Basic Math Examples

\frac{6 y + 54}{24} \cdot \frac{4}{(2 y + 18) (q + 6)} \div \frac{12}{3 q + 18}

$\frac{6 y + 54}{24} \cdot \frac{4}{(2 y + 18) (q + 6)} \div \frac{12}{3 q + 18}$

Step 1

To divide by a fraction, multiply by its reciprocal.

\frac{6 y + 54}{24} \cdot \frac{4}{(2 y + 18) (q + 6)} \frac{3 q + 18}{12}

$\frac{6 y + 54}{24} \cdot \frac{4}{(2 y + 18) (q + 6)} \frac{3 q + 18}{12}$

Step 2

Factor

6

$6$ out of

6 y + 54

$6 y + 54$ .

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Step 2.1

Factor

6

$6$ out of

6 y

$6 y$ .

\frac{6 (y) + 54}{24} \cdot \frac{4}{(2 y + 18) (q + 6)} \frac{3 q + 18}{12}

$\frac{6 (y) + 54}{24} \cdot \frac{4}{(2 y + 18) (q + 6)} \frac{3 q + 18}{12}$

Step 2.2

Factor

6

$6$ out of

54

$54$ .

\frac{6 y + 6 \cdot 9}{24} \cdot \frac{4}{(2 y + 18) (q + 6)} \frac{3 q + 18}{12}

$\frac{6 y + 6 \cdot 9}{24} \cdot \frac{4}{(2 y + 18) (q + 6)} \frac{3 q + 18}{12}$

Step 2.3

Factor

6

$6$ out of

6 y + 6 \cdot 9

$6 y + 6 \cdot 9$ .

\frac{6 (y + 9)}{24} \cdot \frac{4}{(2 y + 18) (q + 6)} \frac{3 q + 18}{12}

$\frac{6 (y + 9)}{24} \cdot \frac{4}{(2 y + 18) (q + 6)} \frac{3 q + 18}{12}$

\frac{6 (y + 9)}{24} \cdot \frac{4}{(2 y + 18) (q + 6)} \frac{3 q + 18}{12}

$\frac{6 (y + 9)}{24} \cdot \frac{4}{(2 y + 18) (q + 6)} \frac{3 q + 18}{12}$

Step 3

Factor

2

$2$ out of

2 y + 18

$2 y + 18$ .

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Step 3.1

Factor

2

$2$ out of

2 y

$2 y$ .

\frac{6 (y + 9)}{24} \cdot \frac{4}{(2 (y) + 18) (q + 6)} \frac{3 q + 18}{12}

$\frac{6 (y + 9)}{24} \cdot \frac{4}{(2 (y) + 18) (q + 6)} \frac{3 q + 18}{12}$

Step 3.2

Factor

2

$2$ out of

18

$18$ .

\frac{6 (y + 9)}{24} \cdot \frac{4}{(2 y + 2 \cdot 9) (q + 6)} \frac{3 q + 18}{12}

$\frac{6 (y + 9)}{24} \cdot \frac{4}{(2 y + 2 \cdot 9) (q + 6)} \frac{3 q + 18}{12}$

Step 3.3

Factor

2

$2$ out of

2 y + 2 \cdot 9

$2 y + 2 \cdot 9$ .

\frac{6 (y + 9)}{24} \cdot \frac{4}{2 (y + 9) (q + 6)} \frac{3 q + 18}{12}

$\frac{6 (y + 9)}{24} \cdot \frac{4}{2 (y + 9) (q + 6)} \frac{3 q + 18}{12}$

\frac{6 (y + 9)}{24} \cdot \frac{4}{2 (y + 9) (q + 6)} \frac{3 q + 18}{12}

$\frac{6 (y + 9)}{24} \cdot \frac{4}{2 (y + 9) (q + 6)} \frac{3 q + 18}{12}$

Step 4

Cancel the common factor of

2 (y + 9)

$2 (y + 9)$ .

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Step 4.1

Factor

2 (y + 9)

$2 (y + 9)$ out of

6 (y + 9)

$6 (y + 9)$ .

\frac{2 (y + 9) (3)}{24} \cdot \frac{4}{2 (y + 9) (q + 6)} \frac{3 q + 18}{12}

$\frac{2 (y + 9) (3)}{24} \cdot \frac{4}{2 (y + 9) (q + 6)} \frac{3 q + 18}{12}$

Step 4.2

Cancel the common factor.

$\frac{2 (y + 9) \cdot 3}{24} \cdot \frac{4}{2 (y + 9) (q + 6)} \frac{3 q + 18}{12}$

Step 4.3

Rewrite the expression.

$\frac{3}{24} \cdot \frac{4}{q + 6} \frac{3 q + 18}{12}$

Step 5

Cancel the common factor of

$4$ .

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Step 5.1

Factor

$4$ out of

$24$ .

$\frac{3}{4 (6)} \cdot \frac{4}{q + 6} \frac{3 q + 18}{12}$

Step 5.2

Cancel the common factor.

$\frac{3}{4 \cdot 6} \cdot \frac{4}{q + 6} \frac{3 q + 18}{12}$

Step 5.3

Rewrite the expression.

$\frac{3}{6} \cdot \frac{1}{q + 6} \frac{3 q + 18}{12}$

Step 6

Multiply

$\frac{3}{6}$ by

$\frac{1}{q + 6}$ .

$\frac{3}{6 (q + 6)} \cdot \frac{3 q + 18}{12}$

Step 7

Cancel the common factor of

$3$ .

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Step 7.1

Factor

$3$ out of

$12$ .

$\frac{3}{6 (q + 6)} \cdot \frac{3 q + 18}{3 (4)}$

Step 7.2

Cancel the common factor.

$\frac{3}{6 (q + 6)} \cdot \frac{3 q + 18}{3 \cdot 4}$

Step 7.3

Rewrite the expression.

$\frac{1}{6 (q + 6)} \cdot \frac{3 q + 18}{4}$

Step 8

Multiply

$\frac{1}{6 (q + 6)}$ by

$\frac{3 q + 18}{4}$ .

$\frac{3 q + 18}{6 (q + 6) \cdot 4}$

Step 9

Multiply

$4$ by

$6$ .

$\frac{3 q + 18}{24 (q + 6)}$

Step 10

Cancel the common factor of

$3 q + 18$ and

$24$ .

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Step 10.1

Factor

$3$ out of

$3 q$ .

$\frac{3 (q) + 18}{24 (q + 6)}$

Step 10.2

Factor

$3$ out of

$18$ .

$\frac{3 q + 3 \cdot 6}{24 (q + 6)}$

Step 10.3

Factor

$3$ out of

$3 q + 3 \cdot 6$ .

$\frac{3 (q + 6)}{24 (q + 6)}$

Step 10.4

Cancel the common factors.

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Step 10.4.1

Factor

$3$ out of

$24 (q + 6)$ .

$\frac{3 (q + 6)}{3 (8 (q + 6))}$

Step 10.4.2

Cancel the common factor.

$\frac{3 (q + 6)}{3 (8 (q + 6))}$

Step 10.4.3

Rewrite the expression.

$\frac{q + 6}{8 (q + 6)}$

Step 11

Cancel the common factor of

$q + 6$ .

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Step 11.1

Cancel the common factor.

$\frac{q + 6}{8 (q + 6)}$

Step 11.2

Rewrite the expression.

$\frac{1}{8}$

Step 12

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{8}$

Decimal Form:

$0.125$