Basic Math Examples

3 \frac{1}{5} - 2 \frac{1}{2}

$3 \frac{1}{5} - 2 \frac{1}{2}$

Step 1

Convert

3 \frac{1}{5}

$3 \frac{1}{5}$ to an improper fraction.

Tap for more steps...

Step 1.1

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

3 + \frac{1}{5} - 2 \frac{1}{2}

$3 + \frac{1}{5} - 2 \frac{1}{2}$

Step 1.2

Add

3

$3$ and

\frac{1}{5}

$\frac{1}{5}$ .

Tap for more steps...

Step 1.2.1

To write

3

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

\frac{5}{5}

$\frac{5}{5}$ .

3 \cdot \frac{5}{5} + \frac{1}{5} - 2 \frac{1}{2}

$3 \cdot \frac{5}{5} + \frac{1}{5} - 2 \frac{1}{2}$

Step 1.2.2

Combine

3

$3$ and

\frac{5}{5}

$\frac{5}{5}$ .

\frac{3 \cdot 5}{5} + \frac{1}{5} - 2 \frac{1}{2}

$\frac{3 \cdot 5}{5} + \frac{1}{5} - 2 \frac{1}{2}$

Step 1.2.3

Combine the numerators over the common denominator.

\frac{3 \cdot 5 + 1}{5} - 2 \frac{1}{2}

$\frac{3 \cdot 5 + 1}{5} - 2 \frac{1}{2}$

Step 1.2.4

Simplify the numerator.

Tap for more steps...

Step 1.2.4.1

Multiply

3

$3$ by

5

$5$ .

\frac{15 + 1}{5} - 2 \frac{1}{2}

$\frac{15 + 1}{5} - 2 \frac{1}{2}$

Step 1.2.4.2

Add

15

$15$ and

1

$1$ .

\frac{16}{5} - 2 \frac{1}{2}

$\frac{16}{5} - 2 \frac{1}{2}$

\frac{16}{5} - 2 \frac{1}{2}

$\frac{16}{5} - 2 \frac{1}{2}$

\frac{16}{5} - 2 \frac{1}{2}

$\frac{16}{5} - 2 \frac{1}{2}$

\frac{16}{5} - 2 \frac{1}{2}

$\frac{16}{5} - 2 \frac{1}{2}$

Step 2

Convert

2 \frac{1}{2}

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

Tap for more steps...

Step 2.1

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

\frac{16}{5} - (2 + \frac{1}{2})

$\frac{16}{5} - (2 + \frac{1}{2})$

Step 2.2

Add

2

$2$ and

\frac{1}{2}

$\frac{1}{2}$ .

Tap for more steps...

Step 2.2.1

To write

2

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

\frac{2}{2}

$\frac{2}{2}$ .

\frac{16}{5} - (2 \cdot \frac{2}{2} + \frac{1}{2})

$\frac{16}{5} - (2 \cdot \frac{2}{2} + \frac{1}{2})$

Step 2.2.2

Combine

2

$2$ and

\frac{2}{2}

$\frac{2}{2}$ .

\frac{16}{5} - (\frac{2 \cdot 2}{2} + \frac{1}{2})

$\frac{16}{5} - (\frac{2 \cdot 2}{2} + \frac{1}{2})$

Step 2.2.3

Combine the numerators over the common denominator.

\frac{16}{5} - \frac{2 \cdot 2 + 1}{2}

$\frac{16}{5} - \frac{2 \cdot 2 + 1}{2}$

Step 2.2.4

Simplify the numerator.

Tap for more steps...

Step 2.2.4.1

Multiply

2

$2$ by

2

$2$ .

\frac{16}{5} - \frac{4 + 1}{2}

$\frac{16}{5} - \frac{4 + 1}{2}$

Step 2.2.4.2

Add

4

$4$ and

1

$1$ .

\frac{16}{5} - \frac{5}{2}

$\frac{16}{5} - \frac{5}{2}$

\frac{16}{5} - \frac{5}{2}

$\frac{16}{5} - \frac{5}{2}$

\frac{16}{5} - \frac{5}{2}

$\frac{16}{5} - \frac{5}{2}$

\frac{16}{5} - \frac{5}{2}

$\frac{16}{5} - \frac{5}{2}$

Step 3

To write

\frac{16}{5}

$\frac{16}{5}$ as a fraction with a common denominator, multiply by

\frac{2}{2}

$\frac{2}{2}$ .

\frac{16}{5} \cdot \frac{2}{2} - \frac{5}{2}

$\frac{16}{5} \cdot \frac{2}{2} - \frac{5}{2}$

Step 4

To write

- \frac{5}{2}

$- \frac{5}{2}$ as a fraction with a common denominator, multiply by

\frac{5}{5}

$\frac{5}{5}$ .

\frac{16}{5} \cdot \frac{2}{2} - \frac{5}{2} \cdot \frac{5}{5}

$\frac{16}{5} \cdot \frac{2}{2} - \frac{5}{2} \cdot \frac{5}{5}$

Step 5

Write each expression with a common denominator of

10

$10$ , by multiplying each by an appropriate factor of

1

$1$ .

Tap for more steps...

Step 5.1

Multiply

\frac{16}{5}

$\frac{16}{5}$ by

\frac{2}{2}

$\frac{2}{2}$ .

\frac{16 \cdot 2}{5 \cdot 2} - \frac{5}{2} \cdot \frac{5}{5}

$\frac{16 \cdot 2}{5 \cdot 2} - \frac{5}{2} \cdot \frac{5}{5}$

Step 5.2

Multiply

5

$5$ by

2

$2$ .

\frac{16 \cdot 2}{10} - \frac{5}{2} \cdot \frac{5}{5}

$\frac{16 \cdot 2}{10} - \frac{5}{2} \cdot \frac{5}{5}$

Step 5.3

Multiply

\frac{5}{2}

$\frac{5}{2}$ by

\frac{5}{5}

$\frac{5}{5}$ .

\frac{16 \cdot 2}{10} - \frac{5 \cdot 5}{2 \cdot 5}

$\frac{16 \cdot 2}{10} - \frac{5 \cdot 5}{2 \cdot 5}$

Step 5.4

Multiply

2

$2$ by

5

$5$ .

\frac{16 \cdot 2}{10} - \frac{5 \cdot 5}{10}

$\frac{16 \cdot 2}{10} - \frac{5 \cdot 5}{10}$

\frac{16 \cdot 2}{10} - \frac{5 \cdot 5}{10}

$\frac{16 \cdot 2}{10} - \frac{5 \cdot 5}{10}$

Step 6

Combine the numerators over the common denominator.

\frac{16 \cdot 2 - 5 \cdot 5}{10}

$\frac{16 \cdot 2 - 5 \cdot 5}{10}$

Step 7

Simplify the numerator.

Tap for more steps...

Step 7.1

Multiply

16

$16$ by

2

$2$ .

\frac{32 - 5 \cdot 5}{10}

$\frac{32 - 5 \cdot 5}{10}$

Step 7.2

Multiply

- 5

$- 5$ by

5

$5$ .

\frac{32 - 25}{10}

$\frac{32 - 25}{10}$

Step 7.3

Subtract

25

$25$ from

32

$32$ .

\frac{7}{10}

$\frac{7}{10}$

\frac{7}{10}

$\frac{7}{10}$

Step 8

The result can be shown in multiple forms.

Exact Form:

\frac{7}{10}

$\frac{7}{10}$

Decimal Form:

0.7

$0.7$