Basic Math Examples

4 \frac{7}{12} \div \frac{3}{4} \cdot \frac{3}{11}

$4 \frac{7}{12} \div \frac{3}{4} \cdot \frac{3}{11}$

Step 1

Convert

4 \frac{7}{12}

$4 \frac{7}{12}$ to an improper fraction.

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Step 1.1

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

(4 + \frac{7}{12}) \div \frac{3}{4} \cdot \frac{3}{11}

$(4 + \frac{7}{12}) \div \frac{3}{4} \cdot \frac{3}{11}$

Step 1.2

Add

4

$4$ and

\frac{7}{12}

$\frac{7}{12}$ .

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Step 1.2.1

To write

4

$4$ as a fraction with a common denominator, multiply by

\frac{12}{12}

$\frac{12}{12}$ .

(4 \cdot \frac{12}{12} + \frac{7}{12}) \div \frac{3}{4} \cdot \frac{3}{11}

$(4 \cdot \frac{12}{12} + \frac{7}{12}) \div \frac{3}{4} \cdot \frac{3}{11}$

Step 1.2.2

Combine

4

$4$ and

\frac{12}{12}

$\frac{12}{12}$ .

(\frac{4 \cdot 12}{12} + \frac{7}{12}) \div \frac{3}{4} \cdot \frac{3}{11}

$(\frac{4 \cdot 12}{12} + \frac{7}{12}) \div \frac{3}{4} \cdot \frac{3}{11}$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{4 \cdot 12 + 7}{12} \div \frac{3}{4} \cdot \frac{3}{11}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply

$4$ by

$12$ .

$\frac{48 + 7}{12} \div \frac{3}{4} \cdot \frac{3}{11}$

Step 1.2.4.2

Add

$48$ and

$7$ .

$\frac{55}{12} \div \frac{3}{4} \cdot \frac{3}{11}$

Step 2

To divide by a fraction, multiply by its reciprocal.

$\frac{55}{12} \cdot \frac{4}{3} \cdot \frac{3}{11}$

Step 3

Cancel the common factor of

$4$ .

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Step 3.1

Factor

$4$ out of

$12$ .

$\frac{55}{4 (3)} \cdot \frac{4}{3} \cdot \frac{3}{11}$

Step 3.2

Cancel the common factor.

$\frac{55}{4 \cdot 3} \cdot \frac{4}{3} \cdot \frac{3}{11}$

Step 3.3

Rewrite the expression.

$\frac{55}{3} \cdot \frac{1}{3} \cdot \frac{3}{11}$

Step 4

Multiply

$\frac{55}{3}$ by

$\frac{1}{3}$ .

$\frac{55}{3 \cdot 3} \cdot \frac{3}{11}$

Step 5

Multiply

$3$ by

$3$ .

$\frac{55}{9} \cdot \frac{3}{11}$

Step 6

Cancel the common factor of

$11$ .

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Step 6.1

Factor

$11$ out of

$55$ .

$\frac{11 (5)}{9} \cdot \frac{3}{11}$

Step 6.2

Cancel the common factor.

$\frac{11 \cdot 5}{9} \cdot \frac{3}{11}$

Step 6.3

Rewrite the expression.

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

Step 7

Cancel the common factor of

$3$ .

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Step 7.1

Factor

$3$ out of

$9$ .

$\frac{5}{3 (3)} \cdot 3$

Step 7.2

Cancel the common factor.

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

Step 7.3

Rewrite the expression.

$\frac{5}{3}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{5}{3}$

Decimal Form:

$1.\overline{6}$

Mixed Number Form:

$1 \frac{2}{3}$