 2.2.4.2

Add

9

$9$ and

1

$1$ .

\frac{7}{3} - \frac{10}{3}

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

\frac{7}{3} - \frac{10}{3}

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

\frac{7}{3} - \frac{10}{3}

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

\frac{7}{3} - \frac{10}{3}

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

Step 3

Combine the numerators over the common denominator.

\frac{7 - 10}{3}

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

Step 4

Simplify the expression.

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Step 4.1

Subtract

10

$10$ from

7

$7$ .

\frac{- 3}{3}

$\frac{- 3}{3}$

Step 4.2

Divide

- 3

$- 3$ by

3

$3$ .

- 1

$- 1$

- 1

$- 1$