Basic Math Examples

$\frac{5}{9} \div \frac{- 4}{15} + {(\frac{1}{5})}^{2} \cdot (\frac{- 5}{7})$

Step 1

Simplify each term.

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Step 1.1

To divide by a fraction, multiply by its reciprocal.

$\frac{5}{9} \cdot \frac{15}{- 4} + {(\frac{1}{5})}^{2} \cdot (\frac{- 5}{7})$

Step 1.2

Cancel the common factor of $3$ .

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Step 1.2.1

Factor $3$ out of $9$ .

$\frac{5}{3 (3)} \cdot \frac{15}{- 4} + {(\frac{1}{5})}^{2} \cdot (\frac{- 5}{7})$

Step 1.2.2

Factor $3$ out of $15$ .

$\frac{5}{3 \cdot 3} \cdot \frac{3 \cdot 5}{- 4} + {(\frac{1}{5})}^{2} \cdot (\frac{- 5}{7})$

Step 1.2.3

Cancel the common factor.

$\frac{5}{3 \cdot 3} \cdot \frac{3 \cdot 5}{- 4} + {(\frac{1}{5})}^{2} \cdot (\frac{- 5}{7})$

Step 1.2.4

Rewrite the expression.

$\frac{5}{3} \cdot \frac{5}{- 4} + {(\frac{1}{5})}^{2} \cdot (\frac{- 5}{7})$

Step 1.3

Multiply $\frac{5}{3}$ by $\frac{5}{- 4}$ .

$\frac{5 \cdot 5}{3 \cdot - 4} + {(\frac{1}{5})}^{2} \cdot (\frac{- 5}{7})$

Step 1.4

Multiply $5$ by $5$ .

$\frac{25}{3 \cdot - 4} + {(\frac{1}{5})}^{2} \cdot (\frac{- 5}{7})$

Step 1.5

Multiply $3$ by $- 4$ .

$\frac{25}{- 12} + {(\frac{1}{5})}^{2} \cdot (\frac{- 5}{7})$

Step 1.6

Move the negative in front of the fraction.

$- \frac{25}{12} + {(\frac{1}{5})}^{2} \cdot (\frac{- 5}{7})$

Step 1.7

Apply the product rule to $\frac{1}{5}$ .

$- \frac{25}{12} + \frac{1^{2}}{5^{2}} \cdot \frac{- 5}{7}$

Step 1.8

Combine.

$- \frac{25}{12} + \frac{1^{2} \cdot - 5}{5^{2} \cdot 7}$

Step 1.9

Cancel the common factor of $- 5$ and $5^{2}$ .

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Step 1.9.1

Rewrite $- 5$ as $- 1 (5)$ .

$- \frac{25}{12} + \frac{1^{2} \cdot (- 1 (5))}{5^{2} \cdot 7}$

Step 1.9.2

Factor $5$ out of $1^{2} \cdot - 1 \cdot 5$ .

$- \frac{25}{12} + \frac{5 \cdot (1^{2} \cdot - 1)}{5^{2} \cdot 7}$

Step 1.9.3

Cancel the common factors.

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Step 1.9.3.1

Factor $5$ out of $5^{2} \cdot 7$ .

$- \frac{25}{12} + \frac{5 \cdot (1^{2} \cdot - 1)}{5 (5 \cdot 7)}$

Step 1.9.3.2

Cancel the common factor.

$- \frac{25}{12} + \frac{5 \cdot (1^{2} \cdot - 1)}{5 (5 \cdot 7)}$

Step 1.9.3.3

Rewrite the expression.

$- \frac{25}{12} + \frac{1^{2} \cdot - 1}{5 \cdot 7}$

Step 1.10

Simplify the numerator.

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Step 1.10.1

Rewrite $1$ as $- 1 (- 1)$ .

$- \frac{25}{12} + \frac{{(- 1 (- 1))}^{2} \cdot - 1}{5 \cdot 7}$

Step 1.10.2

Apply the product rule to $- 1 (- 1)$ .

$- \frac{25}{12} + \frac{{(- 1)}^{2} {(- 1)}^{2} \cdot - 1}{5 \cdot 7}$

Step 1.10.3

Raise $- 1$ to the power of $2$ .

$- \frac{25}{12} + \frac{1 {(- 1)}^{2} \cdot - 1}{5 \cdot 7}$

Step 1.10.4

Multiply ${(- 1)}^{2}$ by $1$ .

$- \frac{25}{12} + \frac{{(- 1)}^{2} \cdot - 1}{5 \cdot 7}$

Step 1.10.5

Multiply ${(- 1)}^{2}$ by $- 1$ by adding the exponents.

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Step 1.10.5.1

Multiply ${(- 1)}^{2}$ by $- 1$ .

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Step 1.10.5.1.1

Raise $- 1$ to the power of $1$ .

$- \frac{25}{12} + \frac{{(- 1)}^{2} \cdot {(- 1)}^{1}}{5 \cdot 7}$

Step 1.10.5.1.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$- \frac{25}{12} + \frac{{(- 1)}^{2 + 1}}{5 \cdot 7}$

Step 1.10.5.2

Add $2$ and $1$ .

$- \frac{25}{12} + \frac{{(- 1)}^{3}}{5 \cdot 7}$

Step 1.11

Multiply $5$ by $7$ .

$- \frac{25}{12} + \frac{{(- 1)}^{3}}{35}$

Step 1.12

Raise $- 1$ to the power of $3$ .

$- \frac{25}{12} + \frac{- 1}{35}$

Step 1.13

Move the negative in front of the fraction.

$- \frac{25}{12} - \frac{1}{35}$

Step 2

To write $- \frac{25}{12}$ as a fraction with a common denominator, multiply by $\frac{35}{35}$ .

$- \frac{25}{12} \cdot \frac{35}{35} - \frac{1}{35}$

Step 3

To write $- \frac{1}{35}$ as a fraction with a common denominator, multiply by $\frac{12}{12}$ .

$- \frac{25}{12} \cdot \frac{35}{35} - \frac{1}{35} \cdot \frac{12}{12}$

Step 4

Write each expression with a common denominator of $420$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{25}{12}$ by $\frac{35}{35}$ .

$- \frac{25 \cdot 35}{12 \cdot 35} - \frac{1}{35} \cdot \frac{12}{12}$

Step 4.2

Multiply $12$ by $35$ .

$- \frac{25 \cdot 35}{420} - \frac{1}{35} \cdot \frac{12}{12}$

Step 4.3

Multiply $\frac{1}{35}$ by $\frac{12}{12}$ .

$- \frac{25 \cdot 35}{420} - \frac{12}{35 \cdot 12}$

Step 4.4

Multiply $35$ by $12$ .

$- \frac{25 \cdot 35}{420} - \frac{12}{420}$

Step 5

Combine the numerators over the common denominator.

$\frac{- 25 \cdot 35 - 12}{420}$

Step 6

Simplify the numerator.

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Step 6.1

Multiply $- 25$ by $35$ .

$\frac{- 875 - 12}{420}$

Step 6.2

Subtract $12$ from $- 875$ .

$\frac{- 887}{420}$

Step 7

Move the negative in front of the fraction.

$- \frac{887}{420}$