Basic Math Examples

\frac{\frac{67}{33} + \frac{1}{66}}{\frac{65}{44}}

$\frac{\frac{67}{33} + \frac{1}{66}}{\frac{65}{44}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

(\frac{67}{33} + \frac{1}{66}) \frac{44}{65}

$(\frac{67}{33} + \frac{1}{66}) \frac{44}{65}$

Step 2

To write

\frac{67}{33}

$\frac{67}{33}$ as a fraction with a common denominator, multiply by

\frac{2}{2}

$\frac{2}{2}$ .

(\frac{67}{33} \cdot \frac{2}{2} + \frac{1}{66}) \frac{44}{65}

$(\frac{67}{33} \cdot \frac{2}{2} + \frac{1}{66}) \frac{44}{65}$

Step 3

Write each expression with a common denominator of

66

$66$ , by multiplying each by an appropriate factor of

1

$1$ .

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Step 3.1

Multiply

\frac{67}{33}

$\frac{67}{33}$ by

\frac{2}{2}

$\frac{2}{2}$ .

(\frac{67 \cdot 2}{33 \cdot 2} + \frac{1}{66}) \frac{44}{65}

$(\frac{67 \cdot 2}{33 \cdot 2} + \frac{1}{66}) \frac{44}{65}$

Step 3.2

Multiply

33

$33$ by

2

$2$ .

(\frac{67 \cdot 2}{66} + \frac{1}{66}) \frac{44}{65}

$(\frac{67 \cdot 2}{66} + \frac{1}{66}) \frac{44}{65}$

(\frac{67 \cdot 2}{66} + \frac{1}{66}) \frac{44}{65}

$(\frac{67 \cdot 2}{66} + \frac{1}{66}) \frac{44}{65}$

Step 4

Combine the numerators over the common denominator.

\frac{67 \cdot 2 + 1}{66} \cdot \frac{44}{65}

$\frac{67 \cdot 2 + 1}{66} \cdot \frac{44}{65}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply

67

$67$ by

2

$2$ .

\frac{134 + 1}{66} \cdot \frac{44}{65}

$\frac{134 + 1}{66} \cdot \frac{44}{65}$

Step 5.2

Add

134

$134$ and

1

$1$ .

\frac{135}{66} \cdot \frac{44}{65}

$\frac{135}{66} \cdot \frac{44}{65}$

\frac{135}{66} \cdot \frac{44}{65}

$\frac{135}{66} \cdot \frac{44}{65}$

Step 6

Cancel the common factor of

5

$5$ .

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Step 6.1

Factor

5

$5$ out of

135

$135$ .

\frac{5 (27)}{66} \cdot \frac{44}{65}

$\frac{5 (27)}{66} \cdot \frac{44}{65}$

Step 6.2

Factor

5

$5$ out of

65

$65$ .

\frac{5 \cdot 27}{66} \cdot \frac{44}{5 \cdot 13}

$\frac{5 \cdot 27}{66} \cdot \frac{44}{5 \cdot 13}$

Step 6.3

Cancel the common factor.

$\frac{5 \cdot 27}{66} \cdot \frac{44}{5 \cdot 13}$

Step 6.4

Rewrite the expression.

$\frac{27}{66} \cdot \frac{44}{13}$

Step 7

Cancel the common factor of

$22$ .

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Step 7.1

Factor

$22$ out of

$66$ .

$\frac{27}{22 (3)} \cdot \frac{44}{13}$

Step 7.2

Factor

$22$ out of

$44$ .

$\frac{27}{22 \cdot 3} \cdot \frac{22 \cdot 2}{13}$

Step 7.3

Cancel the common factor.

$\frac{27}{22 \cdot 3} \cdot \frac{22 \cdot 2}{13}$

Step 7.4

Rewrite the expression.

$\frac{27}{3} \cdot \frac{2}{13}$

Step 8

Multiply

$\frac{27}{3}$ by

$\frac{2}{13}$ .

$\frac{27 \cdot 2}{3 \cdot 13}$

Step 9

Multiply.

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Step 9.1

Multiply

$27$ by

$2$ .

$\frac{54}{3 \cdot 13}$

Step 9.2

Multiply

$3$ by

$13$ .

$\frac{54}{39}$

Step 10

Cancel the common factor of

$54$ and

$39$ .

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Step 10.1

Factor

$3$ out of

$54$ .

$\frac{3 (18)}{39}$

Step 10.2

Cancel the common factors.

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Step 10.2.1

Factor

$3$ out of

$39$ .

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

Step 10.2.2

Cancel the common factor.

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

Step 10.2.3

Rewrite the expression.

$\frac{18}{13}$

Step 11

The result can be shown in multiple forms.

Exact Form:

$\frac{18}{13}$

Decimal Form:

$1.\overline{384615}$

Mixed Number Form:

$1 \frac{5}{13}$