Basic Math Examples

2 \frac{1}{3} - \frac{2}{3} + 1 \frac{4}{5}

$2 \frac{1}{3} - \frac{2}{3} + 1 \frac{4}{5}$

Step 1

Convert

2 \frac{1}{3}

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

Tap for more steps...

Step 1.1

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

2 + \frac{1}{3} - \frac{2}{3} + 1 \frac{4}{5}

$2 + \frac{1}{3} - \frac{2}{3} + 1 \frac{4}{5}$

Step 1.2

Add

2

$2$ and

\frac{1}{3}

$\frac{1}{3}$ .

Tap for more steps...

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} - \frac{2}{3} + 1 \frac{4}{5}

$2 \cdot \frac{3}{3} + \frac{1}{3} - \frac{2}{3} + 1 \frac{4}{5}$

Step 1.2.2

Combine

2

$2$ and

\frac{3}{3}

$\frac{3}{3}$ .

\frac{2 \cdot 3}{3} + \frac{1}{3} - \frac{2}{3} + 1 \frac{4}{5}

$\frac{2 \cdot 3}{3} + \frac{1}{3} - \frac{2}{3} + 1 \frac{4}{5}$

Step 1.2.3

Combine the numerators over the common denominator.

\frac{2 \cdot 3 + 1}{3} - \frac{2}{3} + 1 \frac{4}{5}

$\frac{2 \cdot 3 + 1}{3} - \frac{2}{3} + 1 \frac{4}{5}$

Step 1.2.4

Simplify the numerator.

Tap for more steps...

Step 1.2.4.1

Multiply

2

$2$ by

3

$3$ .

\frac{6 + 1}{3} - \frac{2}{3} + 1 \frac{4}{5}

$\frac{6 + 1}{3} - \frac{2}{3} + 1 \frac{4}{5}$

Step 1.2.4.2

Add

6

$6$ and

1

$1$ .

\frac{7}{3} - \frac{2}{3} + 1 \frac{4}{5}

$\frac{7}{3} - \frac{2}{3} + 1 \frac{4}{5}$

\frac{7}{3} - \frac{2}{3} + 1 \frac{4}{5}

$\frac{7}{3} - \frac{2}{3} + 1 \frac{4}{5}$

\frac{7}{3} - \frac{2}{3} + 1 \frac{4}{5}

$\frac{7}{3} - \frac{2}{3} + 1 \frac{4}{5}$

\frac{7}{3} - \frac{2}{3} + 1 \frac{4}{5}

$\frac{7}{3} - \frac{2}{3} + 1 \frac{4}{5}$

Step 2

Convert

1 \frac{4}{5}

$1 \frac{4}{5}$ to an improper fraction.

Tap for more steps...

Step 2.1

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

\frac{7}{3} - \frac{2}{3} + 1 + \frac{4}{5}

$\frac{7}{3} - \frac{2}{3} + 1 + \frac{4}{5}$

Step 2.2

Add

1

$1$ and

\frac{4}{5}

$\frac{4}{5}$ .

Tap for more steps...

Step 2.2.1

Write

1

$1$ as a fraction with a common denominator.

\frac{7}{3} - \frac{2}{3} + \frac{5}{5} + \frac{4}{5}

$\frac{7}{3} - \frac{2}{3} + \frac{5}{5} + \frac{4}{5}$

Step 2.2.2

Combine the numerators over the common denominator.

\frac{7}{3} - \frac{2}{3} + \frac{5 + 4}{5}

$\frac{7}{3} - \frac{2}{3} + \frac{5 + 4}{5}$

Step 2.2.3

Add

5

$5$ and

4

$4$ .

\frac{7}{3} - \frac{2}{3} + \frac{9}{5}

$\frac{7}{3} - \frac{2}{3} + \frac{9}{5}$

\frac{7}{3} - \frac{2}{3} + \frac{9}{5}

$\frac{7}{3} - \frac{2}{3} + \frac{9}{5}$

\frac{7}{3} - \frac{2}{3} + \frac{9}{5}

$\frac{7}{3} - \frac{2}{3} + \frac{9}{5}$

Step 3

Combine the numerators over the common denominator.

