Basic Math Examples

$\frac{2 \cdot \frac{20}{12} + 3}{5 + \frac{\frac{20}{12} + 1}{4}}$

Step 1

Reduce the expression by cancelling the common factors.

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Step 1.1

Cancel the common factor of $20$ and $12$ .

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Step 1.1.1

Factor $4$ out of $20$ .

$\frac{2 \cdot \frac{4 (5)}{12} + 3}{5 + \frac{\frac{20}{12} + 1}{4}}$

Step 1.1.2

Cancel the common factors.

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Step 1.1.2.1

Factor $4$ out of $12$ .

$\frac{2 \cdot \frac{4 \cdot 5}{4 \cdot 3} + 3}{5 + \frac{\frac{20}{12} + 1}{4}}$

Step 1.1.2.2

Cancel the common factor.

$\frac{2 \cdot \frac{4 \cdot 5}{4 \cdot 3} + 3}{5 + \frac{\frac{20}{12} + 1}{4}}$

Step 1.1.2.3

Rewrite the expression.

$\frac{2 \cdot \frac{5}{3} + 3}{5 + \frac{\frac{20}{12} + 1}{4}}$

Step 1.2

Cancel the common factor of $20$ and $12$ .

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Step 1.2.1

Factor $4$ out of $20$ .

$\frac{2 \cdot \frac{5}{3} + 3}{5 + \frac{\frac{4 (5)}{12} + 1}{4}}$

Step 1.2.2

Cancel the common factors.

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Step 1.2.2.1

Factor $4$ out of $12$ .

$\frac{2 \cdot \frac{5}{3} + 3}{5 + \frac{\frac{4 \cdot 5}{4 \cdot 3} + 1}{4}}$

Step 1.2.2.2

Cancel the common factor.

$\frac{2 \cdot \frac{5}{3} + 3}{5 + \frac{\frac{4 \cdot 5}{4 \cdot 3} + 1}{4}}$

Step 1.2.2.3

Rewrite the expression.

$\frac{2 \cdot \frac{5}{3} + 3}{5 + \frac{\frac{5}{3} + 1}{4}}$

Step 2

Multiply the numerator and denominator of the fraction by $4$ .

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Step 2.1

Multiply $\frac{2 \cdot \frac{5}{3} + 3}{5 + \frac{\frac{5}{3} + 1}{4}}$ by $\frac{4}{4}$ .

$\frac{4}{4} \cdot \frac{2 \cdot \frac{5}{3} + 3}{5 + \frac{\frac{5}{3} + 1}{4}}$

Step 2.2

Combine.

$\frac{4 (2 \cdot \frac{5}{3} + 3)}{4 (5 + \frac{\frac{5}{3} + 1}{4})}$

Step 3

Apply the distributive property.

$\frac{4 (2 \cdot \frac{5}{3}) + 4 \cdot 3}{4 \cdot 5 + 4 \frac{\frac{5}{3} + 1}{4}}$

Step 4

Cancel the common factor of $4$ .

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Step 4.1

Cancel the common factor.

$\frac{4 (2 \cdot \frac{5}{3}) + 4 \cdot 3}{4 \cdot 5 + 4 \frac{\frac{5}{3} + 1}{4}}$

Step 4.2

Rewrite the expression.

$\frac{4 (2 \cdot \frac{5}{3}) + 4 \cdot 3}{4 \cdot 5 + \frac{5}{3} + 1}$

Step 5

Multiply the numerator and denominator of the fraction by $3$ .

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Step 5.1

Multiply $\frac{4 \cdot 2 \cdot \frac{5}{3} + 4 \cdot 3}{4 \cdot 5 + \frac{5}{3} + 1}$ by $\frac{3}{3}$ .

$\frac{3}{3} \cdot \frac{4 \cdot 2 \cdot \frac{5}{3} + 4 \cdot 3}{4 \cdot 5 + \frac{5}{3} + 1}$

Step 5.2

Combine.

$\frac{3 (4 \cdot 2 \cdot \frac{5}{3} + 4 \cdot 3)}{3 (4 \cdot 5 + \frac{5}{3} + 1)}$

Step 6

Apply the distributive property.

