Basic Math Examples

6 \frac{1}{2} + 2 \frac{1}{15} + 8 \frac{9}{10}

$6 \frac{1}{2} + 2 \frac{1}{15} + 8 \frac{9}{10}$

Step 1

Convert

6 \frac{1}{2}

$6 \frac{1}{2}$ to an improper fraction.

Tap for more steps...

Step 1.1

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

6 + \frac{1}{2} + 2 \frac{1}{15} + 8 \frac{9}{10}

$6 + \frac{1}{2} + 2 \frac{1}{15} + 8 \frac{9}{10}$

Step 1.2

Add

6

$6$ and

\frac{1}{2}

$\frac{1}{2}$ .

Tap for more steps...

Step 1.2.1

To write

6

$6$ as a fraction with a common denominator, multiply by

\frac{2}{2}

$\frac{2}{2}$ .

6 \cdot \frac{2}{2} + \frac{1}{2} + 2 \frac{1}{15} + 8 \frac{9}{10}

$6 \cdot \frac{2}{2} + \frac{1}{2} + 2 \frac{1}{15} + 8 \frac{9}{10}$

Step 1.2.2

Combine

6

$6$ and

\frac{2}{2}

$\frac{2}{2}$ .

\frac{6 \cdot 2}{2} + \frac{1}{2} + 2 \frac{1}{15} + 8 \frac{9}{10}

$\frac{6 \cdot 2}{2} + \frac{1}{2} + 2 \frac{1}{15} + 8 \frac{9}{10}$

Step 1.2.3

Combine the numerators over the common denominator.

\frac{6 \cdot 2 + 1}{2} + 2 \frac{1}{15} + 8 \frac{9}{10}

$\frac{6 \cdot 2 + 1}{2} + 2 \frac{1}{15} + 8 \frac{9}{10}$

Step 1.2.4

Simplify the numerator.

Tap for more steps...

Step 1.2.4.1

Multiply

6

$6$ by

2

$2$ .

\frac{12 + 1}{2} + 2 \frac{1}{15} + 8 \frac{9}{10}

$\frac{12 + 1}{2} + 2 \frac{1}{15} + 8 \frac{9}{10}$

Step 1.2.4.2

Add

12

$12$ and

1

$1$ .

\frac{13}{2} + 2 \frac{1}{15} + 8 \frac{9}{10}

$\frac{13}{2} + 2 \frac{1}{15} + 8 \frac{9}{10}$

\frac{13}{2} + 2 \frac{1}{15} + 8 \frac{9}{10}

$\frac{13}{2} + 2 \frac{1}{15} + 8 \frac{9}{10}$

\frac{13}{2} + 2 \frac{1}{15} + 8 \frac{9}{10}

$\frac{13}{2} + 2 \frac{1}{15} + 8 \frac{9}{10}$

\frac{13}{2} + 2 \frac{1}{15} + 8 \frac{9}{10}

$\frac{13}{2} + 2 \frac{1}{15} + 8 \frac{9}{10}$

Step 2

Convert

2 \frac{1}{15}

$2 \frac{1}{15}$ to an improper fraction.

Tap for more steps...

Step 2.1

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

\frac{13}{2} + 2 + \frac{1}{15} + 8 \frac{9}{10}

$\frac{13}{2} + 2 + \frac{1}{15} + 8 \frac{9}{10}$

Step 2.2

Add

2

$2$ and

\frac{1}{15}

$\frac{1}{15}$ .

Tap for more steps...

Step 2.2.1

To write

2

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

\frac{15}{15}

$\frac{15}{15}$ .

\frac{13}{2} + 2 \cdot \frac{15}{15} + \frac{1}{15} + 8 \frac{9}{10}

$\frac{13}{2} + 2 \cdot \frac{15}{15} + \frac{1}{15} + 8 \frac{9}{10}$

Step 2.2.2

Combine

2

$2$ and

\frac{15}{15}

$\frac{15}{15}$ .

\frac{13}{2} + \frac{2 \cdot 15}{15} + \frac{1}{15} + 8 \frac{9}{10}

$\frac{13}{2} + \frac{2 \cdot 15}{15} + \frac{1}{15} + 8 \frac{9}{10}$

Step 2.2.3

Combine the numerators over the common denominator.

\frac{13}{2} + \frac{2 \cdot 15 + 1}{15} + 8 \frac{9}{10}

$\frac{13}{2} + \frac{2 \cdot 15 + 1}{15} + 8 \frac{9}{10}$

Step 2.2.4

Simplify the numerator.

