Basic Math Examples

$\frac{75 \cdot 25 + 35 \cdot 125}{20 \cdot 25 \cdot 125 - 675 \cdot 75}$

Step 1

Reduce the expression by cancelling the common factors.

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Step 1.1

Cancel the common factor of $75 \cdot 25 + 35 \cdot 125$ and $20 \cdot 25 \cdot 125 - 675 \cdot 75$ .

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Step 1.1.1

Factor $25$ out of $75 \cdot 25$ .

$\frac{25 (3 \cdot 25) + 35 \cdot 125}{20 \cdot 25 \cdot 125 - 675 \cdot 75}$

Step 1.1.2

Factor $25$ out of $35 \cdot 125$ .

$\frac{25 (3 \cdot 25) + 25 (35 \cdot 5)}{20 \cdot 25 \cdot 125 - 675 \cdot 75}$

Step 1.1.3

Factor $25$ out of $25 (3 \cdot 25) + 25 (35 \cdot 5)$ .

$\frac{25 (3 \cdot 25 + 35 \cdot 5)}{20 \cdot 25 \cdot 125 - 675 \cdot 75}$

Step 1.1.4

Cancel the common factors.

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Step 1.1.4.1

Factor $25$ out of $20 \cdot 25 \cdot 125$ .

$\frac{25 (3 \cdot 25 + 35 \cdot 5)}{25 (20 \cdot 125) - 675 \cdot 75}$

Step 1.1.4.2

Factor $25$ out of $- 675 \cdot 75$ .

$\frac{25 (3 \cdot 25 + 35 \cdot 5)}{25 (20 \cdot 125) + 25 (- 27 \cdot 75)}$

Step 1.1.4.3

Factor $25$ out of $25 (20 \cdot 125) + 25 (- 27 \cdot 75)$ .

$\frac{25 (3 \cdot 25 + 35 \cdot 5)}{25 (20 \cdot 125 - 27 \cdot 75)}$

Step 1.1.4.4

Cancel the common factor.

$\frac{25 (3 \cdot 25 + 35 \cdot 5)}{25 (20 \cdot 125 - 27 \cdot 75)}$

Step 1.1.4.5

Rewrite the expression.

$\frac{3 \cdot 25 + 35 \cdot 5}{20 \cdot 125 - 27 \cdot 75}$

Step 1.2

Cancel the common factor of $3 \cdot 25 + 35 \cdot 5$ and $20 \cdot 125 - 27 \cdot 75$ .

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Step 1.2.1

Factor $- 1$ out of $20 \cdot 125$ .

$\frac{3 \cdot 25 + 35 \cdot 5}{- (- 20 \cdot 125) - 27 \cdot 75}$

Step 1.2.2

Factor $- 1$ out of $- 27 \cdot 75$ .

$\frac{3 \cdot 25 + 35 \cdot 5}{- (- 20 \cdot 125) - (27 \cdot 75)}$

Step 1.2.3

Factor $- 1$ out of $- (- 20 \cdot 125) - (27 \cdot 75)$ .

$\frac{3 \cdot 25 + 35 \cdot 5}{- (- 20 \cdot 125 + 27 \cdot 75)}$

Step 1.2.4

Rewrite $- (- 20 \cdot 125 + 27 \cdot 75)$ as $- 1 (- 20 \cdot 125 + 27 \cdot 75)$ .

$\frac{3 \cdot 25 + 35 \cdot 5}{- 1 (- 20 \cdot 125 + 27 \cdot 75)}$

Step 1.2.5

Reorder terms.

$\frac{3 \cdot 25 + 35 \cdot 5}{- 1 (27 \cdot 75 - 20 \cdot 125)}$

Step 1.2.6

Factor $5$ out of $3 \cdot 25$ .

$\frac{5 (3 \cdot 5) + 35 \cdot 5}{- 1 (27 \cdot 75 - 20 \cdot 125)}$

Step 1.2.7

Factor $5$ out of $35 \cdot 5$ .

$\frac{5 (3 \cdot 5) + 5 (7 \cdot 5)}{- 1 (27 \cdot 75 - 20 \cdot 125)}$

Step 1.2.8

Factor $5$ out of $5 (3 \cdot 5) + 5 (7 \cdot 5)$ .

$\frac{5 (3 \cdot 5 + 7 \cdot 5)}{- 1 (27 \cdot 75 - 20 \cdot 125)}$

Step 1.2.9

Cancel the common factors.

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Step 1.2.9.1

Factor $5$ out of $- 1 (27 \cdot 75 - 20 \cdot 125)$ .

$\frac{5 (3 \cdot 5 + 7 \cdot 5)}{5 (- 1 (27 \cdot 15 - 4 \cdot 125))}$

Step 1.2.9.2

Cancel the common factor.

$\frac{5 (3 \cdot 5 + 7 \cdot 5)}{5 (- 1 (27 \cdot 15 - 4 \cdot 125))}$

Step 1.2.9.3

Rewrite the expression.

$\frac{3 \cdot 5 + 7 \cdot 5}{- 1 (27 \cdot 15 - 4 \cdot 125)}$

Step 2

Simplify the numerator.

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Step 2.1

Multiply $3$ by $5$ .

$\frac{15 + 7 \cdot 5}{- 1 (27 \cdot 15 - 4 \cdot 125)}$

Step 2.2

Multiply $7$ by $5$ .

$\frac{15 + 35}{- 1 (27 \cdot 15 - 4 \cdot 125)}$

Step 2.3

Add $15$ and $35$ .

$\frac{50}{- 1 (27 \cdot 15 - 4 \cdot 125)}$

Step 3

Simplify the denominator.

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Step 3.1

Multiply $27$ by $15$ .

$\frac{50}{- 1 (405 - 4 \cdot 125)}$

Step 3.2

Multiply $- 4$ by $125$ .

$\frac{50}{- 1 (405 - 500)}$

Step 3.3

Subtract $500$ from $405$ .

$\frac{50}{- 1 \cdot - 95}$

Step 4

Reduce the expression by cancelling the common factors.

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Step 4.1

Multiply $- 1$ by $- 95$ .

$\frac{50}{95}$

Step 4.2

Cancel the common factor of $50$ and $95$ .

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Step 4.2.1

Factor $5$ out of $50$ .

$\frac{5 (10)}{95}$

Step 4.2.2

Cancel the common factors.

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Step 4.2.2.1

Factor $5$ out of $95$ .

$\frac{5 \cdot 10}{5 \cdot 19}$

Step 4.2.2.2

Cancel the common factor.

$\frac{5 \cdot 10}{5 \cdot 19}$

Step 4.2.2.3

Rewrite the expression.

$\frac{10}{19}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{10}{19}$

Decimal Form:

$0.52631578 \dots$