$\frac{3 (4 \cdot 2 \cdot \frac{5}{3}) + 3 (4 \cdot 3)}{3 (4 \cdot 5) + 3 (\frac{5}{3}) + 3 \cdot 1}$

Step 7

Cancel the common factor of $3$ .

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Step 7.1

Cancel the common factor.

$\frac{3 (4 \cdot 2 \cdot \frac{5}{3}) + 3 (4 \cdot 3)}{3 (4 \cdot 5) + 3 (\frac{5}{3}) + 3 \cdot 1}$

Step 7.2

Rewrite the expression.

$\frac{3 (4 \cdot 2 \cdot \frac{5}{3}) + 3 (4 \cdot 3)}{3 (4 \cdot 5) + 5 + 3 \cdot 1}$

Step 8

Simplify the numerator.

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Step 8.1

Multiply $3 \cdot 4 \cdot 2$ .

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Step 8.1.1

Multiply $3$ by $4$ .

$\frac{12 \cdot 2 \cdot \frac{5}{3} + 3 \cdot 4 \cdot 3}{3 \cdot 4 \cdot 5 + 5 + 3 \cdot 1}$

Step 8.1.2

Multiply $12$ by $2$ .

$\frac{24 \cdot \frac{5}{3} + 3 \cdot 4 \cdot 3}{3 \cdot 4 \cdot 5 + 5 + 3 \cdot 1}$

Step 8.2

Cancel the common factor of $3$ .

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Step 8.2.1

Factor $3$ out of $24$ .

$\frac{3 (8) \cdot \frac{5}{3} + 3 \cdot 4 \cdot 3}{3 \cdot 4 \cdot 5 + 5 + 3 \cdot 1}$

Step 8.2.2

Cancel the common factor.

$\frac{3 \cdot 8 \cdot \frac{5}{3} + 3 \cdot 4 \cdot 3}{3 \cdot 4 \cdot 5 + 5 + 3 \cdot 1}$

Step 8.2.3

Rewrite the expression.

$\frac{8 \cdot 5 + 3 \cdot 4 \cdot 3}{3 \cdot 4 \cdot 5 + 5 + 3 \cdot 1}$

Step 8.3

Multiply $8$ by $5$ .

$\frac{40 + 3 \cdot 4 \cdot 3}{3 \cdot 4 \cdot 5 + 5 + 3 \cdot 1}$

Step 8.4

Multiply $3 \cdot 4 \cdot 3$ .

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Step 8.4.1

Multiply $3$ by $4$ .

$\frac{40 + 12 \cdot 3}{3 \cdot 4 \cdot 5 + 5 + 3 \cdot 1}$

Step 8.4.2

Multiply $12$ by $3$ .

$\frac{40 + 36}{3 \cdot 4 \cdot 5 + 5 + 3 \cdot 1}$

Step 8.5

Add $40$ and $36$ .

$\frac{76}{3 \cdot 4 \cdot 5 + 5 + 3 \cdot 1}$

Step 9

Simplify the denominator.

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Step 9.1

Multiply $3 \cdot 4 \cdot 5$ .

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Step 9.1.1

Multiply $3$ by $4$ .

$\frac{76}{12 \cdot 5 + 5 + 3 \cdot 1}$

Step 9.1.2

Multiply $12$ by $5$ .

$\frac{76}{60 + 5 + 3 \cdot 1}$

Step 9.2

Multiply $3$ by $1$ .

$\frac{76}{60 + 5 + 3}$

Step 9.3

Add $60$ and $5$ .

$\frac{76}{65 + 3}$

Step 9.4

Add $65$ and $3$ .

$\frac{76}{68}$

Step 10

Cancel the common factor of $76$ and $68$ .

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Step 10.1

Factor $4$ out of $76$ .

$\frac{4 (19)}{68}$

Step 10.2

Cancel the common factors.

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Step 10.2.1

Factor $4$ out of $68$ .

$\frac{4 \cdot 19}{4 \cdot 17}$

Step 10.2.2

Cancel the common factor.

$\frac{4 \cdot 19}{4 \cdot 17}$

Step 10.2.3

Rewrite the expression.

$\frac{19}{17}$

Step 11

The result can be shown in multiple forms.

Exact Form:

$\frac{19}{17}$

Decimal Form:

$1.11764705 \dots$

Mixed Number Form:

$1 \frac{2}{17}$