Tap for more steps...

Step 2.2.4.1

Multiply

2

$2$ by

15

$15$ .

\frac{13}{2} + \frac{30 + 1}{15} + 8 \frac{9}{10}

$\frac{13}{2} + \frac{30 + 1}{15} + 8 \frac{9}{10}$

Step 2.2.4.2

Add

30

$30$ and

1

$1$ .

\frac{13}{2} + \frac{31}{15} + 8 \frac{9}{10}

$\frac{13}{2} + \frac{31}{15} + 8 \frac{9}{10}$

\frac{13}{2} + \frac{31}{15} + 8 \frac{9}{10}

$\frac{13}{2} + \frac{31}{15} + 8 \frac{9}{10}$

\frac{13}{2} + \frac{31}{15} + 8 \frac{9}{10}

$\frac{13}{2} + \frac{31}{15} + 8 \frac{9}{10}$

\frac{13}{2} + \frac{31}{15} + 8 \frac{9}{10}

$\frac{13}{2} + \frac{31}{15} + 8 \frac{9}{10}$

Step 3

Convert

8 \frac{9}{10}

$8 \frac{9}{10}$ to an improper fraction.

Tap for more steps...

Step 3.1

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

\frac{13}{2} + \frac{31}{15} + 8 + \frac{9}{10}

$\frac{13}{2} + \frac{31}{15} + 8 + \frac{9}{10}$

Step 3.2

Add

8

$8$ and

\frac{9}{10}

$\frac{9}{10}$ .

Tap for more steps...

Step 3.2.1

To write

8

$8$ as a fraction with a common denominator, multiply by

\frac{10}{10}

$\frac{10}{10}$ .

\frac{13}{2} + \frac{31}{15} + 8 \cdot \frac{10}{10} + \frac{9}{10}

$\frac{13}{2} + \frac{31}{15} + 8 \cdot \frac{10}{10} + \frac{9}{10}$

Step 3.2.2

Combine

8

$8$ and

\frac{10}{10}

$\frac{10}{10}$ .

\frac{13}{2} + \frac{31}{15} + \frac{8 \cdot 10}{10} + \frac{9}{10}

$\frac{13}{2} + \frac{31}{15} + \frac{8 \cdot 10}{10} + \frac{9}{10}$

Step 3.2.3

Combine the numerators over the common denominator.

\frac{13}{2} + \frac{31}{15} + \frac{8 \cdot 10 + 9}{10}

$\frac{13}{2} + \frac{31}{15} + \frac{8 \cdot 10 + 9}{10}$

Step 3.2.4

Simplify the numerator.

Tap for more steps...

Step 3.2.4.1

Multiply

8

$8$ by

10

$10$ .

\frac{13}{2} + \frac{31}{15} + \frac{80 + 9}{10}

$\frac{13}{2} + \frac{31}{15} + \frac{80 + 9}{10}$

Step 3.2.4.2

Add

80

$80$ and

9

$9$ .

\frac{13}{2} + \frac{31}{15} + \frac{89}{10}

$\frac{13}{2} + \frac{31}{15} + \frac{89}{10}$

\frac{13}{2} + \frac{31}{15} + \frac{89}{10}

$\frac{13}{2} + \frac{31}{15} + \frac{89}{10}$

\frac{13}{2} + \frac{31}{15} + \frac{89}{10}

$\frac{13}{2} + \frac{31}{15} + \frac{89}{10}$

\frac{13}{2} + \frac{31}{15} + \frac{89}{10}

$\frac{13}{2} + \frac{31}{15} + \frac{89}{10}$

Step 4

Find the common denominator.

Tap for more steps...

Step 4.1

Multiply

\frac{13}{2}

$\frac{13}{2}$ by

\frac{15}{15}

$\frac{15}{15}$ .

\frac{13}{2} \cdot \frac{15}{15} + \frac{31}{15} + \frac{89}{10}

$\frac{13}{2} \cdot \frac{15}{15} + \frac{31}{15} + \frac{89}{10}$

Step 4.2

Multiply

\frac{13}{2}

$\frac{13}{2}$ by

\frac{15}{15}

$\frac{15}{15}$ .

\frac{13 \cdot 15}{2 \cdot 15} + \frac{31}{15} + \frac{89}{10}

$\frac{13 \cdot 15}{2 \cdot 15} + \frac{31}{15} + \frac{89}{10}$

Step 4.3

Multiply

\frac{31}{15}

$\frac{31}{15}$ by

\frac{2}{2}

$\frac{2}{2}$ .