\frac{7 - 2}{3} + \frac{9}{5}

$\frac{7 - 2}{3} + \frac{9}{5}$

Step 4

Subtract

2

$2$ from

7

$7$ .

\frac{5}{3} + \frac{9}{5}

$\frac{5}{3} + \frac{9}{5}$

Step 5

To write

\frac{5}{3}

$\frac{5}{3}$ as a fraction with a common denominator, multiply by

\frac{5}{5}

$\frac{5}{5}$ .

\frac{5}{3} \cdot \frac{5}{5} + \frac{9}{5}

$\frac{5}{3} \cdot \frac{5}{5} + \frac{9}{5}$

Step 6

To write

\frac{9}{5}

$\frac{9}{5}$ as a fraction with a common denominator, multiply by

\frac{3}{3}

$\frac{3}{3}$ .

\frac{5}{3} \cdot \frac{5}{5} + \frac{9}{5} \cdot \frac{3}{3}

$\frac{5}{3} \cdot \frac{5}{5} + \frac{9}{5} \cdot \frac{3}{3}$

Step 7

Write each expression with a common denominator of

15

$15$ , by multiplying each by an appropriate factor of

1

$1$ .

Tap for more steps...

Step 7.1

Multiply

\frac{5}{3}

$\frac{5}{3}$ by

\frac{5}{5}

$\frac{5}{5}$ .

\frac{5 \cdot 5}{3 \cdot 5} + \frac{9}{5} \cdot \frac{3}{3}

$\frac{5 \cdot 5}{3 \cdot 5} + \frac{9}{5} \cdot \frac{3}{3}$

Step 7.2

Multiply

3

$3$ by

5

$5$ .

\frac{5 \cdot 5}{15} + \frac{9}{5} \cdot \frac{3}{3}

$\frac{5 \cdot 5}{15} + \frac{9}{5} \cdot \frac{3}{3}$

Step 7.3

Multiply

\frac{9}{5}

$\frac{9}{5}$ by

\frac{3}{3}

$\frac{3}{3}$ .

\frac{5 \cdot 5}{15} + \frac{9 \cdot 3}{5 \cdot 3}

$\frac{5 \cdot 5}{15} + \frac{9 \cdot 3}{5 \cdot 3}$

Step 7.4

Multiply

5

$5$ by

3

$3$ .

\frac{5 \cdot 5}{15} + \frac{9 \cdot 3}{15}

$\frac{5 \cdot 5}{15} + \frac{9 \cdot 3}{15}$

\frac{5 \cdot 5}{15} + \frac{9 \cdot 3}{15}

$\frac{5 \cdot 5}{15} + \frac{9 \cdot 3}{15}$

Step 8

Combine the numerators over the common denominator.

\frac{5 \cdot 5 + 9 \cdot 3}{15}

$\frac{5 \cdot 5 + 9 \cdot 3}{15}$

Step 9

Simplify the numerator.

Tap for more steps...

Step 9.1

Multiply

5

$5$ by

5

$5$ .

\frac{25 + 9 \cdot 3}{15}

$\frac{25 + 9 \cdot 3}{15}$

Step 9.2

Multiply

9

$9$ by

3

$3$ .

\frac{25 + 27}{15}

$\frac{25 + 27}{15}$

Step 9.3

Add

25

$25$ and

27

$27$ .

\frac{52}{15}

$\frac{52}{15}$

\frac{52}{15}

$\frac{52}{15}$

Step 10

The result can be shown in multiple forms.

Exact Form:

\frac{52}{15}

$\frac{52}{15}$

Decimal Form:

3.4\overline{6}

$3.4\overline{6}$

Mixed Number Form:

3 \frac{7}{15}

$3 \frac{7}{15}$