Basic Math Examples

6 \frac{2}{9} + 2 \frac{1}{6}

$6 \frac{2}{9} + 2 \frac{1}{6}$

Step 1

Convert

6 \frac{2}{9}

$6 \frac{2}{9}$ to an improper fraction.

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Step 1.1

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

6 + \frac{2}{9} + 2 \frac{1}{6}

$6 + \frac{2}{9} + 2 \frac{1}{6}$

Step 1.2

Add

6

$6$ and

\frac{2}{9}

$\frac{2}{9}$ .

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Step 1.2.1

To write

6

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

\frac{9}{9}

$\frac{9}{9}$ .

6 \cdot \frac{9}{9} + \frac{2}{9} + 2 \frac{1}{6}

$6 \cdot \frac{9}{9} + \frac{2}{9} + 2 \frac{1}{6}$

Step 1.2.2

Combine

6

$6$ and

\frac{9}{9}

$\frac{9}{9}$ .

\frac{6 \cdot 9}{9} + \frac{2}{9} + 2 \frac{1}{6}

$\frac{6 \cdot 9}{9} + \frac{2}{9} + 2 \frac{1}{6}$

Step 1.2.3

Combine the numerators over the common denominator.

\frac{6 \cdot 9 + 2}{9} + 2 \frac{1}{6}

$\frac{6 \cdot 9 + 2}{9} + 2 \frac{1}{6}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply

6

$6$ by

9

$9$ .

\frac{54 + 2}{9} + 2 \frac{1}{6}

$\frac{54 + 2}{9} + 2 \frac{1}{6}$

Step 1.2.4.2

Add

54

$54$ and

2

$2$ .

\frac{56}{9} + 2 \frac{1}{6}

$\frac{56}{9} + 2 \frac{1}{6}$

\frac{56}{9} + 2 \frac{1}{6}

$\frac{56}{9} + 2 \frac{1}{6}$

\frac{56}{9} + 2 \frac{1}{6}

$\frac{56}{9} + 2 \frac{1}{6}$

\frac{56}{9} + 2 \frac{1}{6}

$\frac{56}{9} + 2 \frac{1}{6}$

Step 2

Convert

2 \frac{1}{6}

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

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Step 2.1

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

\frac{56}{9} + 2 + \frac{1}{6}

$\frac{56}{9} + 2 + \frac{1}{6}$

Step 2.2

Add

2

$2$ and

\frac{1}{6}

$\frac{1}{6}$ .

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Step 2.2.1

To write

2

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

\frac{6}{6}

$\frac{6}{6}$ .

\frac{56}{9} + 2 \cdot \frac{6}{6} + \frac{1}{6}

$\frac{56}{9} + 2 \cdot \frac{6}{6} + \frac{1}{6}$

Step 2.2.2

Combine

2

$2$ and

\frac{6}{6}

$\frac{6}{6}$ .

\frac{56}{9} + \frac{2 \cdot 6}{6} + \frac{1}{6}

$\frac{56}{9} + \frac{2 \cdot 6}{6} + \frac{1}{6}$

Step 2.2.3

Combine the numerators over the common denominator.

\frac{56}{9} + \frac{2 \cdot 6 + 1}{6}

$\frac{56}{9} + \frac{2 \cdot 6 + 1}{6}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply

2

$2$ by

6

$6$ .

\frac{56}{9} + \frac{12 + 1}{6}

$\frac{56}{9} + \frac{12 + 1}{6}$

Step 2.2.4.2

Add

12

$12$ and

1

$1$ .

\frac{56}{9} + \frac{13}{6}

$\frac{56}{9} + \frac{13}{6}$

\frac{56}{9} + \frac{13}{6}

$\frac{56}{9} + \frac{13}{6}$

\frac{56}{9} + \frac{13}{6}

$\frac{56}{9} + \frac{13}{6}$

\frac{56}{9} + \frac{13}{6}

$\frac{56}{9} + \frac{13}{6}$

Step 3

To write

\frac{56}{9}

$\frac{56}{9}$ as a fraction with a common denominator, multiply by

\frac{2}{2}

$\frac{2}{2}$ .

\frac{56}{9} \cdot \frac{2}{2} + \frac{13}{6}

$\frac{56}{9} \cdot \frac{2}{2} + \frac{13}{6}$

Step 4

To write

\frac{13}{6}

$\frac{13}{6}$ as a fraction with a common denominator, multiply by

\frac{3}{3}

$\frac{3}{3}$ .

\frac{56}{9} \cdot \frac{2}{2} + \frac{13}{6} \cdot \frac{3}{3}

$\frac{56}{9} \cdot \frac{2}{2} + \frac{13}{6} \cdot \frac{3}{3}$

Step 5

Write each expression with a common denominator of

18

$18$ , by multiplying each by an appropriate factor of

1

$1$ .

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Step 5.1

Multiply

\frac{56}{9}

$\frac{56}{9}$ by

\frac{2}{2}

$\frac{2}{2}$ .

\frac{56 \cdot 2}{9 \cdot 2} + \frac{13}{6} \cdot \frac{3}{3}

$\frac{56 \cdot 2}{9 \cdot 2} + \frac{13}{6} \cdot \frac{3}{3}$

Step 5.2

Multiply

9

$9$ by

2

$2$ .

\frac{56 \cdot 2}{18} + \frac{13}{6} \cdot \frac{3}{3}

$\frac{56 \cdot 2}{18} + \frac{13}{6} \cdot \frac{3}{3}$

Step 5.3

Multiply

\frac{13}{6}

$\frac{13}{6}$ by

\frac{3}{3}

$\frac{3}{3}$ .

\frac{56 \cdot 2}{18} + \frac{13 \cdot 3}{6 \cdot 3}

$\frac{56 \cdot 2}{18} + \frac{13 \cdot 3}{6 \cdot 3}$

Step 5.4

Multiply

6

$6$ by

3

$3$ .

\frac{56 \cdot 2}{18} + \frac{13 \cdot 3}{18}

$\frac{56 \cdot 2}{18} + \frac{13 \cdot 3}{18}$

\frac{56 \cdot 2}{18} + \frac{13 \cdot 3}{18}

$\frac{56 \cdot 2}{18} + \frac{13 \cdot 3}{18}$

Step 6

Combine the numerators over the common denominator.

\frac{56 \cdot 2 + 13 \cdot 3}{18}

$\frac{56 \cdot 2 + 13 \cdot 3}{18}$

Step 7

Simplify the numerator.

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Step 7.1

Multiply

56

$56$ by

2

$2$ .

\frac{112 + 13 \cdot 3}{18}

$\frac{112 + 13 \cdot 3}{18}$

Step 7.2

Multiply

13

$13$ by

3

$3$ .

\frac{112 + 39}{18}

$\frac{112 + 39}{18}$

Step 7.3

Add

112

$112$ and

39

$39$ .

\frac{151}{18}

$\frac{151}{18}$

\frac{151}{18}

$\frac{151}{18}$

Step 8

The result can be shown in multiple forms.

Exact Form:

\frac{151}{18}

$\frac{151}{18}$

Decimal Form:

8.3 ¯ 8

$8.3\overline{8}$

Mixed Number Form:

8 \frac{7}{18}

$8 \frac{7}{18}$