Basic Math Examples

10 \frac{5}{6} \div 3 \frac{3}{4}

$10 \frac{5}{6} \div 3 \frac{3}{4}$

Step 1

Convert

10 \frac{5}{6}

$10 \frac{5}{6}$ to an improper fraction.

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Step 1.1

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

(10 + \frac{5}{6}) \div 3 \frac{3}{4}

$(10 + \frac{5}{6}) \div 3 \frac{3}{4}$

Step 1.2

Add

10

$10$ and

\frac{5}{6}

$\frac{5}{6}$ .

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Step 1.2.1

To write

10

$10$ as a fraction with a common denominator, multiply by

\frac{6}{6}

$\frac{6}{6}$ .

(10 \cdot \frac{6}{6} + \frac{5}{6}) \div 3 \frac{3}{4}

$(10 \cdot \frac{6}{6} + \frac{5}{6}) \div 3 \frac{3}{4}$

Step 1.2.2

Combine

10

$10$ and

\frac{6}{6}

$\frac{6}{6}$ .

(\frac{10 \cdot 6}{6} + \frac{5}{6}) \div 3 \frac{3}{4}

$(\frac{10 \cdot 6}{6} + \frac{5}{6}) \div 3 \frac{3}{4}$

Step 1.2.3

Combine the numerators over the common denominator.

\frac{10 \cdot 6 + 5}{6} \div 3 \frac{3}{4}

$\frac{10 \cdot 6 + 5}{6} \div 3 \frac{3}{4}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply

10

$10$ by

6

$6$ .

\frac{60 + 5}{6} \div 3 \frac{3}{4}

$\frac{60 + 5}{6} \div 3 \frac{3}{4}$

Step 1.2.4.2

Add

60

$60$ and

5

$5$ .

\frac{65}{6} \div 3 \frac{3}{4}

$\frac{65}{6} \div 3 \frac{3}{4}$

\frac{65}{6} \div 3 \frac{3}{4}

$\frac{65}{6} \div 3 \frac{3}{4}$

\frac{65}{6} \div 3 \frac{3}{4}

$\frac{65}{6} \div 3 \frac{3}{4}$

\frac{65}{6} \div 3 \frac{3}{4}

$\frac{65}{6} \div 3 \frac{3}{4}$

Step 2

Convert

3 \frac{3}{4}

$3 \frac{3}{4}$ to an improper fraction.

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Step 2.1

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

\frac{65}{6} \div (3 + \frac{3}{4})

$\frac{65}{6} \div (3 + \frac{3}{4})$

Step 2.2

Add

3

$3$ and

\frac{3}{4}

$\frac{3}{4}$ .

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Step 2.2.1

To write

3

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

\frac{4}{4}

$\frac{4}{4}$ .

\frac{65}{6} \div (3 \cdot \frac{4}{4} + \frac{3}{4})

$\frac{65}{6} \div (3 \cdot \frac{4}{4} + \frac{3}{4})$

Step 2.2.2

Combine

3

$3$ and

\frac{4}{4}

$\frac{4}{4}$ .

\frac{65}{6} \div (\frac{3 \cdot 4}{4} + \frac{3}{4})

$\frac{65}{6} \div (\frac{3 \cdot 4}{4} + \frac{3}{4})$

Step 2.2.3

Combine the numerators over the common denominator.

\frac{65}{6} \div \frac{3 \cdot 4 + 3}{4}

$\frac{65}{6} \div \frac{3 \cdot 4 + 3}{4}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply

3

$3$ by

4

$4$ .

\frac{65}{6} \div \frac{12 + 3}{4}

$\frac{65}{6} \div \frac{12 + 3}{4}$

Step 2.2.4.2

Add

12

$12$ and

3

$3$ .

\frac{65}{6} \div \frac{15}{4}

$\frac{65}{6} \div \frac{15}{4}$

\frac{65}{6} \div \frac{15}{4}

$\frac{65}{6} \div \frac{15}{4}$

\frac{65}{6} \div \frac{15}{4}

$\frac{65}{6} \div \frac{15}{4}$

\frac{65}{6} \div \frac{15}{4}

$\frac{65}{6} \div \frac{15}{4}$

Step 3

To divide by a fraction, multiply by its reciprocal.

\frac{65}{6} \cdot \frac{4}{15}

$\frac{65}{6} \cdot \frac{4}{15}$

Step 4

Cancel the common factor of

5

$5$ .

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Step 4.1

Factor

5

$5$ out of

65

$65$ .

\frac{5 (13)}{6} \cdot \frac{4}{15}

$\frac{5 (13)}{6} \cdot \frac{4}{15}$

Step 4.2

Factor

5

$5$ out of

15

$15$ .

\frac{5 \cdot 13}{6} \cdot \frac{4}{5 \cdot 3}

$\frac{5 \cdot 13}{6} \cdot \frac{4}{5 \cdot 3}$

Step 4.3

Cancel the common factor.

$\frac{5 \cdot 13}{6} \cdot \frac{4}{5 \cdot 3}$

Step 4.4

Rewrite the expression.

$\frac{13}{6} \cdot \frac{4}{3}$

Step 5

Cancel the common factor of

$2$ .

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Step 5.1

Factor

$2$ out of

$6$ .

$\frac{13}{2 (3)} \cdot \frac{4}{3}$

Step 5.2

Factor

$2$ out of

$4$ .

$\frac{13}{2 \cdot 3} \cdot \frac{2 \cdot 2}{3}$

Step 5.3

Cancel the common factor.

$\frac{13}{2 \cdot 3} \cdot \frac{2 \cdot 2}{3}$

Step 5.4

Rewrite the expression.

$\frac{13}{3} \cdot \frac{2}{3}$

Step 6

Multiply

$\frac{13}{3}$ by

$\frac{2}{3}$ .

$\frac{13 \cdot 2}{3 \cdot 3}$

Step 7

Multiply.

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Step 7.1

Multiply

$13$ by

$2$ .

$\frac{26}{3 \cdot 3}$

Step 7.2

Multiply

$3$ by

$3$ .

$\frac{26}{9}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{26}{9}$

Decimal Form:

$2.\overline{8}$

Mixed Number Form:

$2 \frac{8}{9}$