\frac{13 \cdot 15}{2 \cdot 15} + \frac{31}{15} \cdot \frac{2}{2} + \frac{89}{10}

$\frac{13 \cdot 15}{2 \cdot 15} + \frac{31}{15} \cdot \frac{2}{2} + \frac{89}{10}$

Step 4.4

Multiply

\frac{31}{15}

$\frac{31}{15}$ by

\frac{2}{2}

$\frac{2}{2}$ .

\frac{13 \cdot 15}{2 \cdot 15} + \frac{31 \cdot 2}{15 \cdot 2} + \frac{89}{10}

$\frac{13 \cdot 15}{2 \cdot 15} + \frac{31 \cdot 2}{15 \cdot 2} + \frac{89}{10}$

Step 4.5

Multiply

\frac{89}{10}

$\frac{89}{10}$ by

\frac{3}{3}

$\frac{3}{3}$ .

\frac{13 \cdot 15}{2 \cdot 15} + \frac{31 \cdot 2}{15 \cdot 2} + \frac{89}{10} \cdot \frac{3}{3}

$\frac{13 \cdot 15}{2 \cdot 15} + \frac{31 \cdot 2}{15 \cdot 2} + \frac{89}{10} \cdot \frac{3}{3}$

Step 4.6

Multiply

\frac{89}{10}

$\frac{89}{10}$ by

\frac{3}{3}

$\frac{3}{3}$ .

$\frac{13 \cdot 15}{2 \cdot 15} + \frac{31 \cdot 2}{15 \cdot 2} + \frac{89 \cdot 3}{10 \cdot 3}$

Step 4.7

Multiply

$2$ by

$15$ .

$\frac{13 \cdot 15}{30} + \frac{31 \cdot 2}{15 \cdot 2} + \frac{89 \cdot 3}{10 \cdot 3}$

Step 4.8

Reorder the factors of

$15 \cdot 2$ .

$\frac{13 \cdot 15}{30} + \frac{31 \cdot 2}{2 \cdot 15} + \frac{89 \cdot 3}{10 \cdot 3}$

Step 4.9

Multiply

$2$ by

$15$ .

$\frac{13 \cdot 15}{30} + \frac{31 \cdot 2}{30} + \frac{89 \cdot 3}{10 \cdot 3}$

Step 4.10

Reorder the factors of

$10 \cdot 3$ .

$\frac{13 \cdot 15}{30} + \frac{31 \cdot 2}{30} + \frac{89 \cdot 3}{3 \cdot 10}$

Step 4.11

Multiply

$3$ by

$10$ .

$\frac{13 \cdot 15}{30} + \frac{31 \cdot 2}{30} + \frac{89 \cdot 3}{30}$

Step 5

Combine the numerators over the common denominator.

$\frac{13 \cdot 15 + 31 \cdot 2 + 89 \cdot 3}{30}$

Step 6

Simplify each term.

Tap for more steps...

Step 6.1

Multiply

$13$ by

$15$ .

$\frac{195 + 31 \cdot 2 + 89 \cdot 3}{30}$

Step 6.2

Multiply

$31$ by

$2$ .

$\frac{195 + 62 + 89 \cdot 3}{30}$

Step 6.3

Multiply

$89$ by

$3$ .

$\frac{195 + 62 + 267}{30}$

Step 7

Reduce the expression by cancelling the common factors.

Tap for more steps...

Step 7.1

Add

$195$ and

$62$ .

$\frac{257 + 267}{30}$

Step 7.2

Add

$257$ and

$267$ .

$\frac{524}{30}$

Step 7.3

Cancel the common factor of

$524$ and

$30$ .

Tap for more steps...

Step 7.3.1

Factor

$2$ out of

$524$ .

$\frac{2 (262)}{30}$

Step 7.3.2

Cancel the common factors.

Tap for more steps...

Step 7.3.2.1

Factor

$2$ out of

$30$ .

$\frac{2 \cdot 262}{2 \cdot 15}$

Step 7.3.2.2

Cancel the common factor.

$\frac{2 \cdot 262}{2 \cdot 15}$

Step 7.3.2.3

Rewrite the expression.

$\frac{262}{15}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{262}{15}$

Decimal Form:

$17.4\overline{6}$

Mixed Number Form:

$17 \frac{7}{15}$