Basic Math Examples

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

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

Step 1

Convert

1 \frac{1}{2}

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

Tap for more steps...

Step 1.1

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

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

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

Step 1.2

Add

1

$1$ and

\frac{1}{2}

$\frac{1}{2}$ .

Tap for more steps...

Step 1.2.1

Write

1

$1$ as a fraction with a common denominator.

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

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

Step 1.2.2

Combine the numerators over the common denominator.

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

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

Step 1.2.3

Add

2

$2$ and

1

$1$ .

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

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

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

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

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

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

Step 2

To write

\frac{3}{2}

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

\frac{3}{3}

$\frac{3}{3}$ .

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

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

Step 3

To write

- \frac{2}{3}

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

\frac{2}{2}

$\frac{2}{2}$ .

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

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

Step 4

Write each expression with a common denominator of

6

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

1

$1$ .

Tap for more steps...

Step 4.1

Multiply

\frac{3}{2}

$\frac{3}{2}$ by

\frac{3}{3}

$\frac{3}{3}$ .

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

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

Step 4.2

Multiply

2

$2$ by

3

$3$ .

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

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

Step 4.3

Multiply

\frac{2}{3}

$\frac{2}{3}$ by

\frac{2}{2}

$\frac{2}{2}$ .

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

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

Step 4.4

Multiply

3

$3$ by

2

$2$ .

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

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

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

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

Step 5

Combine the numerators over the common denominator.

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

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

Step 6

Simplify the numerator.

Tap for more steps...

Step 6.1

Multiply

3

$3$ by

3

$3$ .

\frac{9 - 2 \cdot 2}{6}

$\frac{9 - 2 \cdot 2}{6}$

Step 6.2

Multiply

- 2

$- 2$ by

2

$2$ .

\frac{9 - 4}{6}

$\frac{9 - 4}{6}$

Step 6.3

Subtract

4

$4$ from

9

$9$ .

\frac{5}{6}

$\frac{5}{6}$

\frac{5}{6}

$\frac{5}{6}$

Step 7

The result can be shown in multiple forms.

Exact Form:

\frac{5}{6}

$\frac{5}{6}$

Decimal Form:

0.8 ¯ 3

$0.8\overline{3}$