Basic Math Examples

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

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

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} - 1 \frac{1}{2}

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

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} - 1 \frac{1}{2}

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

Step 1.2.2

Combine

2

$2$ and

\frac{3}{3}

$\frac{3}{3}$ .

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

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

Step 1.2.3

Combine the numerators over the common denominator.

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

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

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} - 1 \frac{1}{2}

$\frac{6 + 1}{3} - 1 \frac{1}{2}$

Step 1.2.4.2

Add

6

$6$ and

1

$1$ .

\frac{7}{3} - 1 \frac{1}{2}

$\frac{7}{3} - 1 \frac{1}{2}$

\frac{7}{3} - 1 \frac{1}{2}

$\frac{7}{3} - 1 \frac{1}{2}$

\frac{7}{3} - 1 \frac{1}{2}

$\frac{7}{3} - 1 \frac{1}{2}$

\frac{7}{3} - 1 \frac{1}{2}

$\frac{7}{3} - 1 \frac{1}{2}$

Step 2

Convert

1 \frac{1}{2}

$1 \frac{1}{2}$ 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} - (1 + \frac{1}{2})

$\frac{7}{3} - (1 + \frac{1}{2})$

Step 2.2

Add

1

$1$ and

\frac{1}{2}

$\frac{1}{2}$ .

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Step 2.2.1

Write

1

$1$ as a fraction with a common denominator.

\frac{7}{3} - (\frac{2}{2} + \frac{1}{2})

$\frac{7}{3} - (\frac{2}{2} + \frac{1}{2})$

Step 2.2.2

Combine the numerators over the common denominator.

\frac{7}{3} - \frac{2 + 1}{2}

$\frac{7}{3} - \frac{2 + 1}{2}$

Step 2.2.3

Add

2

$2$ and

1

$1$ .

\frac{7}{3} - \frac{3}{2}

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

\frac{7}{3} - \frac{3}{2}

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

\frac{7}{3} - \frac{3}{2}

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

Step 3

To write

\frac{7}{3}

$\frac{7}{3}$ as a fraction with a common denominator, multiply by

\frac{2}{2}

$\frac{2}{2}$ .

\frac{7}{3} \cdot \frac{2}{2} - \frac{3}{2}

$\frac{7}{3} \cdot \frac{2}{2} - \frac{3}{2}$

Step 4

To write

- \frac{3}{2}

$- \frac{3}{2}$ as a fraction with a common denominator, multiply by

\frac{3}{3}

$\frac{3}{3}$ .

\frac{7}{3} \cdot \frac{2}{2} - \frac{3}{2} \cdot \frac{3}{3}

$\frac{7}{3} \cdot \frac{2}{2} - \frac{3}{2} \cdot \frac{3}{3}$

Step 5

Write each expression with a common denominator of

6

$6$ , by multiplying each by an appropriate factor of

1

$1$ .

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Step 5.1

Multiply

\frac{7}{3}

$\frac{7}{3}$ by

\frac{2}{2}

$\frac{2}{2}$ .

\frac{7 \cdot 2}{3 \cdot 2} - \frac{3}{2} \cdot \frac{3}{3}

$\frac{7 \cdot 2}{3 \cdot 2} - \frac{3}{2} \cdot \frac{3}{3}$

Step 5.2

Multiply

3

$3$ by

2

$2$ .

\frac{7 \cdot 2}{6} - \frac{3}{2} \cdot \frac{3}{3}

$\frac{7 \cdot 2}{6} - \frac{3}{2} \cdot \frac{3}{3}$

Step 5.3

Multiply

\frac{3}{2}

$\frac{3}{2}$ by

\frac{3}{3}

$\frac{3}{3}$ .

\frac{7 \cdot 2}{6} - \frac{3 \cdot 3}{2 \cdot 3}

$\frac{7 \cdot 2}{6} - \frac{3 \cdot 3}{2 \cdot 3}$

Step 5.4

Multiply

$2$ by

$3$ .

$\frac{7 \cdot 2}{6} - \frac{3 \cdot 3}{6}$

Step 6

Combine the numerators over the common denominator.

$\frac{7 \cdot 2 - 3 \cdot 3}{6}$

Step 7

Simplify the numerator.

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Step 7.1

Multiply

$7$ by

$2$ .

$\frac{14 - 3 \cdot 3}{6}$

Step 7.2

Multiply

$- 3$ by

$3$ .

$\frac{14 - 9}{6}$

Step 7.3

Subtract

$9$ from

$14$ .

$\frac{5}{6}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{5}{6}$

Decimal Form:

$0.8\overline{3}$